Site plan Case Study Example | Topics and Well Written Essays - 1000 words

Site plan - Case Study Example Such information can be acquired by conducting a SWOT analysis of the business in attempts to determine the strengths, weaknesses, opportunities and threats affecting the business. This work evaluates the provided plan of a proposed cupcake shop along the beach by using the SWOT Analysis. In any business, it is vital to assess the industry in order to be fully informed of the requirements. It is essential to have credible information regarding the targeted customers and their needs. The intended business has to meet and satisfy the needs of the targeted customers. If the business achieves this objective efficiently, chances of success are high. Therefore, as far as this proposed business is concerned, SWOT analysis will provide the necessary information to make the business a success. Strengths The site location’s strength is based on the demographics of the area. The demographics, according to Russ (2009) give a person the idea of the population surrounding the area. Since th e site is supposed to host a cup cake studio, the area demographics, which includes the beach, is suited for the site location. People of different age groups love the beach, and this is an opportunity to serve these people with cupcakes. The beachgoers love to relax as they enjoy themselves with their favorite snacks and beverages. Therefore, the fact that there is a cup cake shop near the beach is an advantage to the business since it is near the targeted customers. Also, because the business is located on the first building accessible from the beach is an advantage. Had the business been located in other buildings far away from the beach, proximity could have been affected. It is imperative to have a business located in a place easily accessible to customers. Easier proximity to a business plays a significant role in the growth and development of the business. When customers can easily access the business, the business is guaranteed to succeed. Furthermore, the immediate surround ing area has numerous apartments that will provide the proposed business with the required customer base for the business to

English Literature Essay Example for Free

English Literature Essay On my personal perception, â€Å"art† is composition of own personal – views, beliefs, and felling. Moreover, my representation of â€Å"art† can be in from of – painting, photography, sculpture and music, which are all composed through inspirations and personal characteristics. Personally I am an art fanatic, which I have deeper appreciation on various art pieces like – painting and photography. Furthermore, art for me is an outlet in which a person or an artist releases his or her inner – desire, characteristics, which is known as normally, comes out with art masterpiece. Also, my personal perception on â€Å"art work† is a representation of the present situation or current feelings of the artist in which he or she releases in an artistic way. Also, my own personal view on â€Å"art work† is that it represents not just the current situation or feelings of the artist rather it is as well a reflection of the artist himself. Personally speaking, â€Å"art work† will be more effective as a representation of a certain situation or feelings as a way to transmit a message if the piece is realistically done or composed. On the other hand, â€Å"Gustave Courbet† as an artist is the perfect model of a great â€Å"artist of realism†. With his unquestionable excellence of realism in all of his art works, the native French artist Gustave Courbet was considered to be the most influential realist artist, which had released major art works of realism that received large number of appraisal from both ancient and contemporary artist world wide. At present time it is considered that Gustave Courbet was consider as one of the major artist who had influence the artist through his art works and his profound views to realism. Moreover, one of the most fantastic work of art Gustave Courbet had composed is his representation of â€Å"The Desperate Man†. This painting of Gustave Courbet â€Å"The Desperate Man† was released way back 1844 – 45, which is no doubt wonderful work of art. (The Metropolitan Museum of Art) My own personal thoughts on the painting â€Å"The Desperate Man† is that it is a representation of the artist himself Gustve Courbet. As and artist Gustave Courbet had been through a lot of difficulties and challenges before he had reach the success for his art work. My own personal thoughts about his painting â€Å"The Desperate Man† is that Gustave Courbet is experiencing desperation or dilemma in his personal life on the moment he was composing the painting. Furthermore, my thoughts on painting â€Å"The Desperate Man† is that the man in the painting is really in desperation in which he was willing to do anything satisfy or overcome his frustration. Also, my thoughts on the painting is a representation of a man who is having a serious dilemma in his life in which he is asking for some help to handle and overcome his desperation. On the other hand, my personal thoughts on the painting â€Å"The Desperate Man† by Gustave Courbet had vary by the time I saw the painting in real life. With the personal encounter on the painting my thoughts had changed in which I can see person in the painting as a man who was asking or begging for help. Moreover, when I personally saw the painting in real life my personal thought is that The Desperate Man† is a representation of a hopeless guy who tries to survive in his dilemma in which at the certain point the painting mirrors his shout for help to enlighten his dark situation. Also, my thoughts on the painting had changed when I saw the art work personally that I thought the man is verge losing hope to resolve his dilemma, which the painting represents the aspiration of the man to see light out of his dilemma. On the other hand, my personal analysis on the painting â€Å"The Desperate Man† is that Gustave Courbet as an artist represented a realistic situation of a desperate man in which painting definitely transmits the message of the current situation and feelings of the man. Furthermore, my personal analysis on the painting â€Å"The Desperate Man† is that it defines the profound perception or views of â€Å"Gustave Courbet† on realism. Works Cited The Metropolitan Museum of Art (2008), Gustave Courbet: Retrieved April 30, 2008 from http://www. metmuseum. org/special/gustave_courbet/more. asp

The Subtle Art of Feminism Essay -- Film Analysis India

Bapsi Sidhwa’s novel, Water, realistically presents the circumstances of women and, in particular, widows in 1938 Colonial India. It exposes the gender inequality and double standards that govern that society for no other reason than that is what tradition dictates. Sidhwa presents complexities in her characters, which make them very human and very real, and the widows’ reactions to each other and to the world outside of the ashram create a feminist message. Water poses the problem of gender inequality in India by presenting a realistic and typical situation, and it allows the readers to draw their own conclusions while experiencing the intricacies of the Indian culture. The most obvious example of inequality or mistreatment of women is Chuyia’s situation of becoming a bride and soon after a widow at age eight. By becoming a widow she is forced into the ashram and into isolation from the rest of society. This is a situation that is common in India due to the fact that tradition dictates â€Å"a woman is recognized as a person only when she is one with her husband† (Sidhwa 14). It shows that society views women as worthless unless they are under the control and service of a man. Furthermore, this tradition means that women are married off as soon as possible as to secure their future and purpose in life, while men are able to wait longer to marry. In Indian culture, men are worth more than women, and the novel shows this fact by contrasting Chuyia’s marriage situation with Narayan’s situation. Chuyia has no say in who she must marry because she is female, and her marriage is entirely dependent on her father, who mar ries off six-year-old Chuyia to a forty year old man. Even though Chuyia’s mother tries to stop the marriage a... ...t â€Å"By drifting almost unnoticeably from the commonplace to the horrific, Water implicates the reader† (Jaiarjun). It does more than rant about a feminist agenda; it calls the readers to action by deeply involving them first-hand in the atrocities that are taking place against women. Works Cited Arora, Kamal, Saydia Kamal, and Usamah Ahmad. "Water: Drenched in colonial benevolence." Seven Oaks. 05 Oct 2005. Web. 13 Apr 2010. . Seton, Nora. "Honoring the abandoned." Houston Chronicle (2006). Web. 5 Apr 2010. . Sidhwa, Bapsi. Water. Toronto, Canada: Key Porter Books Limited, 2006. Print. Singh, Jaiarjun. "Whirlpools on the Ghats." Indian Express (2006). Web. 5 Apr 2010. .

Home Alarm Case Essay

1) What is the LTV (looking 8 years out) of a customer who used auto-pay? The Life time value of a customer who used auto-pay is $1670.69 (LTV net of acquisition costs= $1373.69) 2) 2)What is the LTV (looking 8 years out) of a customer who did not use auto-pay? The Life time value of a customer who did not use auto-pay is $1361.87 (LTV net of acquisition costs= $1064. 87) 3) What is the maximum amount that Home Alarm could spend on customer and salesperson incentives to convert a residential customer to auto-pay? The maximum amount that could be spent should be the difference between the Lifetime Value of customers that sign up for non-autopay service ($1064.87) and the LTV for the ones who opted for an autopay service ($1373.69); which is $308,82. So far, Home Alarm doesn’t assign any budget for marketing at the time of sign up, so it could be a good idea to invest this amount ($308,82), or less, for a marketing campaign during the acquisition period, emphasizing the convenience of the automatic payment contract. 4) What new pricing strategies and services should Home Alarm consider to sign up new customers with auto-pay? One strategy to push new customers to sign up with autopay could be offering them the installation for free. In this case the cost of acquisition for each new customer who signs up for the autopay service would be $492 instead of $297. With this option, the lifetime value of each customer who opts for the autopay service will be $1178.69, lower than the amount that could have  been earned had they chosen this solution anyway, but higher than the $1373,69 that the company would earn had they not chosen the autopay. The main problem for this option is that we don’t have any information about the percentage of people that would choose the automatic payment without any incentive; indeed if we assume that 50% of the customer would choose the automatic payment in any case, we would earn 113,82 dollars (1178.69-1064.87) on average for each customer who decides to choose the automatic payment over the non automatic one, but we would lose $195 for each customer that would have chosen this method even without incentives. (Table 1) It could be worthwhile to offer just a reduction of the installation costs. For instance, offering a discount of 50% on the installation cost would increase the LTV of customers that choose autopay over non-autopay by more than $200 and would create a loss of only $97,5 per customer that would have opted for autopay without further incentive. Another strategy could be offering the new customers who opt for an automatic payment service a fixed price for the first three years (not increased by the annual 3% rate). In this case the LTV net of the acquisition costs would be $1305,5, still higher than the one the company would earn whether the customer opts for a not automatic payment. Moreover, offering 8 years of fixed price ($480) is still more profitable than the case in which the chose a not autopay method, but it is, in my opinion, not recommendable, because of the negative effect that it could have on the customer that chose this option before. Indeed they could decide to resign the contract and try to get a new one with the more convenient conditions. (Table 2) 5) What new pricing strategies and services should Home Alarm consider to convert existing customers to auto-pay? Taking in consideration the attrition rate during the past nine years, it seems to be more convenient try to convert the customers as early as possible; indeed the peak of the churn rate is between the third and the fourth year. One solution could be offering discounts for the customers that are willing to switch method, maybe offering them a reduction in the general rate. For example, the customers that opt for convert their payment method  could see their price increase just by 2% per year instead of the 3%. For instance, if the conversion happens during the first year, the LVT net of acquisition costs would be $1243.17 (the retention rate for the first year would be the same of the non autopay situation), significantly higher than the basic case. This numbers are obtained in the optimistic scenario where the attrition rate in case of switch would be exactly the same of the ones who initially chose for the automatic payment. (Table 3) Another option could be offering couple of years with a fixed price, as explained for the new customers.

Finance Test Bank

Chapter 9 Multiple Choice Identify the choice that best completes the statement or answers the question. _e___1. Schalheim Sisters Inc. has always paid out all of its earnings as dividends; hence, the firm has no retained earnings. This same situation is expected to persist in the future. The company uses the CAPM to calculate its cost of equity, and its target capital structure consists of common stock, preferred stock, and debt. Which of the following events would REDUCE its WACC? a. The market risk premium declines. b. The flotation costs associated with issuing new common stock increase. . The company's beta increases. d. Expected inflation increases. e. The flotation costs associated with issuing preferred stock increase. __c__2. Duval Inc. uses only equity capital, and it has two equally-sized divisions. Division A's cost of capital is 10. 0%, Division B's cost is 14. 0%, and the corporate (composite) WACC is 12. 0%. All of Division A's projects are equally risky, as are all of Division B's projects. However, the projects of Division A are less risky than those of Division B. Which of the following projects should the firm accept? a. A Division B project with a 13% return. . A Division B project with a 12% return. c. A Division A project with an 11% return. d. A Division A project with a 9% return. e. A Division B project with an 11% return. 2010 Fall Chapter 10 ___b_3. You are considering two mutually exclusive, equally risky, projects. Both have IRRs that exceed the WACC. Which of the following statements is CORRECT? Assume that the projects have normal cash flows, with one outflow followed by a series of inflows. a. If the two projects' NPV profiles do not cross, then there will be a sharp conflict as to which one should be selected. . If the cost of capital is greater than the crossover rate, then the IRR and the NPV criteria will not result in a conflict between the projects. The same project will rank higher by both criteria. c. If the cost of capit al is less than the crossover rate, then the IRR and the NPV criteria will not result in a conflict between the projects. The same project will rank higher by both criteria. d. For a conflict to exist between NPV and IRR, the initial investment cost of one project must exceed the cost of the other. e.For a conflict to exist between NPV and IRR, one project must have an increasing stream of cash flows over time while the other has a decreasing stream. If both sets of cash flows are increasing or decreasing, then it would be impossible for a conflict to exist, even if one project is larger than the other. 2010 Fall, FIN 6100, Chapter 11, iClicker Questions __e__1. Which of the following is NOT a relevant cash flow and thus should not be reflected in the analysis of a capital budgeting project? a. Changes in net working capital. b. Shipping and installation costs. c. Cannibalization effects. . Opportunity costs. e. Sunk costs that have been expensed for tax purposes. __a__3. Which of t he following should be considered when a company estimates the cash flows used to analyze a proposed project? a. The new project is expected to reduce sales of one of the company's existing products by 5%. b. Since the firm's director of capital budgeting spent some of her time last year to evaluate the new project, a portion of her salary for that year should be charged to the project's initial cost. c. The company has spent and expensed $1 million on R associated with the new project. d.The company spent and expensed $10 million on a marketing study before its current analysis regarding whether to accept or reject the project. e. The firm would borrow all the money used to finance the new project, and the interest on this debt would be $1. 5 million per year. __c__4. Dalrymple Inc. is considering production of a new product. In evaluating whether to go ahead with the project, which of the following items should NOT be explicitly considered when cash flows are estimated? a. The com pany will produce the new product in a vacant building that was used to produce another product until last year.The building could be sold, leased to another company, or used in the future to produce another of the firm's products. b. The project will utilize some equipment the company currently owns but is not now using. A used equipment dealer has offered to buy the equipment. c. The company has spent and expensed for tax purposes $3 million on research related to the new detergent. These funds cannot be recovered, but the research may benefit other projects that might be proposed in the future. d. The new product will cut into sales of some of the firm's other products. . If the project is accepted, the company must invest $2 million in working capital. However, all of these funds will be recovered at the end of the project's life. __e__7. A firm is considering a new project whose risk is greater than the risk of the firm's average project, based on all methods for assessing risk . In evaluating this project, it would be reasonable for management to do which of the following? a. Increase the estimated IRR of the project to reflect its greater risk. b. Increase the estimated NPV of the project to reflect its greater risk. c.Reject the project, since its acceptance would increase the firm's risk. d. Ignore the risk differential if the project would amount to only a small fraction of the firm's total assets. e. Increase the cost of capital used to evaluate the project to reflect its higher-than-average risk. Chapter 12 iClicker Questions __b__1. Which of the following assumptions is embodied in the AFN equation? a. None of the firm's ratios will change. b. Accounts payable and accruals are tied directly to sales. c. Common stock and long-term debt are tied directly to sales. d. Fixed assets, but not urrent assets, are tied directly to sales. e. Last year's total assets were not optimal for last year's sales. __b__2. The term â€Å"additional funds needed (AFN) † is generally defined as follows: a. Funds that are obtained automatically from routine business transactions. b. Funds that a firm must raise externally from non-spontaneous sources, i. e. , by borrowing or by selling new stock to support operations. c. The amount of assets required per dollar of sales. d. The amount of internally generated cash in a given year minus the amount of cash needed to acquire the new assets needed to support growth. . A forecasting approach in which the forecasted percentage of sales for each balance sheet account is held constant. _b___4. A company expects sales to increase during the coming year, and it is using the AFN equation to forecast the additional capital that it must raise. Which of the following conditions would cause the AFN to increase? a. The company previously thought its fixed assets were being operated at full capacity, but now it learns that it actually has excess capacity. b. The company increases its dividend payout ratio. c. The company begins to pay employees monthly rather than weekly. . The company's profit margin increases. e. The company decides to stop taking discounts on purchased materials. Chapter 13 iClicker Questions Multiple Choice Identify the choice that best completes the statement or answers the question. __b__1. Which of the following statements is NOT CORRECT? a. The corporate valuation model can be used both for companies that pay dividends and those that do not pay dividends. b. The corporate valuation model discounts free cash flows by the required return on equity. c. The corporate valuation model can be used to find the value of a division. . An important step in applying the corporate valuation model is forecasting the firm's pro forma financial statements. e. Free cash flows are assumed to grow at a constant rate beyond a specified date in order to find the horizon, or terminal, value. __a__2. Which of the following does NOT always increase a company's market value? a. Increasin g the expected growth rate of sales. b. Increasing the expected operating profitability (NOPAT/Sales). c. Decreasing the capital requirements (Capital/Sales). d. Decreasing the weighted average cost of capital. e.Increasing the expected rate of return on invested capital. _a___3. Which of the following is NOT normally regarded as being a barrier to hostile takeovers? a. Abnormally high executive compensation. b. Targeted share repurchases. c. Shareholder rights provisions. d. Restricted voting rights. e. Poison pills. Chapter 14 iClicker Questions Multiple Choice Identify the choice that best completes the statement or answers the question. __d__1. Which of the following should not influence a firm's dividend policy decision? a. The firm's ability to accelerate or delay investment projects. . A strong preference by most shareholders for current cash income versus capital gains. c. Constraints imposed by the firm's bond indenture. d. The fact that much of the firm's equipment has bee n leased rather than bought and owned. e. The fact that Congress is considering changes in the tax law regarding the taxation of dividends versus capital gains. __a__2. Trenton Publishing follows a strict residual dividend policy. All else equal, which of the following factors would be most likely to lead to an increase in the firm's dividend per share? a. The firm's net income increases. b.The company increases the percentage of equity in its target capital structure. c. The number of profitable potential projects increases. d. Congress lowers the tax rate on capital gains. The remainder of the tax code is not changed. e. Earnings are unchanged, but the firm issues new shares of common stock. Chapter 15 iClicker Questions Multiple Choice Identify the choice that best completes the statement or answers the question. _b___1. Which of the following statements is CORRECT? a. A firm's business risk is determined solely by the financial characteristics of its industry. b.The factors that affect a firm's business risk are affected by industry characteristics and economic conditions. Unfortunately, these factors are generally beyond the control of the firm's management. c. One of the benefits to a firm of being at or near its target capital structure is that this eliminates any risk of bankruptcy. d. A firm's financial risk can be minimized by diversification. e. The amount of debt in its capital structure can under no circumstances affect a company's business risk. __c__2. Which of the following statements is CORRECT? a. Increasing financial leverage is one way to increase a firm's basic earning power (BEP). . If a firm lowered its fixed costs while increasing its variable costs, holding total costs at the present level of sales constant, this would decrease its operating leverage. c. The debt ratio that maximizes EPS generally exceeds the debt ratio that maximizes share price. d. If a company were to issue debt and use the money to repurchase common stock, this act ion would have no impact on its basic earning power ratio. (Assume that the repurchase has no impact on the company's operating income. ) e. If changes in the bankruptcy code made bankruptcy less costly to orporations, this would likely reduce the average corporation's debt ratio. Chapter 23 Multiple Choice Identify the choice that best completes the statement or answers the question. __e__1. Which of the following are NOT ways risk management can be used to increase the value of a firm? a. Risk management can increase debt capacity. b. Risk management can help a firm maintain its optimal capital budget. c. Risk management can reduce the expected costs of financial distress. d. Risk management can help firms minimize taxes. e. Risk management can allow managers to defer receipt of their bonuses and thus postpone tax payments.

Women’s rights essayEssay Writing Service

Women’s rights essayEssay Writing Service Women’s rights essay Women’s rights essayThe issue regarding women’s rights is not a new one. In the past, there were distinctive differences between men and women, between their roles in society and their models of behavior. However, considerable changes have been found since those times. Today gender roles have been shifted, making strong impact on society. Women in the Western culture are now no more satisfied with the role of a homemaker; they prefer to make their own careers and share the same rights with men (Howie, 2010).   This fact means women’s rights are based on freedom that can be viewed as a virtue, but not as a burden. Women continue to fight for their rights. The emergence of feminist movements and ideologies united under the title of feminism (Gillis Hollows, 2008). Today, there is a continuous discourse on the behalf of both opponents and proponents of feminism, but the main thing is to understand the very roots and reasons of the phenomenon (Gillis et al., 2007) . Therefore, the major goal of this study is to find out the objective state of the problem and conclude whether women do win by acquiring the equal status with men in human society. For that end, the existing literature covering different perspectives will be analyzed. In particular, the study will be focused on proto-feminist movements in Europe of the 19-the century; passing the Representation of the People Act in 1918; demonstrations on women’s suffrage; women’s efforts during the First World War and the Second World War; the first wave, the second wave and the third wave feminism on the whole. The research is expected to prove that although social reconstruction of sex and gender is not always beneficial neither for women nor for men, the struggle for equal opportunities has become a historically determined stage of social development. These events reflect the changes in feminist movements and help to better understand the successes and failures of women in fighti ng for their rights. The impact of each event or development that will be discussed in this paper is connected with the changing role of women and with their changing opportunities in achievement of the established goals. Thesis statement: Women’s role in the struggle for equal opportunities highlights the positive effects of feminism on the social reconstruction of sex and gender that was caused by a number of important historical events and developments, such as the development of proto-feminist movements in Europe of the 19-the century; passing the Representation of the People Act in 1918; demonstrations on women’s suffrage; women’s efforts during the First World War and the Second World War; the development of the first wave, the second wave and the third wave feminism.The major goal of this paper is to review the historical events and developments which involve women from 1865 to the present. This paper will explore six specific events or developments that span the years covered by this course, based on their impact on the topic â€Å"women’s role in history†.   The research is focused on the analysis of both European Womens rights and the womens rights movements launched in the U.S, defined as the first wave, the second wave and the third wave feminism.Proto-feminist movements in Europe of the 19-the centuryThe development of proto-feminist movements in Europe of the 19-the century played an important role in the promotion of the philosophy of feminism. Women were inspired by proto-feminist concerns that women should be equal to men. Proto-feminist movements contributed to women’s achievements in different spheres of human activity. Actually, in the 19-th century, women’s condition under the law differed from that of men. In economics and politics, women had no power. However, women’s consciousness was more progressive compared with that of women who lived earlier than the 19-tyh century (Worell, 2000). In other words, the development of proto-feminist movements is connected with the development of feminist consciousness focused on the expansion of women’s rights and development of women’s rights movements. The Female Moral Reform Society is an example of effective proto-feminist movement aimed at representation women in a powerful position, placing emphasis on the public advocacy of personal ethics (Gillis Hollows, 2008; Worell, 2000).Passing the Representation of the People Act in 1918The Representation of the People Act (1918) criticized the limited rights of women and continued to call for equal rights. This act provided an opportunity to establish fair relationships between men and women, promoting the idea of equal pay for equal work. New reforms of the 1900s contributed to the growth of feminism. According to the Representation of the People Act of 1918, all women included in the local governmental register, aged 30 and over, were enfranchised (Gillis Hollows, 2008; Worell, 2000). The right to vote was granted to women who were householders, the householders’ wives, and who occupied the property with an annual rent of L5 and more, and who were the graduates of British universities (Gillis Hollows, 2008).Moreover, the debate regarding the passage of the Representation of the People Act raised the issues about the effects of the law, but it failed to change the established culture of parliamentary politics. Many women politicians did not criticize male-dominated political parties, remaining loyal to men’s power (Early video on the emancipation of women, 1930). In the 1900s, men remained in the positions of power, although the political movement regarding women’s suffrage in the U.K. began before the WWI (Worell, 2000).  Demonstrations on women’s suffrage  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Many demonstrations were organized to address women’s suffrage rights. The first demonstration was the parade organized by Blatch in New York in 1910. Harriot Stanton Blatch was one of activists who promoted the idea of bringing a new suffrage bill, which could become the first step to women’s voting rights. In 1907, she established the Equality League of Self-Supporting Women. In 1913, the suffrage match was held in Washington D.C. More than 5000 women activist took part in this match, hoping to win public support for suffrage. In 1916, the Women’s Political Union organized many demonstrations on women’s suffrage. In the U.S., President Wilson agreed to support the idea of women’s suffrage in 1918 after numerous protests organized by feminists. As a result, women’s rights activists were aimed at equality in all spheres of human activity based on women’s suffrage. In 1919, the Nineteenth Amendment was passed by the U.S. Congress (Howie, 2010; Worell, 2000).  Women’s efforts during the First World War  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã ‚  Ã‚  Ã‚  Ã‚   Women’s role during the First World War reflected their social and economic position. Feminists were not satisfied with the idea that women’s work was classified as less important than men’s work. Besides, the working class women who were the representatives of the first wave feminism promoted the ideas of feminism at work and in homes, in stores, halls and local newspapers. They believed in their rights and were focused on the promotion of collective actions aimed at realization of their agenda. However, men opposed women’s involvement into male jobs during the First World War. Male trade unions defended the division of labor based on gender (Gillis Hollows, 2008).  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Finally, women’s activism in the era of the First World War, the considerable increases in the cost of living in that period, as well as the recognition of the established trade unions and the passage of the constitutional ame ndment to support women’s suffrage contributed to women’s mobilization during the war. According to Howie (2010), patriotic women highlighted the importance of the ideas of feminism. Due to the diversity of experiences during that period, women could become more independent in their choices. Although many women realized that their rights were limited, they supported feminism and motivated others to join wartime mobilization (Howie, 2010).Women’s efforts during the Second World War  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Women’s efforts during the Second World War were focused on more radical changes. Unlike in the First World War, during the Second World War women’s position was more stable. The governments allowed women to join the armed forces and be involved in the war-related production.   All women aged under 40 years old were divided into two categories: mobile and immobile. Mobile women were allowed to join army and carry out war work duties. Immobile women were responsible for caring children and elderly people. Many of them were involved in voluntary work, either in industry or in voluntary organizations (Howie, 2010).   Women were allowed to work 16 hours a day and perform men’s duties. However, women were paid less than men. Besides, they were discriminated in the workplace. Thus, women played an important role in the war effort, although their position in society was still less valuable, comparing with men’s position (Howie, 2010; Gillis Hollows, 2008).  The first wave, the second wave and the third wave feminism  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   As the American women’s movement is characterizes as â€Å"waves†, there is a necessity to refer to three waves of feminism and identify certain differences between them. Actually, the development of the first wave, the second wave and the third wave feminism highlight the importance of women’s involvement in social reconstruction of sex and gender (Howie, 2010). Although these waves are closely connected with one another, there are some differences in their philosophies. It has been found that each wave of feminism is based on the successes and failures of previous generations of women. For example, the first wave feminism is reflected by the following successes: suffrage and voting rights. These developments occurred in the late 1800s- the early 1900s, influencing further changes in women’s representation (MacKinnon, 1995).  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   In addition, the second wave feminism, which was launched in the 1960s, placed emphasis on the role of personal politics in human society. The banner of the second wave feminism was â€Å"the personal is political†. Actually, it was based on women’s rights, such as abortion rights, child care rights, as well as other issues, including women’s recognition of unpaid labor, access to health care services and equal pay for equal work. Catharine MacKinnon, the Professor of Law at the University of Michigan and the author of the book Toward a Feminist Theory of the State, argues that women’s rights are still limited and there is a necessity for broader horizons for women. A variety of issues of concern remain unsolved. Women continue to fight for their rights (MacKinnon, 1995). According to Hollows, and Moseley (2006), there is a close relationship between the second wave feminism and popular culture, but feminism cannot be viewed as a â€Å"monolithic and homogeneous movement† (p. 3).  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Moreover, the first wave and the second wave feminism created certain challenges, such as the concerns about racism and discrimination, tensions between generations, etc. These concerns can be found in the next wave of feminism – the third wave feminism, which was launched in the 1990s (MacKinnon, 1995). The third wave feminism is based on criticism of collective past of women’s movement and building more diverse and dynamic movement. In other word it is characterized by the increased role of multiculturalism (MacKinnon, 1995). Alice Walker (1983) helps to assess the role of virtues, beliefs and values in the creation of a womanist virtue ethic, which forms the basis of third wave feminism. She states that social activism helps in promotion of feminist ideas and addresses the challenges caused by diverse society.Conclusion  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Thus, it is necessary to conclude that women have always played an important role in the development of history.   This paper is based on providing evidence regarding the effects of social reconstruction of sex and gender on women and their participation in the struggle for equal opportunities, which has become a historically determined stage of social development. The history that involves women has been developed over centuries, constantly chang ing its goals and forms, increasing the popularity of women’s movement, mainly in the 20-th century, when suffrage and voting rights were popularized. The role of women in the 19-th century differed from their roles in the 20-th century. The events that occurred in the 1900s contributed to the developments in the later decades. For example, proto-feminist movements in Europe of the 19-the century contributed to the development of more independent views on women’s rights and duties. The third wave feminism completely changes women’s views on their role in social development through the relationship between feminist movement and popular culture. Generally speaking, women’s role in the struggle for equal opportunities throughput the history emphasizes the positive effects of feminist ideas on the social reconstruction of sex and gender that was caused by a number of important historical developments, including the development of proto-feminist movements in E urope of the 19-the century; passing the Representation of the People Act in 1918; demonstrations on women’s suffrage; women’s efforts during the First World War and the Second World War; the development of the first wave, the second wave and the third wave feminism.

Guide to Writing a Great Expository Essay

Guide to Writing a Great Expository Essay Here youll get the basic information on how to write an expository essay. What Is an Expository Essay? Assigned to write an expository essay? First look for the expository essay definition to make clear what expository writing is: An expository essay is a type of written discourse that serves the purpose of explaining, describing and providing information to the reader. This is a simple expository essay definition. Expository essays can also be accurately termed the information or informative essays. An expository essay serves to explain a topic in a logical and straightforward manner. Without many complications, these essays present fair and balanced analyses of different subjects based on facts, without any references to the author’s opinions or emotions. One of the typical expository essay prompts to a writer is to use the words â€Å"explain† or â€Å"define†. This expository essay prompt  makes the writer â€Å"explain† in a simple, plain and direct manner. Expository Essay Outline The common method of writing an expository essay is a 5-paragraph approach. However, this is not the only formula for writing expository essays but it provides a basic and clear outline for easy reading. This format gives the expository essay an introduction, 3 body paragraphs, and a conclusion, hence the name is a 5-paragraph approach. Basically, the paragraphs entail: Introduction. The introduction brings up the main thoughts of the essay and can be a great tool to capture your reader. Body paragraphs. The body paragraphs discuss and provide in-depth information to the reader regarding the mentioned topic. Your thoughts should flow well, and get interesting one after the other to keep your reader interested in wanting to know more. Conclusion. The conclusion echoes your introduction by showing that the introductory statement has been verified or explained in detail. Analyzed events of situations should be reviews from several sources to make the essay stay focused on the context and be objective. The conclusion in your essay should never come as a surprise to the reader as it needs to easily come out from the essay. The conclusions and the analysis should be well connected to not leave your reader guessing what you meant. If you are looking for expository essay examples here is a great one: Expository Essay Example Expository essays require you to avoid incorporating your emotions or opinions, therefore, you have to write in a way that will enable you to remain objective and imperative. The 3rd person writing is the most logical in this case. You need to keep a neutral voice and avoid pronouns like I, we, and you. Connection words such as for example, such as, furthermore, whereas, similarly, and conversely among more are used in these articles. 5 Steps to Writing a Winning  Expository Essay Step 1:  Pre-write the expository essay. Students should take the time to brainstorm on the topic and main ideas, research, and take notes. Design an expository essay outline to show how the information will be presented in each paragraph in a logical sequence. Step 2:  Draft the expository essay.  Consider how you will present your ideas with the 5-paragraph approach. Consider how the introductory paragraph will be, the 3 body paragraphs, and how the conclusion will spice up your essay. Step 3:  Revise the expository essay.  Here you will need to review, modify and reorganize the work with the goal of making it the best it can be. Has the information been clearly communicated to the reader? Step 4:  Edit the expository essay.  Proofread and correct the grammatical errors, and edit to improve the style and clarity. Step 5:  Publish the expository essay.  Share your essay with the class or friends to get some reviews and know how they feel about it. Check out the list of expository essay topics our writers have prepared for you: 50 Most Popular Expository Essay Topics The topic is chosen. The time has come to get some expository essay prompts from the professional writers: When writing your expository bear in mind that a great essay is made by: 1. A clear, concise, and well-defined thesis statement that is presented in the first paragraph 2. Clear and logical transitions between the introduction, the body paragraphs, and the conclusion. Without logical progression of thought in your essay, a reader is unable to follow the essay’s argument, and its structure will crumble 3. Body paragraphs with reliable evidence support. These can be logical, factual or anecdotal. The body paragraphs should also have some or a strong logical connection to the thesis statement in the opening paragraph 4. Creativity to give your readers a lasting impression on essay’s evaluation 5. A catchy conclusion that spices up your expository essay content in style. It should not restate the thesis but instead, refer to it with reference to the evidence provided. If you are looking for an excellent expository essay that will be written according to your requirements, will contain proper formatting, language, and structure, feel free to contact our writing staff and place your order. We have written hundreds of expository papers in the past and have developed extensive expertise in expository essay writing. You will be able to use the paper we deliver as a writing sample and thus better understand how expository essays need to be written. is the service you can trust to write your expository essay.

The 7 Personality Traits that Can Destroy Your Career

The 7 Personality Traits that Can Destroy Your Career Of all the things you think may destroy your career, you probably didn’t expect your own personality to be one of them. But while some character traits are innate, others are under your control. It’s up to you to tend your own garden- rip out the weeds and plant seeds for stronger, better plants. Whatever you do, make sure to keep an eye out for these 7 traits, which can really put a damper on your career.1. NarcissismMost people you work with are going to be able to tell if you’re an insufferable narcissist. You have an aversion to teamwork? Your colleagues can tell. Remember: your pain, your annoyance, your moods, and your bad day are no worse or more important than anybody else’s. Try to think about others every now and then. Your career will thank you.2. Complaining After the FactYou’ve had a meeting and things have been debated and discussed thoroughly. If you didn’t speak up then, you’ve forfeited your right to speak after. If yo u don’t have the guts to voice your opinions or contribute in the meeting, then keep your complaints to yourself.3.  Ignoring Your TeamDon’t pretend that you’ve done everything yourself with each small victory. Most workplace accomplishments are not solo ventures. Thank the people that helped you score those victories. Don’t ever be the guy who says â€Å"that’s not my job.† Pitch in! And never never throw anyone under the bus.4. GossipingNobody loves a gossip. You might make a few shallow friends fairly quickly at the water cooler, but you won’t keep them, and you could get yourself in real social and professional trouble.5.  Constant ComplainingNobody likes a pessimist. Start counting the number of times you complain or say something negative in a day. If it’s more than 3, you have a problem. If it’s more than 30, you’re well on track to being the most hated dude in the office.6. CrudenessYou don’t ha ve to be Suzy Perfect, but you should try to keep a little decorum. Try not to be flatulent or curse so much that no one wants to be around you. Be a force for good in your office!7.  Excessive SarcasmBe generous and nice. If you feel the urge to be sarcastic or snide, hold it back. There is a way to be a good person and make people laugh. Try not to get your way or get a laugh at anybody else’s expense.If you have any one (or more) of these traits, it might be time to start thinking about how to prune your bad angels and start watering your good ones.

An Investigation on the Selection of Social Service Provider and Buyer Dissertation

An Investigation on the Selection of Social Service Provider and Buyer Behaviour - Dissertation Example According to (Pires and Stanton, 2002), social services are of key importance to the society as these help in strengthening the quality of life of individuals. Although, social service provision is more popularly linked to governmental organizations, there are in fact, a number of non-governmental social service providers as well. Some of these are professionally managed by trained personnel working full-time and paid adequately while others may be formed by volunteers working in their leisure time (Munday, 2007).The users of social services may vary in terms of the urgency of their needs and degree of their dependency on service providers. There may be a dying day-laborer requiring immediate medical care from the nearest possible provider on one hand, while a child laborer in the need of proper education for a bright future on the other. The need and dependency of the former does not leave him much scope to dwell on choices and selection criterion whereas the latter can improve his chances of continuous support and future employment by making a prudent choice. A consumer of general commercial or other services follows certain steps, knowingly or unknowingly, in order to reach a decision while making a choice of a service provider. One of the models defining such a process is the EKB (Engel, James, David Kollat and Roger Blackwell) model with stages of problem recognition, internal and external search, alternative evaluation, purchase and outcome (Engel, J., Kollat, D. and Blackwell, R. (1968). But a consumer of social services differs from the general consumer on a number of significant parameters including sources of information, aptitude and spending capacity (Pires and Stanton, 2002). This affects the process followed adversely more often than not.The selection process of these consumers may be influenced by familiarity, proximity, endorsement and acceptance of claims prima facie without due diligence (Schiffman et al, 1997). This paper therefore proposes t hat there is a need to understand the decision making process and criteria employed by the buyers of social service, so that more targeted promotion or reach out programs can be developed by the social service providers. Social service providers across the UK are funded by the government and private donations and it is essential that the funding is justified in terms of concerted and targeted help made available to those who are in real need. However, the selection of a service is largely dependent on the individual who needs it, and therefore it is important that the service providers are aware of how this selection process occurs. 2. Research Objectives -To evaluate the factors that influence the selection of service provider It is expected that there will be both external situational factors as well as internal, psychological or personality factors that impact which criteria are adopted by the consumers. -To explore the specific criteria that the consumers of social service emplo y in selecting a service The proposed objective of the research is to understand the criteria that social service buyers adopt in selecting a social service for themselves. -To develop a framework for consumer behaviour for selection of social service provider Another aim of the research is to develop a framework that can be used to predict consumer behaviour for consumers of social services. 6. Literature Review A preliminary review of the available literature has

A Quantitative Comparison of Academic Achievement In New York City Dissertation

A Quantitative Comparison of Academic Achievement In New York City Public Schools vs. New York City Charter Schools As Measured By 2009 - 2010 New York State ELA And Math Exams - Dissertation Example The intention of this study are charter schools - the public schools that operate independently of the district board of education, making them a one-school public school district. They have their own charters written by private individuals: parents, educators, community leaders that enumerate their laws, governance structure and principles. This autonomous setup results in bigger accountabilities for the school. Because of this autonomy and â€Å"customized† curricula, many people believe that charter schools are far more beneficial to children, as compared to public schools. People also believe that charter schools provide better services because of the high standards they set for themselves. There are studies that compare the effectiveness of public schools versus charter schools. However, they differ in their findings. The growing appreciation for the potential benefits of quality educational programs has strengthened funding agencies’ and policy makers’ comm itment to ensuring all families have access to programming that can support and enhance children’s development, growth, and learning. These benefits can be realized, however, only in high-quality programs with characteristics linked to positive outcomes for children. However, deciding whether a public or charter school will best suit the needs of the child can be a harrowing and difficult decision for parents to make and requires a method for determining which scholastic institution will provide the best educational experience for the child. The establishment of a stable formula for measuring the academic achievement of the students from public schools and charter schools is needed. According to research conducted by Lubienski and Lubienski (2006

English Essay Example | Topics and Well Written Essays - 1000 words - 23

English - Essay Example The absence of the physical identity of the individuals in the internet tended to loosened them up as they become invisible behind their digital personality. This has created problems such as; â€Å"the growing incidence of online fraud and identity theft, privacy incursions, copyright infringements, trademark violations, domain name disputes, spamming, computer viruses, inadequate or vaguely defined consumer protection laws, and terrorist-related and pornographic websites† (David 2006). These issues became so alarming that the idea of regulating internet came into mind. Many people are suggesting that perhaps it is now time for the government to step in to enforce its police power to stop these issues online. But one cannot help to think whether it is proper for the government to step in the cyberspace and whether it will be effective if ever it has to step in. Without doubt, the internet needs some sort of regulation of acceptable conduct but whether it should be the government who should enforce it is questionable. Governments are limited by geography and laws are relative depending on what country are you from. What is acceptable in one country may not be permissible in another. Say for example in China where it is not advisable to speak against the government while it is perfectly alright in the United States and such right is even protected by its laws. Given such relativity of laws, it would be difficult for any government to enforce its laws on other sovereign state for that would tantamount to conflict. Government is also a suspect in terms of policing the cyberspace. We have already seen in other countries how government can react when given the prerogative to regulate the internet. It abridges information and censures freedom of speech. Classic example is Libya where anti-government forces has to find creative means to access the internet just to share to the world what is happening there during its revolution. Libyan government literally

Business Economics Referred Coursework Assignment Essay

Business Economics Referred Coursework Assignment - Essay Example Middle East suffered a decline of wheat production of 7.4 million tons or about 19 percent because of the worst drought the country had experienced in 2008. (Commodity Intelligence Report, 15 December 2008) China and Iran, had each, reported worse effects of droughts to wheat crops. Drought in China as of October, 2010 had affected 7.73 million hectares of wheat plantation (China Daily). Iran estimated a decline of their 2008 production by 20% due to effects of drought (USDA Foreign Agricultural Service. 15 December 2008). A decline in production would mean a gap in supply and demand that raises price. The price of wheat is also affected by the weakening US dollar because this will mean a decline in the purchasing power of a dollar. The U.S. dollar is a world trading currency; meaning all prices of commodities are linked to its price, and devaluation would have a great impact to international trade. In anticipation of devaluation, all countries will immediately raise their prices. Co mmodities such as wheat, oil, coffee, etc. will now set their price records to protect their investments. Farmers know that the dollars they are receiving for the wheat is declining in purchasing power, so they have to adjust their prices in anticipation for the devaluation; that is why we have a higher price of wheat now. As an example, if the US dollar declines by 30%, and the farmer has $1 million in wheat, his million dollars will now be able to buy $700,000 worth of goods or services, so he lost $300,000 in purchasing power. 2. Identify the factors that determine the demand for goods and services in general? Consider how these factors affect the demand for wheat. In general, determinants of demand are income, tastes, prices of related goods and services, expectations and the number of buyers. We know that if we lower the price of a good without altering its quality or quantity, people will flock to you to buy as this the law of demand. We will illustrate the law of demand by ex ample in demand for wheat. The law of demand applies to a well defined good – the wheat. Then the second phase indicates that people must not only want to purchase the wheat but must be able to purchase the wheat in order to be counted as part of demand. But although willing, consumer is not able at the price of $111.00, so buyer thinks of something else to replace the need for wheat. The next step is to think of the price and quantity demanded; that is as the price rises, the quantity demanded falls, and as the price falls, the quantity demanded increases. 3. What are the major factors increasing the demand for wheat? [Make sure you use the concept of income elasticity of demand for wheat (Ardy, 2010, p. 5). The factors that increase demand for wheat are price, price of substitute goods; preferences, population and income. These factors are discussed in the following paragraphs. Price. As the price of wheat increases, assuming that all other factors remain equal, less people would demand for wheat. The demand slope is downward looking . As the price of wheat increases, people would naturally avoid consumption and look for substitute products that they would value more. The price of substitute goods. A substitute product is a good or service which may be bought instead of another when the price of the latter changes or if it becomes unavailable. For instance, the increase in wheat price will increase in the demand for corn,

The Possible Power of Electronic Media Essay Example | Topics and Well Written Essays - 1250 words

The Possible Power of Electronic Media - Essay Example So in order to bring a revolution onto the island a new leadership would be evolving. The old regime policies would be abandoned and new and clearly sought strategies would be implemented in order to recover from the old losses. The strategies would not only benefit the national government but also the individuals living in the island of Angic. The new government is going to take initiatives which are in line with the individuals vested interests. Different forms of media help is being pursued by the current government so as to implement their strategies and gain support amongst the people. Media is said to have a strong impact on the individuals living in this world. It not only tells the individuals where they are heading to but also urges them to take a certain step if required. Thus different types of electronic media is being sought by the government so as to implement such programs which are in line with the governments policy. The government has used radio to aware people of t he new friendly strategies which they are about to implement with their new policies. The individual benefits are pointed out in such a strategy and points laid out in which they tell people about how they are going to prosper. They reveal the corruptions and wrong doings of the past government which has put the state in an unstable condition. Thus they tell the individuals through radio that a new government is to come to bring a revolution on the island so that the island can survive the unfriendly conditions. The facts and figures of the previous government are provided to the public so as to make them aware of the present conditions prevailing in the state. The state of Angic has gone into a total chaos after the previous governments harsh and unfriendly strategies. The strategies have not proved to be successful and have turned out to be a failure. The role of radio can be put to be very important as it tells

How and why did the Industrial Revolution change the class system of Research Paper

How and why did the Industrial Revolution change the class system of Great Britain - Research Paper Example The low class was at the lowest level of the pyramid and was made of majority of the British population who worked in the farms and industries owned by other citizens. The upper class was the top most system and was majorly made of the members of the royal family among other rich and influential members of the societies. The emergence of the industrial revolution in the country created a major shift in the class system in the country, resulting into an upset and the empowerment of the low class citizens. Industrial revolution created a major shift on the traditional class systems in the country and led to the empowerment and enlightenment of the low class. Industrial revolution changed the British social fabric in a number of ways and this influenced the position of the low and high class citizens alike. During this period in the history of Great Britain, the citizens thinking and behavior was confined to their status in the society. This created a situation where emphasis was placed on the position of the family and the place of birth of an individual as opposed to their abilities and skills2. However, the emergence of the industrial revolution during the Victorian period completely changed everything in the country. As opposed to emphasis and focus on the social hierarchy, this period witnessed a shift towards economic class and empowerment. The industrial revolution contributed to the shuttering of the traditional Georgian society and focuses on social class and defined the new Victorian era. The 18th century social changes that were witnessed in Great Britain came as a result of the new invention, legislations and impetus that added to the country’s economy3. Before the industrial revolution, the royal reserve and bank system was under the control of the high class members of the society. Few citizens were allowed to access loans and therefore participate in the different industrial and agricultural

The Possible Power of Electronic Media Essay Example | Topics and Well Written Essays - 1250 words

The Possible Power of Electronic Media - Essay Example So in order to bring a revolution onto the island a new leadership would be evolving. The old regime policies would be abandoned and new and clearly sought strategies would be implemented in order to recover from the old losses. The strategies would not only benefit the national government but also the individuals living in the island of Angic. The new government is going to take initiatives which are in line with the individuals vested interests. Different forms of media help is being pursued by the current government so as to implement their strategies and gain support amongst the people. Media is said to have a strong impact on the individuals living in this world. It not only tells the individuals where they are heading to but also urges them to take a certain step if required. Thus different types of electronic media is being sought by the government so as to implement such programs which are in line with the governments policy. The government has used radio to aware people of t he new friendly strategies which they are about to implement with their new policies. The individual benefits are pointed out in such a strategy and points laid out in which they tell people about how they are going to prosper. They reveal the corruptions and wrong doings of the past government which has put the state in an unstable condition. Thus they tell the individuals through radio that a new government is to come to bring a revolution on the island so that the island can survive the unfriendly conditions. The facts and figures of the previous government are provided to the public so as to make them aware of the present conditions prevailing in the state. The state of Angic has gone into a total chaos after the previous governments harsh and unfriendly strategies. The strategies have not proved to be successful and have turned out to be a failure. The role of radio can be put to be very important as it tells

The culture high Movie Review Example | Topics and Well Written Essays - 750 words

The culture high - Movie Review Example Although the position supported in a film is arguable, its creators did a good work to make â€Å"The Culture High† informative and engaging to watch. The plot of the film is centered on the discussion of the current status of marijuana in the United States with its creators openly arguing for marijuana legalization. A significant part the film is dedicated to explaining the side of proponents of legalization, who state that marijuana is not more dangerous or harmful than alcohol, but its prohibition allows underground business and cartels to prosper and conduct more violence. As it is argued, â€Å"marijuana does not cause lung cancer while more than 5 millions annually die from tobacco worldwide.† (The Culture High) Further, it is exposed that criminalization of marijuana can be linked to the government and other private organizations making profit from it by massively incarcerating the population. However, at this time, other sectors of the economy are in need of funds. Since President Richard Nixon declared the â€Å"War on Drugs†, millions were imprisoned on minor marijuana charges. (The Culture High) As a resul t, rose the need for private prisons, which according to Howard Bloom, â€Å"make it profitable to incarcerate people† (The Culture High) Subsequently, it is suggested that marijuana prohibition is needless, but is still maintained not for the sake of keeping order in the society and protecting a common citizen, but for continuing militarization of the police forces and gaining profit while denying Americans their rights, manipulating and misleading them. Although â€Å"The Culture High† mostly operates with popular arguments, it is quite informative for a person who is not an adept at the issue being raised. From one side, the film contains much information that has been actively and often discussed in the media, leaving little space for a kind of a discovery to be made.

Band Rate List Essay Example for Free

Band Rate List Essay By storing the Band Rate List in a computer system it can be used to attach payments due automatically to each video when a member returns it late. The system can also be efficiently updated. The use of a computer system would also enable Jean to generate a daily report for each shop detailing unreturned tapes and their subsequent charges. By having all member details on account no report would need to be written to County Court as Jean could simply e-mail all relevant information in a matter of seconds. Saving both time and money. By implementing a scanning device/system on the drop box, linked to a computer, staff will immediately be notified when videos are returned preventing any more lost sales. Introduction of a computer system network will mean any number of staff can access the member files at the same time (as long as there are sufficient servers). It will also put an end to anyones struggle to decipher handwriting. To solve the problem of parking Jean could purchase extra space if possible, alternatively he could use the less busy shop 3 to pilot an innovative scheme where customers can choose to get a drive-thru video. This would cut down on the number requiring parking spaces if successful. Two windows could be formed at the side, one to take the order, receive payment and swipe the membership card, while the other is used to give the video to the member. If the idea catches on Jean could patent it and introduce it to his other shops before retiring with a large sum in the bank as a result (or maybe I should do that). A computer system would allow Jean access to all files from wherever he desired. It would also allow him to organise members easily, e. g. by postcode for mailing, and he would no longer have to start from scratch every time he wanted to update it. Security could also be improved as the shops can efficiently communicate using the computer network. In future a gang member who has stolen from one shop would be expected in the other shops on the same day so relevant actions can be taken before they arrive. Information relevant to Jean in terms of financing any forthcoming I. T. installation is detailed in the section entitled costs. An investments payback period in years (and months, weeks or even days) is equal to the net investment amount divided by the average annual cash flow from the investment. It basically means: How long will it take to get my money back? This refers to the time it takes for an investment to repay the initial outlay. In calculating the payback period, it is usual to work to the nearest month. This month can be obtained using the following formula: Month of Payback = (Income Required / Contribution per Month) Or to find the day of payback: Day of Payback = (Income Required / Contribution per Day) When using this method to choose between projects, the shortest payback period will be chosen. For a business, payback is a simple calculation to make. It gives a good indication of the level of risk associated with potential investments because the longer the payback period, the longer the firms money is at risk, and the greater the likelihood that something unexpected may negatively affect the business. The payback period also takes into account the timing of cash flows. Firms might adopt this method if they have cash flow problems. This is because the project chosen will payback the investment more quickly than others. Strengths of the Payback method are: Its easy to compute, easy to understand and provides some indication of risk by separating long-term projects from short-term projects. It is particularly useful for firms with difficult cash flow positions as it helps them to identify how long it will take for the cash to be restored. Also, the further ahead a forecast looks, the less likely it is to be accurate due to uncertainty increasing over time. For this reason payback is advantageous as it only focuses on the short-term. Weaknesses: It doesnt measure profitability, doesnt account for the time value of money and ignores financial performance after the break-even period. Using this method may also encourage a short-termist attitude within the business.

Momadays Angle of Geese and Other Poems Essay -- Momadays Angle of

Angle of Geese and Other Poems MOMADAY had been writing poetry since his college days at University of New Mexico, and this volume incorporates many of his earlier efforts. Momaday admired the poetry of Hart Crane as an undergraduate, and early poems like "Los Alamos" show Crane's influence. Under the tutelage of Yvor Winters at Stanford Momaday developed an ability to provide clear, precise details and images in his verse. As a graduate student at Stanford, Momaday absorbed the influence of an eclectic group of poets including Emily Dickinson, Wallace Stevens, Paul Valery, Charles Baudelaire, and Frederick Goddard Tuckerman, the subject of Momaday's PhD dissertation. What these poets had in common, at least in the eyes of Momaday and Winters, was the practice of establishing a conceptual theme, but then giving it meaning with concrete, sensory images. The title poem, "Angle of Geese," shows how Momaday employs sensory experience as an integral part of the message, not just as ornament. In the first part of the poem, Momaday relates his reactions to the funeral of a ...

Social Movements Compartion Essay -- Sociology

Introduction Why is it that specific movements succeed in broadening the scope and scales of the struggle, whereas other do not? Given the dearth of resources at their disposal, social movements see to attract the attention, empathy, and support of third parties, as a way to balance the unfavorable asymmetric power structure in which they are situated. The importance of expanding the scope of contention and attracting supporters become even more critical in cases of ethnic driven movements, given the nature of their goals and the frequency with which restrictions are imposed on their collective sentiments by the state. Globalization and the Battle of Seattle Globalization describes what a number of people perceive as a fundamental change in the conditions of human life. Just what has changed and how it has changed, however, are matters of great contention. Nonetheless, current writing on globalization focuses on some specific trends that appear to have pushed the sources and implications of social action beyond state borders. Recent transformations in transportation and communications technologies have altered our sense of distance, radically compressing time and space. Territorial states have apparently lost some of their capacities to establish order or mediate change within their borders. The number and power of intergovernmental institutions and multinational corporations have grown remarkably. The communications media are increasingly global in both their reference and their reach, and the media also help provide resources in the building of transnational epistemic communities of immigrants or like-minded activists. Social movements ride the waves of these global processes and formations; in turn, they begin to define ne... .... (1997). Arab national communism in the Jewish state. Gainesville, FL: Florida University Press Keck, Margaret, and Kathryn Sikkink. 1998. Activists Beyond Borders: Advocacy Networks in International Politics. Ithaca, NY: Cornell University Press.. Landau, J. (1991). The Arab minority in Israel, 1967– 1991: Political aspects. New York: Oxford University Press. Lustick, I. (1980b). Arabs in the Jewish State: A study in the effective control of a minority population. Austin, TX: University of Texas Press. Neuberger, B. (1993). The Arab minority in Israeli politics 1948-1992: From marginality to influence. Asian and Africa Studies, 27, 149-169 Peoples’ Global Action. 2000. â€Å"Worldwide Resistance Roundup: Newsletter ‘Inspired by’ Peoples’ Global Action.† London. UN Development Programme. 2000. Human development report 2000: Overcoming human poverty. New York: UNCP

ALL SOULS REFLECTIVE ESSAY Essay

Michael Patrick Macdonald was bought up in Southie’s Old Colony housing project. He describes the way this world felt to the troubled yet keenly gifted observer he was even as a child. With radiant insight, he opens up a contradictory world, where residents are troubled by gangs and crime but refuse to admit any problems, remaining fiercely loyal to their community. MacDonald also introduces us to the unforgettable people who inhabit this proud neighborhood. We meet his mother, Ma MacDonald, an accordion-playing, spiked-heel-wearing, indomitable mother to all; Whitey Bulger, the lord of Southie, gangster and father figure, protector and punisher; and Michael’s beloved siblings, nearly half of whom were lost forever to drugs, murder, or suicide. By turns explosive and touching, All Souls ultimately shares a powerful message of hope, renewal, and redemption. Macdonald eloquently describes us to us the importance of family, friends, race and everything in between. †All Souls is the written equivalent of an Irish wake where revelers dance and sing the dead person’s praises.† Michael Patrick MacDonald was in third grade when the riots broke out. â€Å"The man ran from the crowd as people threw rocks at him,† MacDonald writes. †He was trying to get away, but there was nowhere to go. . . . ‘Kill the nigger!’ my neighbor shouted. That was Molly’s mother, running to join the commotion. Molly’s mother is a prime symbol of what MacDonald tries to explain about race in Southie. She is despised, impoverished and barely surviving in a dismal housing project. By shouting †Kill the nigger,† she displays the only attribute that sets her above the blacks that she so hates. MacDonald’s account is filled with vivid episodes: of his brother Davey’s horrific incarceration in Mass Mental and ultimate suicide; of the time Helen took her older kids to the hospital, where her current lover was a patient, to beat him up after he denied he was the father of the child she was carrying; of the murder of his brother Frankie by his compatriots after the police shot him in an armored-car robbery. But perhaps most shocking is the accusation that the FBI was paying Southie’s leading gangster, Whitey Bulger, as an informant although they knew he was the neighborhood kingpin. Within the closed world of the projects, there is a code of silence about the extent of death and destruction around them. In certain ways, my group walkabout through Boston’s Chinatown did reflect what Macdonald wrote in his novel, not through the drugs,the gangs or violence that existed during the time, but through the solidarity and compassion the residents feel for each other. Like Macdonald’s mother, â€Å"Ma† who managed to raise ten children despite various abusive relationships and other difficulties of life; the people of Chinatown and other Boston towns never seem to let the signs of the times affect their livelihood or wellbeing. No matter what kind of hardships they encounter, the family unit always comes first, an admirable trait difficult to come by. MacDonald’s conversational style whips readers in rage towards the unfairness of the uncontrollable situations, and makes them long for the type of tight-knit community that existed in South Boston decades ago. This is a powerful story that finally captures the essence of long-ignored Southie. As New York Times put it–â€Å"The book leavens tragedy with humor but preserves the heartbreaking details† MLA: â€Å"All Souls: A Family Story from Southie: Michael Patrick †¦Ã¢â‚¬  Insert Name of Site in Italics. N.p., n.d. Web. 28 Nov. 2012 . â€Å"Michael Patrick MacDonald – All Souls: A Family Story from †¦Ã¢â‚¬  Insert Name of Site in Italics. N.p., n.d. Web. 28 Nov. 2012 . â€Å"A Prayer for the Dead – The New York Times – Breaking News †¦Ã¢â‚¬  Insert Name of Site in Italics. N.p., n.d. Web. 28 Nov. 2012 . â€Å"A Prayer for the Dead – The New York Times – Breaking News †¦Ã¢â‚¬  Insert Name of Site in Italics. N.p., n.d. Web. 28 Nov. 2012 . â€Å"All Souls: A Family Story from Southie: Michael Patrick †¦Ã¢â‚¬  Insert Name of Site in Italics. N.p., n.d. Web. 28 Nov. 2012 . â€Å"John’s Book Reviews: All Souls – University of California †¦Ã¢â‚¬  Insert Name of Site in Italics. N.p., n.d. Web. 28 Nov. 2012 .

Dai Park Textbook

Stochastic Manufacturing & Service Systems Jim Dai and Hyunwoo Park School of Industrial and Systems Engineering Georgia Institute of Technology October 19, 2011 2 Contents 1 Newsvendor Problem 1. 1 Pro? t Maximization 1. 2 Cost Minimization . 1. 3 Initial Inventory . . 1. 4 Simulation . . . . . . 1. 5 Exercise . . . . . . . 5 5 12 15 17 19 25 25 27 29 29 31 32 33 34 39 39 40 40 42 44 46 47 48 49 51 51 51 52 54 55 57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Queueing Theory 2. 1 Introduction . . . . . . . 2. 2 Lindley Equation . . . . 2. 3 Tra? c Intensity . . . . . 2. 4 Kingman Approximation 2. 5 Little’s Law . . . . . . . 2. 6 Throughput . . . . . . . 2. 7 Simulation . . . . . . . . 2. 8 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . Formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Discrete Time Markov Chain 3. 1 Introduction . . . . . . . . . . . . . . . . . . . . 3. 1. 1 State Space . . . . . . . . . . . . . . . . 3. 1. 2 Transition Probability Matrix . . . . . . 3. 1. 3 Initial Distribution . . . . . . . . . . . . 3. 1. 4 Markov Property . . . . . . . . . . . . . 3. 1. 5 DTMC Models . . . . . . . . . . . . . . 3. 2 Stationary Distribution . . . . . . . . . . . . . 3. 2. 1 Interpretation of Stationary Distribution 3. 2. 2 Function of Stationary Distribution . . 3. 3 Irreducibility . . . . . . . . . . . . . . . . . . . 3. 3. 1 Transition Diagram . . . . . . . . . . 3. 3. 2 Accessibility of States . . . . . . . . . . 3. 4 Periodicity . . . . . . . . . . . . . . . . . . . . . 3. 5 Recurrence and Transience . . . . . . . . . . . 3. 5. 1 Geometric Random Variable . . . . . . 3. 6 Absorption Probability . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. 7 3. 8 3. 9 3. 0 Computing Stationary Distribution Using Cut Method Introduction to Binomial Stock Price Model . . . . . . Simulation . . . . . . . . . . . . . . . . . . . . . . . . . Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . CONTENTS . . . . . . . . . . . . . . . . . . . . 59 61 62 63 71 71 72 73 75 78 80 80 80 82 84 91 91 96 97 100 101 103 103 104 106 107 107 108 109 111 111 117 117 130 135 148 159 4 Poisson Process 4. 1 Exponential Distribution . . . . . . . 4. 1. 1 Memoryless Property . . . . 4. 1. 2 Comparing Two Exponentials 4. 2 Homogeneous Poisson Process . . . . 4. 3 Non-homogeneous Poisson Process . 4. Thinning and Merging . . . . . . . . 4. 4. 1 Merging Poisson Process . . . 4. 4. 2 Thinning Poisson Process . . 4. 5 Simulation . . . . . . . . . . . . . . . 4. 6 Exercise . . . . . . . . . . . . . . . . 5 Continuous Time Markov Chain 5. 1 Introduction . . . . . . . . . . . 5. 1. 1 Holding Times . . . . . 5. 1. 2 Generator Matrix . . . . 5. 2 Stationary Distribution . . . . 5. 3 M/M/1 Queue . . . . . . . . . 5. 4 Variations of M/M/1 Queue . . 5. 4. 1 M/M/1/b Queue . . . . 5. 4. 2 M/M/? Queue . . . . . 5. 4. 3 M/M/k Queue . . . . . 5. 5 Open Jackson Network . . . . . 5. 5. 1 M/M/1 Queue Review . 5. 5. 2 Tandem Queue . . . . . 5. 5. Failure Inspection . . . 5. 6 Simulation . . . . . . . . . . . . 5. 7 Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Exercise Answers 6. 1 Newsvendor Problem . . . . . . . 6. 2 Queueing Theory . . . . . . . . . 6. 3 Discrete Time Markov Chain . . 6. 4 Poisson Process . . . . . . . . . . 6. 5 Continuous Time Markov Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter 1 Newsvendor Problem In this course, we will learn how to design, analyze, and manage a manufacturing or service system with uncertainty. Our ? rst step is to understand how to solve a single period decision problem containing uncertainty or randomness. 1. 1 Pro? t Maximization We will start with the simplest case: selling perishable items. Suppose we are running a business retailing newspaper to Georgia Tech campus. We have to order a speci? c number of copies from the publisher every evening and sell those copies the next day.One day, if there is a big news, the number of GT people who want to buy and read a paper from you may be very high. Another day, people may just not be interested in reading a paper at all. Hence, you as a retailer, will encounter the demand variability and it is the primary un certainty you need to handle to keep your business sustainable. To do that, you want to know what is the optimal number of copies you need to order every day. By intuition, you know that there will be a few other factors than demand you need to consider. †¢ Selling price (p): How much will you charge per paper? Buying price (cv ): How much will the publisher charge per paper? This is a variable cost, meaning that this cost is proportional to how many you order. That is why it is denoted by cv . †¢ Fixed ordering price (cf ): How much should you pay just to place an order? Ordering cost is ? xed regardless of how many you order. †¢ Salvage value (s) or holding cost (h): There are two cases about the leftover items. They could carry some monetary value even if expired. Otherwise, you have to pay to get rid of them or to storing them. If they have some value, it is called salvage value. If you have to pay, it is called 5 6 CHAPTER 1.NEWSVENDOR PROBLEM holding cost. Hence , the following relationship holds: s = ? h. This is per-item value. †¢ Backorder cost (b): Whenever the actual demand is higher than how many you prepared, you lose sales. Loss-of-sales could cost you something. You may be bookkeeping those as backorders or your brand may be damaged. These costs will be represented by backorder cost. This is per-item cost. †¢ Your order quantity (y): You will decide how many papers to be ordered before you start a day. That quantity is represented by y. This is your decision variable. As a business, you are assumed to want to maximize your pro? t. Expressing our pro? t as a function of these variables is the ? rst step to obtain the optimal ordering policy. Pro? t can be interpreted in two ways: (1) revenue minus cost, or (2) money you earn minus money you lose. Let us adopt the ? rst interpretation ? rst. Revenue is represented by selling price (p) multiplied by how many you actually sell. The actual sales is bounded by the realized dema nd and how many you prepared for the period. When you order too many, you can sell at most as many as the number of people who want to buy. When you order too few, you can only sell what you prepared. Hence, your revenue is minimum of D and y, i. . min(D, y) or D ? y. Thinking about the cost, ? rst of all, you have to pay something to the publisher when buying papers, i. e. cf +ycv . Two types of additional cost will be incurred to you depending on whether your order is above or below the actual demand. When it turns out you prepared less than the demand for the period, the backorder cost b per every missed sale will occur. The amount of missed sales cannot be negative, so it can be represented by max(D ? y, 0) or (D ? y)+ . When it turns out you prepared more, the quantity of left-over items also cannot go negative, so it can be expressed as max(y ? D, 0) or (y ? D)+ .In this way of thinking, we have the following formula. Pro? t =Revenue ? Cost =Revenue ? Ordering cost ? Holding c ost ? Backorder cost =p(D ? y) ? (cf + ycv ) ? h(y ? D)+ ? b(D ? y)+ (1. 1) How about the second interpretation of pro? t? You earn p ? cv dollars every time you sell a paper. For left-over items, you lose the price you bought in addition to the holding cost per paper, i. e. cv + h. When the demand is higher than what you prepared, you lose b backorder cost. Of course, you also have to pay the ? xed ordering cost cf as well when you place an order. With this logic, we have the following pro? t function. Pro? t =Earning ?Loss =(p ? cv )(D ? y) ? (cv + h)(y ? D)+ ? b(D ? y)+ ? cf (1. 2) 1. 1. PROFIT MAXIMIZATION 7 Since we used two di? erent approaches to model the same pro? t function, (1. 1) and (1. 2) should be equivalent. Comparing the two equations, you will also notice that (D ? y) + (y ? D)+ = y. Now our quest boils down to maximizing the pro? t function. However, (1. 1) and (1. 2) contain a random element, the demand D. We cannot maximize a function of random element if we all ow the randomness to remain in our objective function. One day demand can be very high. Another day it is also possible nobody wants to buy a single paper. We have to ? ure out how to get rid of this randomness from our objective function. Let us denote pro? t for the nth period by gn for further discussion. Theorem 1. 1 (Strong Law of Large Numbers). Pr g1 + g2 + g3 +  ·  ·  · + gn = E[g1 ] n>? n lim =1 The long-run average pro? t converges to the expected pro? t for a single period with probability 1. Based on Theorem 1. 1, we can change our objective function from just pro? t to expected pro? t. In other words, by maximizing the expected pro? t, it is guaranteed that the long-run average pro? t is maximized because of Theorem 1. 1. Theorem 1. 1 is the foundational assumption for the entire course.When we will talk about the long-run average something, it involves Theorem 1. 1 in most cases. Taking expectations, we obtain the following equations corresponding to (1. 1) and ( 1. 2). E[g(D, y)] =pE[D ? y] ? (cf + ycv ) ? hE[(y ? D)+ ] ? bE[(D ? y)+ ] =(p ? cv )E[D ? y] ? (cv + h)E[(y ? D)+ ] ? bE[(D ? y)+ ] ? cf (1. 4) (1. 3) Since (1. 3) and (1. 4) are equivalent, we can choose either one of them for further discussion and (1. 4) will be used. Before moving on, it is important for you to understand what E[D? y], E[(y? D)+ ], E[(D ? y)+ ] are and how to compute them. Example 1. 1. Compute E[D ? 18], E[(18 ? D)+ ], E[(D ? 8)+ ] for the demand having the following distributions. 1. D is a discrete random variable. Probability mass function (pmf) is as follows. d Pr{D = d} 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 Answer: For a discrete random variable, you ? rst compute D ? 18, (18 ? D)+ , (D ? 18)+ for each of possible D values. 8 d CHAPTER 1. NEWSVENDOR PROBLEM 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 Pr{D = d} D ? 18 (18 ? D)+ (D ? 18)+ 10 8 0 15 3 0 18 0 2 18 0 7 18 0 12 Then, you take the weighted average using corresponding Pr{D = d} for each possible D. 1 1 1 1 1 125 (10) + (15) + (18) + (18) + (18) = 4 8 8 4 4 8 1 1 1 1 1 19 + E[(18 ?D) ] = (8) + (3) + (0) + (0) + (0) = 4 8 8 4 4 8 1 1 1 1 1 + E[(D ? 18) ] = (0) + (0) + (2) + (7) + (12) = 5 4 8 8 4 4 E[D ? 18] = 2. D is a continuous random variable following uniform distribution between 10 and 30, i. e. D ? Uniform(10, 30). Answer: Computing expectation of continuous random variable involves integration. A continuous random variable has probability density function usually denoted by f . This will be also needed to compute the expectation. In this case, fD (x) = 1 20 , 0, if x ? [10, 30] otherwise Using this information, compute the expectations directly by integration. ? E[D ? 18] = ? 30 (x ? 18)fD (x)dx (x ? 18) 10 18 = = 10 18 1 dx 20 1 20 dx + 30 (x ? 18) x 10 dx + 18 30 (x ? 18) 1 20 dx 1 20 dx = = x2 40 1 20 + 18 x=18 x=10 18x 20 18 x=30 x=18 The key idea is to remove the ? operator that we cannot handle by separating the integration interval into two. The other two expectations can 1. 1. PROFIT MAXIMIZATION be computed in a similar way. 9 ? E[(18 ? D)+ ] = 30 (18 ? x)+ fD (x)dx (18 ? x)+ 10 18 = = 10 18 1 dx 20 1 20 1 20 +0 30 (18 ? x)+ (18 ? x) 10 x2 2 x=18 dx + 18 30 (18 ? x)+ 0 18 1 20 dx = dx + 1 20 dx 18x ? = 20 x=10 ? E[(D ? 18)+ ] = 30 (18 ? x)+ fD (x)dx (x ? 8)+ 10 18 = = 10 18 1 dx 20 1 20 30 (x ? 18)+ 0 10 x2 2 dx + 18 30 (x ? 18)+ 1 20 dx 1 20 dx = =0 + 1 20 dx + 18 x=30 (x ? 18) ? 18x 20 x=18 Now that we have learned how to compute E[D? y], E[(y? D)+ ], E[(D? y)+ ], we have acquired the basic toolkit to obtain the order quantity that maximizes the expected pro? t. First of all, we need to turn these expectations of the pro? t function formula (1. 4) into integration forms. For now, assume that the demand is a nonnegative continuous random variable. 10 CHAPTER 1. NEWSVENDOR PROBLEM E[g(D, y)] =(p ? cv )E[D ? y] ? (cv + h)E[(y ? D)+ ] ? bE[(D ? y)+ ] ? f ? =(p ? cv ) 0 (x ? y)fD (x)dx ? ? (cv + h) 0 ? (y ? x)+ fD (x)dx ?b 0 (x ? y)+ fD (x)dx ? cf y ? =(p ? cv ) 0 xfD (x)dx + y y yfD (x)dx ? (cv + h) 0 ? (y ? x)fD (x)dx ?b y (x ? y)fD (x)dx ? cf y y =(p ? cv ) 0 xfD (x)dx + y 1 ? 0 y y fD (x)dx xfD (x)dx ? (cv + h) y 0 y fD (x)dx ? 0 y ? b E[D] ? 0 xfD (x)dx ? y 1 ? 0 fD (x)dx ? cf (1. 5) There can be many ways to obtain the maximum point of a function. Here we will take the derivative of (1. 5) and set it to zero. y that makes the derivative equal to zero will make E[g(D, y)] either maximized or minimized depending on the second derivative.For now, assume that such y will maximize E[g(D, y)]. We will check this later. Taking the derivative of (1. 5) will involve di? erentiating an integral. Let us review an important result from Calculus. Theorem 1. 2 (Fundamental Theorem of Calculus). For a function y H(y) = c h(x)dx, we have H (y) = h(y), where c is a constant. Theorem 1. 2 can be translated as follows for our case. y d xfD (x)dx =yfD (y) dy 0 y d fD (x)dx =fD (y) dy 0 (1. 6) (1. 7) Also remember the relationship between cd f and pdf of a continuous random variable. y FD (y) = fD (x)dx (1. 8) 1. 1. PROFIT MAXIMIZATION Use (1. 6), (1. 7), (1. ) to take the derivative of (1. 5). d E[g(D, y)] =(p ? cv ) (yfD (y) + 1 ? FD (y) ? yfD (y)) dy ? (cv + h) (FD (y) + yfD (y) ? yfD (y)) ? b (? yfD (y) ? 1 + FD (y) + yfD (y)) =(p + b ? cv )(1 ? FD (y)) ? (cv + h)FD (y) =(p + b ? cv ) ? (p + b + h)FD (y) = 0 If we di? erentiate (1. 9) one more time to obtain the second derivative, d2 E[g(D, y)] = ? (p + b + h)fD (y) dy 2 11 (1. 9) which is always nonpositive because p, b, h, fD (y) ? 0. Hence, taking the derivative and setting it to zero will give us the maximum point not the minimum point. Therefore, we obtain the following result. Theorem 1. 3 (Optimal Order Quantity).The optimal order quantity y ? is the smallest y such that FD (y) = p + b ? cv ? 1 or y = FD p+b+h p + b ? cv p+b+h . for continuous demand D. Looking at Theorem 1. 3, it provides the following intuitions. †¢ Fixed cost cf does not a? ect the o ptimal quantity you need to order. †¢ If you can procure items for free and there is no holding cost, you will prepare as many as you can. †¢ If b h, b cv , you will also prepare as many as you can. †¢ If the buying cost is almost as same as the selling price plus backorder cost, i. e. cv ? p + b, you will prepare nothing. You will prepare only upon you receive an order.Example 1. 2. Suppose p = 10, cf = 100, cv = 5, h = 2, b = 3, D ? Uniform(10, 30). How many should you order for every period to maximize your long-run average pro? t? Answer: First of all, we need to compute the criterion value. p + b ? cv 10 + 3 ? 5 8 = = p+b+h 10 + 3 + 2 15 Then, we will look up the smallest y value that makes FD (y) = 8/15. 12 1 CHAPTER 1. NEWSVENDOR PROBLEM CDF 0. 5 0 0 5 10 15 20 25 30 35 40 D Therefore, we can conclude that the optimal order quantity 8 62 = units. 15 3 Although we derived the optimal order quantity solution for the continuous demand case, Theorem 1. applies to t he discrete demand case as well. I will ? ll in the derivation for discrete case later. y ? = 10 + 20 Example 1. 3. Suppose p = 10, cf = 100, cv = 5, h = 2, b = 3. Now, D is a discrete random variable having the following pmf. d Pr{D = d} 10 1 4 15 1 8 20 1 8 25 1 4 30 1 4 What is the optimal order quantity for every period? Answer: We will use the same value 8/15 from the previous example and look up the smallest y that makes FD (y) = 8/15. We start with y = 10. 1 4 1 1 3 FD (15) = + = 4 8 8 1 1 1 1 FD (20) = + + = 4 8 8 2 1 1 1 1 3 FD (25) = + + + = 4 8 8 4 4 ? Hence, the optimal order quantity y = 25 units.FD (10) = 8 15 8 < 15 8 < 15 8 ? 15 < 1. 2 Cost Minimization Suppose you are a production manager of a large company in charge of operating manufacturing lines. You are expected to run the factory to minimize the cost. Revenue is another person’s responsibility, so all you care is the cost. To model the cost of factory operation, let us set up variables in a slightly di? erent way. 1. 2. COST MINIMIZATION 13 †¢ Understock cost (cu ): It occurs when your production is not su? cient to meet the market demand. †¢ Overstock cost (co ): It occurs when you produce more than the market demand.In this case, you may have to rent a space to store the excess items. †¢ Unit production cost (cv ): It is the cost you should pay whenever you manufacture one unit of products. Material cost is one of this category. †¢ Fixed operating cost (cf ): It is the cost you should pay whenever you decide to start running the factory. As in the pro? t maximization case, the formula for cost expressed in terms of cu , co , cv , cf should be developed. Given random demand D, we have the following equation. Cost =Manufacturing Cost + Cost associated with Understock Risk + Cost associated with Overstock Risk =(cf + ycv ) + cu (D ? )+ + co (y ? D)+ (1. 10) (1. 10) obviously also contains randomness from D. We cannot minimize a random objective itself. Instead, based on Theorem 1. 1, we will minimize expected cost then the long-run average cost will be also guaranteed to be minimized. Hence, (1. 10) will be transformed into the following. E[Cost] =(cf + ycv ) + cu E[(D ? y)+ ] + co E[(y ? D)+ ] ? ? =(cf + ycv ) + cu 0 ? (x ? y)+ fD (x)dx + co 0 y (y ? x)+ fD (x)dx (y ? x)fD (x)dx (1. 11) 0 =(cf + ycv ) + cu y (x ? y)fD (x)dx + co Again, we will take the derivative of (1. 11) and set it to zero to obtain y that makes E[Cost] minimized.We will verify the second derivative is positive in this case. Let g here denote the cost function and use Theorem 1. 2 to take the derivative of integrals. d E[g(D, y)] =cv + cu (? yfD (y) ? 1 + FD (y) + yfD (y)) dy + co (FD (y) + yfD (y) ? yfD (y)) =cv + cu (FD (y) ? 1) + co FD (y) ? (1. 12) The optimal production quantity y is obtained by setting (1. 12) to be zero. Theorem 1. 4 (Optimal Production Quantity). The optimal production quantity that minimizes the long-run average cost is the smallest y such tha t FD (y) = cu ? cv or y = F ? 1 cu + co cu ? cv cu + co . 14 CHAPTER 1. NEWSVENDOR PROBLEM Theorem 1. can be also applied to discrete demand. Several intuitions can be obtained from Theorem 1. 4. †¢ Fixed cost (cf ) again does not a? ect the optimal production quantity. †¢ If understock cost (cu ) is equal to unit production cost (cv ), which makes cu ? cv = 0, then you will not produce anything. †¢ If unit production cost and overstock cost are negligible compared to understock cost, meaning cu cv , co , you will prepare as much as you can. To verify the second derivative of (1. 11) is indeed positive, take the derivative of (1. 12). d2 E[g(D, y)] = (cu + co )fD (y) dy 2 (1. 13) (1. 13) is always nonnegative because cu , co ? . Hence, y ? obtained from Theorem 1. 4 minimizes the cost instead of maximizing it. Before moving on, let us compare criteria from Theorem 1. 3 and Theorem 1. 4. p + b ? cv p+b+h and cu ? cv cu + co Since the pro? t maximization problem solved previously and the cost minimization problem solved now share the same logic, these two criteria should be somewhat equivalent. We can see the connection by matching cu = p + b, co = h. In the pro? t maximization problem, whenever you lose a sale due to underpreparation, it costs you the opportunity cost which is the selling price of an item and the backorder cost.Hence, cu = p + b makes sense. When you overprepare, you should pay the holding cost for each left-over item, so co = h also makes sense. In sum, Theorem 1. 3 and Theorem 1. 4 are indeed the same result in di? erent forms. Example 1. 4. Suppose demand follows Poisson distribution with parameter 3. The cost parameters are cu = 10, cv = 5, co = 15. Note that e? 3 ? 0. 0498. Answer: The criterion value is cu ? cv 10 ? 5 = = 0. 2, cu + co 10 + 15 so we need to ? nd the smallest y such that makes FD (y) ? 0. 2. Compute the probability of possible demands. 30 ? 3 e = 0. 0498 0! 31 Pr{D = 1} = e? 3 = 0. 1494 1! 32 ? Pr{D = 2} = e = 0. 2241 2! Pr{D = 0} = 1. 3. INITIAL INVENTORY Interpret these values into FD (y). FD (0) =Pr{D = 0} = 0. 0498 < 0. 2 FD (1) =Pr{D = 0} + Pr{D = 1} = 0. 1992 < 0. 2 FD (2) =Pr{D = 0} + Pr{D = 1} + Pr{D = 2} = 0. 4233 ? 0. 2 Hence, the optimal production quantity here is 2. 15 1. 3 Initial Inventory Now let us extend our model a bit further. As opposed to the assumption that we had no inventory at the beginning, suppose that we have m items when we decide how many we need to order. The solutions we have developed in previous sections assumed that we had no inventory when placing an order.If we had m items, we should order y ? ? m items instead of y ? items. In other words, the optimal order or production quantity is in fact the optimal order-up-to or production-up-to quantity. We had another implicit assumption that we should order, so the ? xed cost did not matter in the previous model. However, if cf is very large, meaning that starting o? a production line or placing an order i s very expensive, we may want to consider not to order. In such case, we have two scenarios: to order or not to order. We will compare the expected cost for the two scenarios and choose the option with lower expected cost.Example 1. 5. Suppose understock cost is $10, overstock cost is $2, unit purchasing cost is $4 and ? xed ordering cost is $30. In other words, cu = 10, co = 2, cv = 4, cf = 30. Assume that D ? Uniform(10, 20) and we already possess 10 items. Should we order or not? If we should, how many items should we order? Answer: First, we need to compute the optimal amount of items we need to prepare for each day. Since cu ? cv 1 10 ? 4 = , = cu + co 10 + 2 2 the optimal order-up-to quantity y ? = 15 units. Hence, if we need to order, we should order 5 = y ? ? m = 15 ? 10 items. Let us examine whether we should actually order or not. . Scenario 1: Not To Order If we decide not to order, we will not have to pay cf and cv since we order nothing actually. We just need to conside r understock and overstock risks. We will operate tomorrow with 10 items that we currently have if we decide not to order. E[Cost] =cu E[(D ? 10)+ ] + co E[(10 ? D)+ ] =10(E[D] ? 10) + 2(0) = $50 16 CHAPTER 1. NEWSVENDOR PROBLEM Note that in this case E[(10 ? D)+ ] = 0 because D is always greater than 10. 2. Scenario 2: To Order If we decide to order, we will order 5 items. We should pay cf and cv accordingly. Understock and overstock risks also exist in this case.Since we will order 5 items to lift up the inventory level to 15, we will run tomorrow with 15 items instead of 10 items if we decide to order. E[Cost] =cf + (15 ? 10)cv + cu E[(D ? 15)+ ] + co E[(15 ? D)+ ] =30 + 20 + 10(1. 25) + 2(1. 25) = $65 Since the expected cost of not ordering is lower than that of ordering, we should not order if we already have 10 items. It is obvious that if we have y ? items at hands right now, we should order nothing since we already possess the optimal amount of items for tomorrow’s op eration. It is also obvious that if we have nothing currently, we should order y ? items to prepare y ? tems for tomorrow. There should be a point between 0 and y ? where you are indi? erent between order and not ordering. Suppose you as a manager should give instruction to your assistant on when he/she should place an order and when should not. Instead of providing instructions for every possible current inventory level, it is easier to give your assistant just one number that separates the decision. Let us call that number the critical level of current inventory m? . If we have more than m? items at hands, the expected cost of not ordering will be lower than the expected cost of ordering, so we should not order.Conversely, if we have less than m? items currently, we should order. Therefore, when we have exactly m? items at hands right now, the expected cost of ordering should be equal to that of not ordering. We will use this intuition to obtain m? value. The decision process is s ummarized in the following ? gure. m* Critical level for placing an order y* Optimal order-up-to quantity Inventory If your current inventory lies here, you should order. Order up to y*. If your current inventory lies here, you should NOT order because your inventory is over m*. 1. 4. SIMULATION 17 Example 1. 6.Given the same settings with the previous example (cu = 10, cv = 4, co = 2, cf = 30), what is the critical level of current inventory m? that determines whether you should order or not? Answer: From the answer of the previous example, we can infer that the critical value should be less than 10, i. e. 0 < m? < 10. Suppose we currently own m? items. Now, evaluate the expected costs of the two scenarios: ordering and not ordering. 1. Scenario 1: Not Ordering E[Cost] =cu E[(D ? m? )+ ] + co E[(m? ? D)+ ] =10(E[D] ? m? ) + 2(0) = 150 ? 10m? 2. Scenario 2: Ordering In this case, we will order.Given that we will order, we will order y ? ?m? = 15 ? m? items. Therefore, we will start tomorrow with 15 items. E[Cost] =cf + (15 ? 10)cv + cu E[(D ? 15)+ ] + co E[(15 ? D)+ ] =30 + 4(15 ? m? ) + 10(1. 25) + 2(1. 25) = 105 ? 4m? At m? , (1. 14) and (1. 15) should be equal. 150 ? 10m? = 105 ? 4m? ? m? = 7. 5 units (1. 15) (1. 14) The critical value is 7. 5 units. If your current inventory is below 7. 5, you should order for tomorrow. If the current inventory is above 7. 5, you should not order. 1. 4 Simulation Generate 100 random demands from Uniform(10, 30). p = 10, cf = 30, cv = 4, h = 5, b = 3 1 p + b ? v 10 + 3 ? 4 = = p + b + h 10 + 3 + 5 2 The optimal order-up-to quantity from Theorem 1. 3 is 20. We will compare the performance between the policies of y = 15, 20, 25. Listing 1. 1: Continuous Uniform Demand Simulation # Set up parameters p=10;cf=30;cv=4;h=5;b=3 # How many random demands will be generated? n=100 # Generate n random demands from the uniform distribution 18 Dmd=runif(n,min=10,max=30) CHAPTER 1. NEWSVENDOR PROBLEM # Test the policy where we order 15 it ems for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 33. 4218 # Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 44. 37095 # Test the policy where we order 25 items for every period y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 32. 62382 You can see the policy with y = 20 maximizes the 100-period average pro? t as promised by the theory. In fact, if n is relatively small, it is not guaranteed that we have maximized pro? t even if we run based on the optimal policy obtained from this section.The underlying assumption is that we should operate with this policy for a long time. Then, Theorem 1. 1 guarantees that the average pro? t will be maximized when we use the optimal ordering policy. Discrete demand case can also be simulated. Suppose the demand has the following distribution. All other parameters remain same. d Pr{D = d} 10 1 4 15 1 8 20 1 4 25 1 8 30 1 4 The theoretic optimal order-up-to quantity in this case is also 20. Let us test three policies: y = 15, 20, 25. Listing 1. 2: Discrete Demand Simulation # Set up parameters p=10;cf=30;cv=4;h=5;b=3 # How many random demands will be generated? =100 # Generate n random demands from the discrete demand distribution Dmd=sample(c(10,15,20,25,30),n,replace=TRUE,c(1/4,1/8,1/4,1/8,1/4)) # Test the policy where we order 15 items for every period y=15 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 19. 35 # Test the policy where we order 20 items for every period y=20 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 31. 05 # Test the policy where we order 25 items for every period 1. 5. EXERCISE y=25 mean(p*pmin(Dmd,y)-cf-y*cv-h*pmax(y-Dmd,0)-b*pmax(Dmd-y,0)) > 26. 55 19There are other distributions such as triangular, normal, Poisson or binomial distributions available in R. When you do your senior project, for example, you will observe the demand for a departm ent or a factory. You ? rst approximate the demand using these theoretically established distributions. Then, you can simulate the performance of possible operation policies. 1. 5 Exercise 1. Show that (D ? y) + (y ? D)+ = y. 2. Let D be a discrete random variable with the following pmf. d Pr{D = d} Find (a) E[min(D, 7)] (b) E[(7 ? D)+ ] where x+ = max(x, 0). 3. Let D be a Poisson random variable with parameter 3.Find (a) E[min(D, 2)] (b) E[(3 ? D)+ ]. Note that pmf of a Poisson random variable with parameter ? is Pr{D = k} = ? k e . k! 5 1 10 6 3 10 7 4 10 8 1 10 9 1 10 4. Let D be a continuous random variable and uniformly distributed between 5 and 10. Find (a) E[max(D, 8)] (b) E[(D ? 8)? ] where x? = min(x, 0). 5. Let D be an exponential random variable with parameter 7. Find (a) E[max(D, 3)] 20 (b) E[(D ? 4)? ]. CHAPTER 1. NEWSVENDOR PROBLEM Note that pdf of an exponential random variable with parameter ? is fD (x) = ? e x for x ? 0. 6. David buys fruits and vegetables wholesal e and retails them at Davids Produce on La Vista Road.One of the more di? cult decisions is the amount of bananas to buy. Let us make some simplifying assumptions, and assume that David purchases bananas once a week at 10 cents per pound and retails them at 30 cents per pound during the week. Bananas that are more than a week old are too ripe and are sold for 5 cents per pound. (a) Suppose the demand for the good bananas follows the same distribution as D given in Problem 2. What is the expected pro? t of David in a week if he buys 7 pounds of banana? (b) Now assume that the demand for the good bananas is uniformly distributed between 5 and 10 like in Problem 4.What is the expected pro? t of David in a week if he buys 7 pounds of banana? (c) Find the expected pro? t if David’s demand for the good bananas follows an exponential distribution with mean 7 and if he buys 7 pounds of banana. 7. Suppose we are selling lemonade during a football game. The lemonade sells for $18 per g allon but only costs $3 per gallon to make. If we run out of lemonade during the game, it will be impossible to get more. On the other hand, leftover lemonade has a value of $1. Assume that we believe the fans would buy 10 gallons with probability 0. 1, 11 gallons with probability 0. , 12 gallons with probability 0. 4, 13 gallons with probability 0. 2, and 14 gallons with probability 0. 1. (a) What is the mean demand? (b) If 11 gallons are prepared, what is the expected pro? t? (c) What is the best amount of lemonade to order before the game? (d) Instead, suppose that the demand was normally distributed with mean 1000 gallons and variance 200 gallons2 . How much lemonade should be ordered? 8. Suppose that a bakery specializes in chocolate cakes. Assume the cakes retail at $20 per cake, but it takes $10 to prepare each cake. Cakes cannot be sold after one week, and they have a negligible salvage value.It is estimated that the weekly demand for cakes is: 15 cakes in 5% of the weeks, 1 6 cakes in 20% of the weeks, 17 cakes in 30% of the weeks, 18 cakes in 25% of the weeks, 19 cakes in 10% of the weeks, and 20 cakes in 10% of the weeks. How many cakes should the bakery prepare each week? What is the bakery’s expected optimal weekly pro? t? 1. 5. EXERCISE 21 9. A camera store specializes in a particular popular and fancy camera. Assume that these cameras become obsolete at the end of the month. They guarantee that if they are out of stock, they will special-order the camera and promise delivery the next day.In fact, what the store does is to purchase the camera from an out of state retailer and have it delivered through an express service. Thus, when the store is out of stock, they actually lose the sales price of the camera and the shipping charge, but they maintain their good reputation. The retail price of the camera is $600, and the special delivery charge adds another $50 to the cost. At the end of each month, there is an inventory holding cost of $25 fo r each camera in stock (for doing inventory etc). Wholesale cost for the store to purchase the cameras is $480 each. (Assume that the order can only be made at the beginning of the month. (a) Assume that the demand has a discrete uniform distribution from 10 to 15 cameras a month (inclusive). If 12 cameras are ordered at the beginning of a month, what are the expected overstock cost and the expected understock or shortage cost? What is the expected total cost? (b) What is optimal number of cameras to order to minimize the expected total cost? (c) Assume that the demand can be approximated by a normal distribution with mean 1000 and standard deviation 100 cameras a month. What is the optimal number of cameras to order to minimize the expected total cost? 10.Next month’s production at a manufacturing company will use a certain solvent for part of its production process. Assume that there is an ordering cost of $1,000 incurred whenever an order for the solvent is placed and the solvent costs $40 per liter. Due to short product life cycle, unused solvent cannot be used in following months. There will be a $10 disposal charge for each liter of solvent left over at the end of the month. If there is a shortage of solvent, the production process is seriously disrupted at a cost of $100 per liter short. Assume that the initial inventory level is m, where m = 0, 100, 300, 500 and 700 liters. a) What is the optimal ordering quantity for each case when the demand is discrete with Pr{D = 500} = Pr{D = 800} = 1/8, Pr{D = 600} = 1/2 and Pr{D = 700} = 1/4? (b) What is the optimal ordering policy for arbitrary initial inventory level m? (You need to specify the critical value m? in addition to the optimal order-up-to quantity y ? . When m ? m? , you make an order. Otherwise, do not order. ) (c) Assume optimal quantity will be ordered. What is the total expected cost when the initial inventory m = 0? What is the total expected cost when the initial inventory m = 700? 22 CHAPTER 1. NEWSVENDOR PROBLEM 11.Redo Problem 10 for the case where the demand is governed by the continuous uniform distribution varying between 400 and 800 liters. 12. An automotive company will make one last production run of parts for Part 947A and 947B, which are not interchangeable. These parts are no longer used in new cars, but will be needed as replacements for warranty work in existing cars. The demand during the warranty period for 947A is approximately normally distributed with mean 1,500,000 parts and standard deviation 500,000 parts, while the mean and standard deviation for 947B is 500,000 parts and 100,000 parts. (Assume that two demands are independent. Ignoring the cost of setting up for producing the part, each part costs only 10 cents to produce. However, if additional parts are needed beyond what has been produced, they will be purchased at 90 cents per part (the same price for which the automotive company sells its parts). Parts remaining at the end of the warr anty period have a salvage value of 8 cents per part. There has been a proposal to produce Part 947C, which can be used to replace either of the other two parts. The unit cost of 947C jumps from 10 to 14 cents, but all other costs remain the same. (a) Assuming 947C is not produced, how many 947A should be produced? b) Assuming 947C is not produced, how many 947B should be produced? (c) How many 947C should be produced in order to satisfy the same fraction of demand from parts produced in-house as in the ? rst two parts of this problem. (d) How much money would be saved or lost by producing 947C, but meeting the same fraction of demand in-house? (e) Is your answer to question (c), the optimal number of 947C to produce? If not, what would be the optimal number of 947C to produce? (f) Should the more expensive part 947C be produced instead of the two existing parts 947A and 947B. Why? Hint: compare the expected total costs.Also, suppose that D ? Normal( µ, ? 2 ). q xv 0 (x?  µ)2 1 e? 2? 2 dx = 2 q (x ?  µ) v 0 q (x?  µ)2 1 e? 2? 2 dx 2 + µ =  µ2 v 0 (q?  µ)2 (x?  µ)2 1 e? 2? 2 dx 2 t 1 v e? 2? 2 dt +  µPr{0 ? D ? q} 2 2 where, in the 2nd step, we changed variable by letting t = (x ?  µ)2 . 1. 5. EXERCISE 23 13. A warranty department manages the after-sale service for a critical part of a product. The department has an obligation to replace any damaged parts in the next 6 months. The number of damaged parts X in the next 6 months is assumed to be a random variable that follows the following distribution: x Pr{X = x} 100 . 1 200 . 2 300 . 5 400 . 2The department currently has 200 parts in stock. The department needs to decide if it should make one last production run for the part to be used for the next 6 months. To start the production run, the ? xed cost is $2000. The unit cost to produce a part is $50. During the warranty period of next 6 months, if a replacement request comes and the department does not have a part available in house, it has to buy a part from the spot-market at the cost of $100 per part. Any part left at the end of 6 month sells at $10. (There is no holding cost. ) Should the department make the production run? If so, how many items should it produce? 4. A store sells a particular brand of fresh juice. By the end of the day, any unsold juice is sold at a discounted price of $2 per gallon. The store gets the juice daily from a local producer at the cost of $5 per gallon, and it sells the juice at $10 per gallon. Assume that the daily demand for the juice is uniformly distributed between 50 gallons to 150 gallons. (a) What is the optimal number of gallons that the store should order from the distribution each day in order to maximize the expected pro? t each day? (b) If 100 gallons are ordered, what is the expected pro? t per day? 15. An auto company is to make one ? al purchase of a rare engine oil to ful? ll its warranty services for certain car models. The current price for the engine oil is $1 per g allon. If the company runs out the oil during the warranty period, it will purchase the oil from a supply at the market price of $4 per gallon. Any leftover engine oil after the warranty period is useless, and costs $1 per gallon to get rid of. Assume the engine oil demand during the warranty is uniformly distributed (continuous distribution) between 1 million gallons to 2 million gallons, and that the company currently has half million gallons of engine oil in stock (free of charge). a) What is the optimal amount of engine oil the company should purchase now in order to minimize the total expected cost? (b) If 1 million gallons are purchased now, what is the total expected cost? 24 CHAPTER 1. NEWSVENDOR PROBLEM 16. A company is obligated to provide warranty service for Product A to its customers next year. The warranty demand for the product follows the following distribution. d Pr{D = d} 100 . 2 200 . 4 300 . 3 400 . 1 The company needs to make one production run to satisfy the wa rranty demand for entire next year. Each unit costs $100 to produce; the penalty cost of a unit is $500.By the end of the year, the savage value of each unit is $50. (a) Suppose that the company has currently 0 units. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. (b) Suppose that the company has currently 100 units at no cost and there is $20000 ? xed cost to start the production run. What is the optimal quantity to produce in order to minimize the expected total cost? Find the optimal expected total cost. 17. Suppose you are running a restaurant having only one menu, lettuce salad, in the Tech Square.You should order lettuce every day 10pm after closing. Then, your supplier delivers the ordered amount of lettuce 5am next morning. Store hours is from 11am to 9pm every day. The demand for the lettuce salad for a day (11am-9pm) has the following distribution. d Pr{D = d} 20 1/6 25 1/3 30 1/3 35 1/6 One lettu ce salad requires two units of lettuce. The selling price of lettuce salad is $6, the buying price of one unit of lettuce is $1. Of course, leftover lettuce of a day cannot be used for future salad and you have to pay 50 cents per unit of lettuce for disposal. (a) What is the optimal order-up-to quantity of lettuce for a day? b) If you ordered 50 units of lettuce today, what is the expected pro? t of tomorrow? Include the purchasing cost of 50 units of lettuce in your calculation. Chapter 2 Queueing Theory Before getting into Discrete-time Markov Chains, we will learn about general issues in the queueing theory. Queueing theory deals with a set of systems having waiting space. It is a very powerful tool that can model a broad range of issues. Starting from analyzing a simple queue, a set of queues connected with each other will be covered as well in the end. This chapter will give you the background knowledge when you read the required book, The Goal.We will revisit the queueing the ory once we have more advanced modeling techniques and knowledge. 2. 1 Introduction Think about a service system. All of you must have experienced waiting in a service system. One example would be the Student Center or some restaurants. This is a human system. A bit more automated service system that has a queue would be a call center and automated answering machines. We can imagine a manufacturing system instead of a service system. These waiting systems can be generalized as a set of bu? ers and servers. There are key factors when you try to model such a system.What would you need to analyze your system? †¢ How frequently customers come to your system? > Inter-arrival Times †¢ How fast your servers can serve the customers? > Service Times †¢ How many servers do you have? > Number of Servers †¢ How large is your waiting space? > Queue Size If you can collect data about these metrics, you can characterize your queueing system. In general, a queueing system can be denoted as follows. G/G/s/k 25 26 CHAPTER 2. QUEUEING THEORY The ? rst letter characterizes the distribution of inter-arrival times. The second letter characterizes the distribution of service times.The third number denotes the number of servers of your queueing system. The fourth number denotes the total capacity of your system. The fourth number can be omitted and in such case it means that your capacity is in? nite, i. e. your system can contain any number of people in it up to in? nity. The letter â€Å"G† represents a general distribution. Other candidate characters for this position is â€Å"M† and â€Å"D† and the meanings are as follows. †¢ G: General Distribution †¢ M: Exponential Distribution †¢ D: Deterministic Distribution (or constant) The number of servers can vary from one to many to in? nity.The size of bu? er can also be either ? nite or in? nite. To simplify the model, assume that there is only a single server and we have in? ni te bu? er. By in? nite bu? er, it means that space is so spacious that it is as if the limit does not exist. Now we set up the model for our queueing system. In terms of analysis, what are we interested in? What would be the performance measures of such systems that you as a manager should know? †¢ How long should your customer wait in line on average? †¢ How long is the waiting line on average? There are two concepts of average. One is average over time.This applies to the average number of customers in the system or in the queue. The other is average over people. This applies to the average waiting time per customer. You should be able to distinguish these two. Example 2. 1. Assume that the system is empty at t = 0. Assume that u1 = 1, u2 = 3, u3 = 2, u4 = 3, v1 = 4, v2 = 2, v3 = 1, v4 = 2. (ui is ith customer’s inter-arrival time and vi is ith customer’s service time. ) 1. What is the average number of customers in the system during the ? rst 10 minutes? 2 . What is the average queue size during the ? rst 10 minutes? 3.What is the average waiting time per customer for the ? rst 4 customers? Answer: 1. If we draw the number of people in the system at time t with respect to t, it will be as follows. 2. 2. LINDLEY EQUATION 3 2 1 0 27 Z(t) 0 1 2 3 4 5 6 7 8 9 10 t E[Z(t)]t? [0,10] = 1 10 10 Z(t)dt = 0 1 (10) = 1 10 2. If we draw the number of people in the queue at time t with respect to t, it will be as follows. 3 2 1 0 Q(t) 0 1 2 3 4 5 6 7 8 9 10 t E[Q(t)]t? [0,10] = 1 10 10 Q(t)dt = 0 1 (2) = 0. 2 10 3. We ? rst need to compute waiting times for each of 4 customers. Since the ? rst customer does not wait, w1 = 0.Since the second customer arrives at time 4, while the ? rst customer’s service ends at time 5. So, the second customer has to wait 1 minute, w2 = 1. Using the similar logic, w3 = 1, w4 = 0. E[W ] = 0+1+1+0 = 0. 5 min 4 2. 2 Lindley Equation From the previous example, we now should be able to compute each customerâ€℠¢s waiting time given ui , vi . It requires too much e? ort if we have to draw graphs every time we need to compute wi . Let us generalize the logic behind calculating waiting times for each customer. Let us determine (i + 1)th customer’s waiting 28 CHAPTER 2. QUEUEING THEORY time.If (i + 1)th customer arrives after all the time ith customer waited and got served, (i + 1)th customer does not have to wait. Its waiting time is 0. Otherwise, it has to wait wi + vi ? ui+1 . Figure 2. 1, and Figure 2. 2 explain the two cases. ui+1 wi vi wi+1 Time i th arrival i th service start (i+1)th arrival i th service end Figure 2. 1: (i + 1)th arrival before ith service completion. (i + 1)th waiting time is wi + vi ? ui+1 . ui+1 wi vi Time i th arrival i th service start i th service end (i+1)th arrival Figure 2. 2: (i + 1)th arrival after ith service completion. (i + 1)th waiting time is 0.Simply put, wi+1 = (wi + vi ? ui+1 )+ . This is called the Lindley Equation. Example 2. 2. Given the f ollowing inter-arrival times and service times of ? rst 10 customers, compute waiting times and system times (time spent in the system including waiting time and service time) for each customer. ui = 3, 2, 5, 1, 2, 4, 1, 5, 3, 2 vi = 4, 3, 2, 5, 2, 2, 1, 4, 2, 3 Answer: Note that system time can be obtained by adding waiting time and service time. Denote the system time of ith customer by zi . ui vi wi zi 3 4 0 4 2 3 2 5 5 2 0 2 1 5 1 6 2 2 4 6 4 2 2 4 1 1 3 4 5 4 0 4 3 2 1 3 2 3 1 4 2. 3. TRAFFIC INTENSITY 9 2. 3 Suppose Tra? c Intensity E[ui ] =mean inter-arrival time = 2 min E[vi ] =mean service time = 4 min. Is this queueing system stable? By stable, it means that the queue size should not go to the in? nity. Intuitively, this queueing system will not last because average service time is greater than average inter-arrival time so your system will soon explode. What was the logic behind this judgement? It was basically comparing the average inter-arrival time and the average serv ice time. To simplify the judgement, we come up with a new quantity called the tra? c intensity. De? nition 2. 1 (Tra? Intensity). Tra? c intensity ? is de? ned to be ? = 1/E[ui ] ? =  µ 1/E[vi ] where ? is the arrival rate and  µ is the service rate. Given a tra? c intensity, it will fall into one of the following three categories. †¢ If ? < 1, the system is stable. †¢ If ? = 1, the system is unstable unless both inter-arrival times and service times are deterministic (constant). †¢ If ? > 1, the system is unstable. Then, why don’t we call ? utilization instead of tra? c intensity? Utilization seems to be more intuitive and user-friendly name. In fact, utilization just happens to be same as ? if ? < 1.However, the problem arises if ? > 1 because utilization cannot go over 100%. Utilization is bounded above by 1 and that is why tra? c intensity is regarded more general notation to compare arrival and service rates. De? nition 2. 2 (Utilization). Utilization is de? ned as follows. Utilization = ? , 1, if ? < 1 if ? ? 1 Utilization can also be interpreted as the long-run fraction of time the server is utilized. 2. 4 Kingman Approximation Formula Theorem 2. 1 (Kingman’s High-tra? c Approximation Formula). Assume the tra? c intensity ? < 1 and ? is close to 1. The long-run average waiting time in 0 a queue E[W ] ? E[vi ] CHAPTER 2. QUEUEING THEORY ? 1 c2 + c2 a s 2 where c2 , c2 are squared coe? cient of variation of inter-arrival times and service a s times de? ned as follows. c2 = a Var[u1 ] (E[u1 ]) 2, c2 = s Var[v1 ] (E[v1 ]) 2 Example 2. 3. 1. Suppose inter-arrival time follows an exponential distribution with mean time 3 minutes and service time follows an exponential distribution with mean time 2 minutes. What is the expected waiting time per customer? 2. Suppose inter-arrival time is constant 3 minutes and service time is also constant 2 minutes. What is the expected waiting time per customer?Answer: 1. Tra? c intensity is ? = 1/E[ui ] 1/3 2 ? = = = .  µ 1/E[vi ] 1/2 3 Since both inter-arrival times and service times are exponentially distributed, E[ui ] = 3, Var[ui ] = 32 = 9, E[vi ] = 2, Var[vi ] = 22 = 4. Therefore, c2 = Var[ui ]/(E[ui ])2 = 1, c2 = 1. Hence, s a E[W ] =E[vi ] =2 ? c2 + c2 s a 1 2 2/3 1+1 = 4 minutes. 1/3 2 2. Tra? c intensity remains same, 2/3. However, since both inter-arrival times and service times are constant, their variances are 0. Thus, c2 = a c2 = 0. s E[W ] = 2 2/3 1/3 0+0 2 = 0 minutes It means that none of the customers will wait upon their arrival.As shown in the previous example, when the distributions for both interarrival times and service times are exponential, the squared coe? cient of variation term becomes 1 from the Kingman’s approximation formula and the formula 2. 5. LITTLE’S LAW 31 becomes exact to compute the average waiting time per customer for M/M/1 queue. E[W ] =E[vi ] ? 1 Also note that if inter-arrival time or service time distribution is deterministic, c2 or c2 becomes 0. a s Example 2. 4. You are running a highway collecting money at the entering toll gate. You reduced the utilization level of the highway from 90% to 80% by adopting car pool lane.How much does the average waiting time in front of the toll gate decrease? Answer: 0. 8 0. 9 = 9, =4 1 ? 0. 9 1 ? 0. 8 The average waiting time in in front of the toll gate is reduced by more than a half. The Goal is about identifying bottlenecks in a plant. When you become a manager of a company and are running a expensive machine, you usually want to run it all the time with full utilization. However, the implication of Kingman formula tells you that as your utilization approaches to 100%, the waiting time will be skyrocketing. It means that if there is any uncertainty or random ? ctuation input to your system, your system will greatly su? er. In lower ? region, increasing ? is not that bad. If ? near 1, increasing utilization a little bit can lead to a disaster. Atl anta, 10 years ago, did not su? er that much of tra? c problem. As its tra? c infrastructure capacity is getting closer to the demand, it is getting more and more fragile to uncertainty. A lot of strategies presented in The Goal is in fact to decrease ?. You can do various things to reduce ? of your system by outsourcing some process, etc. You can also strategically manage or balance the load on di? erent parts of your system.You may want to utilize customer service organization 95% of time, while utilization of sales people is 10%. 2. 5 Little’s Law L = ? W The Little’s Law is much more general than G/G/1 queue. It can be applied to any black box with de? nite boundary. The Georgia Tech campus can be one black box. ISyE building itself can be another. In G/G/1 queue, we can easily get average size of queue or service time or time in system as we di? erently draw box onto the queueing system. The following example shows that Little’s law can be applied in broade r context than the queueing theory. 32 CHAPTER 2. QUEUEING THEORY Example 2. 5 (Merge of I-75 and I-85).Atlanta is the place where two interstate highways, I-75 and I-85, merge and cross each other. As a tra? c manager of Atlanta, you would like to estimate the average time it takes to drive from the north con? uence point to the south con? uence point. On average, 100 cars per minute enter the merged area from I-75 and 200 cars per minute enter the same area from I-85. You also dispatched a chopper to take a aerial snapshot of the merged area and counted how many cars are in the area. It turned out that on average 3000 cars are within the merged area. What is the average time between entering and exiting the area per vehicle?Answer: L =3000 cars ? =100 + 200 = 300 cars/min 3000 L = 10 minutes ? W = = ? 300 2. 6 Throughput Another focus of The Goal is set on the throughput of a system. Throughput is de? ned as follows. De? nition 2. 3 (Throughput). Throughput is the rate of output ? ow from a system. If ? ? 1, throughput= ?. If ? > 1, throughput=  µ. The bounding constraint of throughput is either arrival rate or service rate depending on the tra? c intensity. Example 2. 6 (Tandem queue with two stations). Suppose your factory production line has two stations linked in series. Every raw material coming into your line should be processed by Station A ? rst.Once it is processed by Station A, it goes to Station B for ? nishing. Suppose raw material is coming into your line at 15 units per minute. Station A can process 20 units per minute and Station B can process 25 units per minute. 1. What is the throughput of the entire system? 2. If we double the arrival rate of raw material from 15 to 30 units per minute, what is the throughput of the whole system? Answer: 1. First, obtain the tra? c intensity for Station A. ?A = ? 15 = = 0. 75  µA 20 Since ? A < 1, the throughput of Station A is ? = 15 units per minute. Since Station A and Station B is linked in series, the throughput of Station . 7. SIMULATION A becomes the arrival rate for Station B. ?B = ? 15 = = 0. 6  µB 25 33 Also, ? B < 1, the throughput of Station B is ? = 15 units per minute. Since Station B is the ? nal stage of the entire system, the throughput of the entire system is also ? = 15 units per minute. 2. Repeat the same steps. ?A = 30 ? = = 1. 5  µA 20 Since ? A > 1, the throughput of Station A is  µA = 20 units per minute, which in turn becomes the arrival rate for Station B. ?B =  µA 20 = 0. 8 =  µB 25 ?B < 1, so the throughput of Station B is  µA = 20 units per minute, which in turn is the throughput of the whole system. 2. 7 SimulationListing 2. 1: Simulation of a Simple Queue and Lindley Equation N = 100 # Function for Lindley Equation lindley = function(u,v){ for (i in 1:length(u)) { if(i==1) w = 0 else { w = append(w, max(w[i-1]+v[i-1]-u[i], 0)) } } return(w) } # # u v CASE 1: Discrete Distribution Generate N inter-arrival times and service times = sample( c(2,3,4),N,replace=TRUE,c(1/3,1/3,1/3)) = sample(c(1,2,3),N,replace=TRUE,c(1/3,1/3,1/3)) # Compute waiting time for each customer w = lindley(u,v) w # CASE 2: Deterministic Distribution # All inter-arrival times are 3 minutes and all service times are 2 minutes # Observe that nobody waits in this case. 4 u = rep(3, 100) v = rep(2, 100) w = lindley(u,v) w CHAPTER 2. QUEUEING THEORY The Kingman’s approximation formula is exact when inter-arrival times and service times follow iid exponential distribution. E[W ] = 1  µ ? 1 We can con? rm this equation by simulating an M/M/1 queue. Listing 2. 2: Kingman Approximation # lambda = arrival rate, mu = service rate N = 10000; lambda = 1/10; mu = 1/7 # Generate N inter-arrival times and service times from exponential distribution u = rexp(N,rate=lambda) v = rexp(N,rate=mu) # Compute the average waiting time of each customer w = lindley(u,v) mean(w) > 16. 0720 # Compare with Kingman approximation rho = lambda/mu (1/mu)*(rho/(1-rho)) > 16. 33333 The Kingman’s approximation formula becomes more and more accurate as N grows. 2. 8 Exercise 1. Let Y be a random variable with p. d. f. ce? 3s for s ? 0, where c is a constant. (a) Determine c. (b) What is the mean, variance, and squared coe? cient of variation of Y where the squared coe? cient of variation of Y is de? ned to be Var[Y ]/(E[Y ]2 )? 2. Consider a single server queue. Initially, there is no customer in the system.Suppose that the inter-arrival times of the ? rst 15 customers are: 2, 5, 7, 3, 1, 4, 9, 3, 10, 8, 3, 2, 16, 1, 8 2. 8. EXERCISE 35 In other words, the ? rst customer will arrive at t = 2 minutes, and the second will arrive at t = 2 + 5 minutes, and so on. Also, suppose that the service time of the ? rst 15 customers are 1, 4, 2, 8, 3, 7, 5, 2, 6, 11, 9, 2, 1, 7, 6 (a) Compute the average waiting time (the time customer spend in bu? er) of the ? rst 10 departed customers. (b) Compute the average system time (waiting time plus service time) of the ? st 10 departed customers. (c) Compute the average queue size during the ? rst 20 minutes. (d) Compute the average server utilization during the ? rst 20 minutes. (e) Does the Little’s law of hold for the average queue size in the ? rst 20 minutes? 3. We want to decide whether to employ a human operator or buy a machine to paint steel beams with a rust inhibitor. Steel beams are produced at a constant rate of one every 14 minutes. A skilled human operator takes an average time of 700 seconds to paint a steel beam, with a standard deviation of 300 seconds.An automatic painter takes on average 40 seconds more than the human painter to paint a beam, but with a standard deviation of only 150 seconds. Estimate the expected waiting time in queue of a steel beam for each of the operators, as well as the expected number of steel beams waiting in queue in each of the two cases. Comment on the e? ect of variability in service time. 4. The arrival rate of customers to an ATM machi ne is 30 per hour with exponentially distirbuted in- terarrival times. The transaction times of two customers are independent and identically distributed.Each transaction time (in minutes) is distributed according to the following pdf: f (s) = where ? = 2/3. (a) What is the average waiting for each customer? (b) What is the average number of customers waiting in line? (c) What is the average number of customers at the site? 5. A production line has two machines, Machine A and Machine B, that are arranged in series. Each job needs to processed by Machine A ? rst. Once it ? nishes the processing by Machine A, it moves to the next station, to be processed by Machine B. Once it ? nishes the processing by Machine B, it leaves the production line.Each machine can process one job at a time. An arriving job that ? nds the machine busy waits in a bu? er. 4? 2 se? 2? s , 0, if s ? 0 otherwise 36 CHAPTER 2. QUEUEING THEORY (The bu? er sizes are assumed to be in? nite. ) The processing times fo r Machine A are iid having exponential distribution with mean 4 minutes. The processing times for Machine B are iid with mean 2 minutes. Assume that the inter-arrival times of jobs arriving at the production line are iid, having exponential distribution with mean of 5 minutes. (a) What is the utilization of Machine A?What is the utilization of Machine B? (b) What is the throughput of the production system? (Throughput is de? ned to be the rate of ? nal output ? ow, i. e. how many items will exit the system in a unit time. ) (c) What is the average waiting time at Machine A, excluding the service time? (d) It is known the average time in the entire production line is 30 minutes per job. What is the long-run average number of jobs in the entire production line? (e) Suppose that the mean inter-arrival time is changed to 1 minute. What are the utilizations for Machine A and Machine B, respectively?What is the throughput of the production system? 6. An auto collision shop has roughly 10 cars arriving per week for repairs. A car waits outside until it is brought inside for bumping. After bumping, the car is painted. On the average, there are 15 cars waiting outside in the yard to be repaired, 10 cars inside in the bump area, and 5 cars inside in the painting area. What is the average length of time a car is in the yard, in the bump area, and in the painting area? What is the average length of time from when a car arrives until it leaves? 7. A small bank is sta? d by a single server. It has been observed that, during a normal business day, the inter-arrival times of customers to the bank are iid having exponential distribution with mean 3 minutes. Also, the the processing times of customers are iid having the following distribution (in minutes): x Pr{X = x} 1 1/4 2 1/2 3 1/4 An arrival ? nding the server busy joins the queue. The waiting space is in? nite. (a) What is the long-run fraction of time that the server is busy? (b) What the the long-run average waiting tim e of each customer in the queue, excluding the processing time? c) What is average number of customers in the bank, those in queue plus those in service? 2. 8. EXERCISE (d) What is the throughput of the bank? 37 (e) If the inter-arrival times have mean 1 minute. What is the throughput of the bank? 8. You are the manager at the Student Center in charge of running the food court. The food court is composed of two parts: cooking station and cashier’s desk. Every person should go to the cooking station, place an order, wait there and pick up ? rst. Then, the person goes to the cashier’s desk to check out. After checking out, the person leaves the food court.The coo