# Marginal Cost and Optimal Stocking Quantity

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IEOR E4210: Assignment 5 (Solutions) Problem #1 a. Using the simulation in the spreadsheet would yields Q=584 b. [pic] Problem #2 a. Using solver to solve the embedded model in the Excel sheet or by trying different values for h the optimum value will be obtained as “h=4” b. Marginal Revenue = Marginal Benefit [pic] c. Optimal profit from Problem #1 = 331 Current optimal profit = 371 The difference is due to the effect of Sheen’s effort on the demand. This relation is not surprising. Players in the different stages of a supply chain can increase demand for their product through efforts in advertisement, product development etc. Problem #3 a. Armentrout’s optimal stocking quantity is…show more content…
The final solution is when the transfer price is set to 1-e when “e” is as small as possible. In this situation the Buyback price is also roughly 1. In fact the retailer (Armentrout) is practically eliminated from the chain and has no role. Thus the chain acts as an integrated chain and reaches its optimum. c. A franchise wouldn’t affect Armentrout’s overage and underage cost. Therefore it does not change his fraction and does not change his decisions. However in extreme cases the nature of problem changes. If Sheen charges a very high franchise price she would have no incentive to sell any paper (since her main profit is from franchise and not the sale) but then Armentrout may not buy because he can not make any profit. Problem #6 a. Sheen’s VMI plan is similar to vertically integrated channel – since Sheen gets all the benefits and costs from the sales we can expect her to choose effort levels and quantity levels that are optimal for the channel. Armentrout does not make any decisions. Sheen could compensate him sufficiently with a slotting allowance to ensure that he earns more money under the VMI plan than he was earning in a differentiated channel where he was making stocking decision. b. The VMI plan might perform worse than the