ISyE 6230 HW8: Optimal Order Quantity & Profits in Supplier-Retailer Relationships - Prof., Assignments of Systems Engineering

Download ISyE 6230 HW8: Optimal Order Quantity & Profits in Supplier-Retailer Relationships - Prof. and more Assignments Systems Engineering in PDF only on Docsity! Homework 8 ISyE 6230 1. Suppose a supplier provides product to a retailer who sells to a market with demand of P=100-2Q. Unit cost to the supplier is $5. Answer the following: a. If the supplier and retailer are centralized, compute the optimal order quantity and total profits. b. Find an intermediate price w where the supplier and retailer split the profits equally, and compute the corresponding profits (make sure and verify that it equals the total profits in a). c. Now suppose that the supplier and retailer are separate companies and that the retailer charges a wholesale price of $20. What would the solution be in this case? d. Compare the solutions in b and c. e. Suppose a revenue sharing arrangement is to be used. Find any arrangement which strictly improves both parties compared to c. f. Find the range of α values for which revenue sharing in this example is “coordinating”, i.e., where the total profits of the decentralized case are the same as the centralized case and where no party is made worse off. 2. Suppose in problem 1 that the item satisfies the condition of the “newskid problem” (i.e., it is a “fashion” good sold over a single period). The price in this case is set at $20 with a unsold items selling at $3 salvage. Demand for the item over the period is: 25% of the time it is 200, 40% of the time it is 100, and 35% of the time it is 50. Answer the following: a. If the supplier and retailer are centralized, find the optimal order quantity and corresponding profit.1 In this case, ignore the wholesale price. b. Find the solution to the decentralized solution. c. Compare you answers found in a and b. d. Develop a buy back contract scheme that coordinates the supply chain. 1 Recall that solution to the newskid problem is to find the smallest Q where F(Q)≥(p-c)/(p-s).