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Exam Name__________________________ 3 ISyE 4803 Spring 2006 Please sign the following statement: I give my word that I will not discuss this exam or any of the content with anyone until after next Wednesday ___________________________________ Sign your name Show all work for partial credit. 1. (15 points) A manufacturer wants to hire a subcontractor to make a component for them. An alternative contract exists for the subcontractor at a value of $100 if they do not take the offer from the manufacturer. The output for the subcontractor depends on the level of effort (in terms of applying appropriate resources) applied to the project. The manufacturer wants to devise a contract that will pay the subcontractor for performance (in terms of output observed). If the subcontractor applies a high level of effort, then this gives value VH to the manufacturer 70% of the time (the other 30% is shows as VL due to poor support logistics from the manufacturer). If the subcontractor applies a low effort, then it shows as VL 60% of the time (the other 40% of the time it shows as VH). The subcontractors utility is defined by the contract value (w) minus the level of effort (eH or eL), and the manufacturer desires the subcontractor to have a high level of effort. Write the participation and the incentive compatibility constraints for the contract the manufacturer would need to offer (and label them). There is no need to solve them for w. 2. (25 points) Two companies (A and B) each have unit cost c=10. The price they get per part is defined by market demand P(Q) = 200-5Q, where Q=qA+qB. Answer the following: a. Solve for the Nash output quantities for each firm. b. Determine the market price, and what the total profit for the two firms would be. c. Suppose the three firms merged and became a single firm. What would the output quantity and market price be in this case? Compare this answer to what you found in b. 3. (25 points) A manufacturer sells parts to a store which packages the parts and sells them to the customers. The manufacturer has a cost of $5 for each part it makes, and the store spends another $2 per part it packages. The store sells parts to customers at a price of $15 each (demand is uniformly distributed between 200 and 400). The parts are perishable, and so the newsvendor assumptions hold1. The salvage value for an unsold part is $1. Answer the following: a. If this were a centralized system, determine the optimal order quantity. b. If this were a decentralized system, and the manufacturer sold parts to the store at a price of $9 each, determine the order quantity. c. Suppose for this decentralized system, the manufacturer wants to incentivize the store to order the same quantity as under the centralized system. What transfer price should they charge? d. Explain what would need to happen to try to coordinate the supply chain using the transfer price in c. Don t worry about computing the profits, but explain in sufficient detail. 1 Note that for the Newsvendor model, the critical ratio is F(Q) = cu/(cu+co) where cu is the cost of being under (i.e., the cost of not having a part to meet demand), and co is the cost of being over (i.e., the cost of having a part for which there is no demand). 4. (6 points) In chapter 8 of the text, the author discussed commission pay that will attract hard working employees. Explain how a real estate company could attract hard workers to them through the use of salary and commission. 5. (9 points) In class we discussed the problem of exploitable quasirents . What does this mean, and what do we need to do to be careful in entering into contracts (you can use the same class example to motivate your discussion). 6. (20 points) A manufacturer (M) supplies a store (S). The cost for M to produce a part is $10, and the cost for S to label the part is $1. The price that S charges per part is $20. If M and S were centralized, S would sell 200 parts. If M and S were decentralized, S would sell 140 parts. Determine whether or not in this case a straight transfer payment scheme would work to coordinate the supply chain. If so, give transfer the payment amount. Reminder: If you haven t done so already, please take the time to fill out the student course evaluations for this class. I would also appreciate any written comments there as well as this is the first time this has been taught, and I want to make sure and improve it for next year. Name__________________________ Exam 3b ISyE 4803 Spring 2006 Show all work for partial credit 1. (15 points) A manufacturer (M) supplies a retailer (R) that sells to customers. For the centralized system, the optimal order quantity for the retailer is Q*. Explain in detail an example where R would: a. order less that Q* when decentralized b. order more than Q* when decentralized For each example, explain the type of risk and who has it. 2. (34 points) A manufacturer (M) supplies a retailer (R). The cost to the manufacturer is $5 per unit. The transportation cost from M to R is $1 per unit. Finally, R spends $3 per unit in labeling and repackaging. The sales price to customers is $25 per unit and demand is uniformly distributed between 200 and 400 (and newsvendor assumptions2 hold and there is no salvage value). Answer the following: c. (7 points) If M and R are centralized (and M and R equally split the revenue between them), determine the optimal order quantity, the profit for the centralized chain, and the profit for M and R. d. (7 points) Suppose M and R are separate companies, and M charges R $15 per unit (and R still charges customers $25/unit). Determine the corresponding order quantity and profit for M and R. e. (10 points) Develop a revenue sharing contract that will lead to the same order quantity as if M and R were centralized, but where both parties will be better off than if decentralized as in part b (if possible). f. (10 points) Develop a transfer payment scheme that will result in the same order quantity as if M and R were centralized, but where both parties will be better off than if decentralized as in part b (if possible). 2 Note that for the Newsvendor model, the critical ratio is F(Q) = cu/(cu+co) where cu is the cost of being under (i.e., the cost of not having a part to meet demand), and co is the cost of being over (i.e., the cost of having a part for which there is no demand). 3. (21 points) A restaurant owner has two waiters. The revenue (value) that the owner brings in depends on the effort of the waiters by the following relationship: V = (e1 )1 / 3 + (e2 )1 / 3 The utility of each waiter is defined by the wage they earn minus the effort they exert (assume each waiter is a utility maximizer). Do the following: a. Solve for the Nash equilibrium level of effort of the waiters if the owner gives each waiter 1/3 of the revenue (value) brought in. b. Compare this to the optimal level of effort from the restaurant owner s perspective. Would this also be optimal for the waiters? 4. (6 points) In chapter 8 of the text, the author discussed commission pay that will attract hard working employees. Explain how a real estate company could attract hard workers to them through the use of salary and commission. 5. (6 points) Consider the vendor-managed inventory scheme between Mayfield Dairy and Kroger Grocery where Kroger would pay Mayfield upon receipt of milk and Mayfield would determine the stocking level in Kroger. Why is this an example of a poorly designed contract and what could be done to correct it? 6. (18 points) Consider the case where there are two types of cars: high quality (peaches, P) and low quality (lemons, L). Sellers value a P at $3000 and an L at $1500. Buyers value a P at $3500 and an L at $2000. There is more demand for cars than there is supply, and there are twice as many L as P. Answer the following: g. If neither buyers or sellers know the quality, what will happen? h. If sellers know the quality but buyers don t, what will happen? Reminder: If you haven t done so already, please take the time to fill out the student course evaluations for this class. I would also appreciate any written comments there as well as this is the first time this has been taught, and I want to make sure and improve it for next year.

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