Use the Powerpoint picture File below to complete the exercise. All business decision problems have certain common characteristics. These four items below constitute a formal description of the problem and provide the structure necessary for a solution: 1. A decision-maker 2. Choices or alternative courses of action (strategies) 3. Events or states of nature 4. Consequences or payoffs. Suppose you are the inventory manager of T-Shirts R Us. Your company is an online store that sells T-shirts and nothing else. You have to decide how many men's T-shirts to order for the summer season. You buy the T-shirts from an offshore manufacturer who imposes a condition on you; you have to order in batches of 100. If only 100 T-shirts are ordered, the cost is $10 per shirt, if 200 or more are ordered, the cost is $9 per shirt; and if 300 or more shirts are ordered the cost is $8.50 per shirt. The results of market survey provide you with information that the selling price will be $12 per shirt and that the possible sales levels are 100, 150, or 200 units; but you cannot assign any probability estimate to the alternative levels of demand or sales. If any T- shirt remains unsold during summer, it can be disposed off at half the price ($6) in winter. The marketing manager also feels that there is a goodwill loss of $.50 for each T-shirt that consumers want to purchase from your shop but cannot because of stock-outs. It is not possible for you to wait for some time to study the nature (or determine the level) of demand, nor can you place more than one order. Thus, complete uncertainty prevails. As the inventory manager, you must decide how many T- shirts to order in the face of uncertain demand. The three alternative strategies are to order 100 shirts (A1), 200 shirts (A2) or 300 shirts (A3). The states of nature are three levels of demand: 100 (D1), 150 (D2), or 200 (D3). You are forced to make this decision in the face of uncertainty because you don't know what the demand level will be. Consequences are measures of the net benefit or payoff (reward) association with each of the levels of demand. The specific consequence or outcome depends not only on the decision (A1, A2, or A3) that is made but also on the event (D1, D2, or D3) that occurs. There is a consequence or outcome associated with each combination of decision or action and event. These consequences are generally summarized in a payoff matrix. The Payoff Matrix: A payoff matrix is an essential tool of decision-making. It is a nice way of summarizing the interactions of various alternative action and events. Thus we can say that a payoff matrix provides the decision-maker with quantitative measures of the payoff for each possible consequence and for each alternative under consideration. Use the Powerpoint file named T-Shirts R Us to Create the payoff matrix Determine the best alternative order level (100, 200, or 300) using each of the following methods: Laplace Maximin Maximax Hurwicz Criterion(= .6) Regret Criterion Complete the Regret Criterion Matrix Answer the two questions on the last slide #10.

AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments A Cut Layout A Ev EE v A Shape Fill [ Copy v Paste New B I U ab AV . Aav L Av Convert to Picture Shapes Text Arrange Quick Shape Outline v Design Format Slide Section v SmartArt Box Styles Ideas MAKING DECISIONS UNDER UNCERTAINTY Uncertainty (no probabilities associated with the market conditions) Payoff Matrix Uncertainty Ino probabilities associated with the market conditional Payull Mantire Choice States of Final 1. There are 3 alternatives: (Alter- Nature Position Al Order 100 shirts at a cost of $10 each A2 Order 200 shirts at a cost of $9 each natives) (Events) (FP) A3 Order 300 shirts at a cost of $8.50 each 2 Laplace Order 100 D1 100 2. There are 3 states of nature or events: D1 Demand Level 1 you sell 100 shirts (market condition) is equally Wooly- A1 D2 150 D2 Demand Level 2 you sell 150 shirts Cost $10 D3 200 D3 Demand Level 3 you sell 200 shirts Each shirt sells for $12 regardless of demand level. Order 200 D1 100 3. If you have stock-outs meaning your demand is Maximin Payoff What is the butt of the minimum payath in each A2 D2 150 higher than your order level, there is a loss of goodwill that cost $.50 per shirt. Cost $9 D3 200 4. At the end of the season, you can sell any unsold merchandise to a liquidator for $6 per shirt. Order 300 D1 100 A3 D2 150 5. Calculate the final position for each alternative at Maximax Payoff What is the butt of the mar um payath in each Cost $8.50 D3 200 each demand level. 6 Hurwicz Criterion. Coefficient of Optimism Slide 2 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 128%AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments A Cut Layout A EE v A Shape Fill [ Copy v Paste New B I U ab AV . Aa v L Av Convert to Picture Shapes Text Arrange Quick Shape Outline v Design Format Slide Section v SmartArt Box Styles Ideas MAKING DECISIONS UNDER UNCERTAINTY Laplace Uncertainty Ino probabilities associated with . Assume the probability of each state of nature (market condition) is equally likely. Laplace market condition is equally Wooly- EV(A1) = (.3333 x FP1) + (.3333 x FP2) + (.3333 x FP3) Maximin Payoff EV(A2) = (.3333 x FP1) + (.3333 x FP2) + (.3333 x FP3) What is the butt of the minimum payath in each EV(A3) = (.3333 x FP1) + (.3333 x FP2) + (.3333 x FP3) Maximax Payoff What is the butt of the mar um payath in each 6 Hurwicz Criterion: Coefficient of Optimism Slide 3 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 9 12070AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments A Cut Layout A SEE EE v A Shape Fill [ Copy v Paste New B I U ab x AV . Aav L Av Convert to Picture Shapes Text Arrange Quick Design Format Slide Section v Shape Outline v SmartArt Box Styles Ideas MAKING DECISIONS UNDER UNCERTAINTY Maximin Payoff Uncertainty Ino probabilities associated with . What is the best of the minimum payoffs in each market? Choice State of Final Choice State of Final Laplace Amname the pressality of auch state of nature Nature Position Nature Position A1 D A1 D1 D2 A2 D Maximin Payoff D3 A3 D What is the butt of the minimum payath in each A2 D1 D2 D3 Which alternative offers the best of the minimums? It represents the A3 D1 Maximax Payoff MAXIMIN PAYOFF. What is the butt of the mar um payath in each D2 Used by pessimistic or risk averse D3 investors. Laplace 6 Hurwicz Criterion. Coefficient of Optimism Slide 4 of 10 English (Nigeria) Accessibility: Investigate Notes Comments BE 12070AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments X Cut Layout A HE EE v A Shape Fill [ Copy v Reset Paste New Format Section v B I Slide U ab x x, AV . Aav L Av Convert to Picture Shapes Text Arrange Quick Shape Outline v Design SmartArt Box Styles Ideas Uncertainty Ino probabilities associated with Payoff Mainis Maximax Payoff . What is the best of the maximum payoffs in each Laplace " Ausame the probability of such state of nucare market? [market condition) is equally Wooly. Choice State of Final Choice State of Final Nature Position Nature Position A1 D Maximin Payoff " What is the best of the minimum payath in each A1 D1 D2 A2 D D3 A3 D A2 D1 Maximax Payoff D2 What is the butt of the maximum payath in each D3 Which alternative offers the best of the maximums. It represents the A3 D1 MAXIMAX PAYOFF. D2 Used by optimistic or risk tolerant D3 6 investors. Hurwicz Criterion Coefficient of Optimism Slide 5 of 10 English (Nigeria) Accessibility: Investigate Notes Comments 12070AutoSave . OFF n A 1 . G ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments A Cut Layout A EE v A Shape Fill [ Copy v Reset Paste New BI L Av Convert to Picture Shapes Text Arrange Quick Format Slide Section v U ab AV . Aav Design SmartArt Box Styles Shape Outline v Ideas 2... # Hurwicz Criterion- Coefficient of Optimism Laplace (market cosdthe Is He Had Maximin Payoff What is the best of the minimum payath in such 0% Degree of Optimism 100% Maximax Payoff . What is the best of the maximum pryath in such a = 0 means pessimistic (no optimism) a = 1 means completely optimistic 6 Hurwicz Criterion- Coefficient of Optimism If a represents the Coefficient of Optimism, then (1- a) represents the Coefficient of Pessimism. Hurwicz Criterion Coefficient of Optimism Slide 6 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 120/0AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments X Cut Layout A EE v A Shape Fill [ Copy v Reset Paste New Format Section v B I U ab Slide AV . Aav L Av Convert to Picture Shapes Text Arrange Quick Design SmartArt Box Styles Shape Outline v Ideas [market condition) is equally Wooly. Hurwicz Criterion- Coefficient of Optimism Maximin Payoff What is the best of the minimum payath in such Choice Maximum Minimum a = .6 (coefficient of optimism) Payoff Payoff Maximax Payoff A1 (1-a ) = .4 (coefficient of . What is the butt of the maximum guyath in such pessimism) A2 A3 16 Hurwicz Criterion Coefficient of Optimism EV(A1) = (.6 x Max Al) + (.4 x Min Al) Which alternative yields the best EV(A2) = (.6 x Max A2) + (.4 x Min A2) return? Hurwicz Criterion- Coefficient of Optimism EV(A3) = (.6 x Max A3) + (.4 x Min A3) = Pureice Creamon Coefficient of Optimum Regret Criterion than maximal decision. ed with making a law " A repet motrin shows how much you would lose Slide 7 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 120/0AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments X Cut Layout A EE EE v A Shape Fill [ Copy v Paste New B I U ab AV . Aav L Av Convert to Picture Shapes Text Arrange Quick Section v Shape Outline v Design Slide SmartArt Box Styles Ideas 5 Maximax Payof What is the bust of the maximum payath in each Regret Criterion . The opportunity cost associated with making a less Hurwicz Criterion Coefficient of Optimism than maximal decision. . A regret matrix shows how much you would lose for each decision. Hurwicz Criterion Coefficient of Optimism Regret Criterion " The opportunity cost an todated with making a lou for back decision. 9 Regret Criterion Original Fayoth Regent Matela Slide 8 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 12070AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments X Cut Layout A EE EE v [ Copy v A Shape Fill Paste New Format Section v BI U ab AV . Aa L Av Convert to Picture Shapes Text Arrange Quick Slide SmartArt Box Shape Outline v Design styles Ideas Hurwicz Criterion- Coefficient of Optimism Regret Criterion Original Payoffs Regret Matrix Choice State of Final Choice State of Final Nature Position Nature Position Hurwicz Criterion Coefficient of Optimism A1 D1 A1 D1 D2 D2 D3 D3 18 Regret Criterion A2 D1 A2 D1 than medal darkin d with making a low D2 for each dee shows how much you would lose D2 D3 D3 A3 D2 A3 D1 19 D2 D2 Regret Criterion Original Fayott Repeat Matrix D3 D3 10 heyput Criterion Certainty and the Regret Matrix " If you know that demand is gary to be 150 T-shirts, what is the optimal order aire?" Slide 9 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 12070AutoSave . OFF AH ? C ... T-Shirts R Us Home Insert Draw Design Transitions Animations Slide Show Review View Tell me Share Comments X Cut Layout A EE v A Shape Fill [ Copy v Paste New Format Section v BI Arrange Quick Slide AV . Aav L Av Convert to Picture Shapes Text Design SmartArt Box Styles Shape Outline v Ideas 6 Hurwicz Criterion Coefficient of Optimism Certainty and the Regret Matrix Hurwicz Criterion. Coefficient of Optimism . If you know that demand is going to be 150 T-shirts, what is the optimal order size? Regret Criterion than mandmaldecision, h making a law . What would the opportunity loss be if you had only 19 ordered 100 T-Shirts? Regret Criterion Original Favors Regent Matrix 10 Certainty and the Regret Matrix " If you know that demand is going to be 150 T-shirts, what is the optimal order aire? "What would the opportunity lom be if you had only Slide 10 of 10 English (Nigeria) Accessibility: Investigate = Notes Comments 12070