# Marginal Cost and Optimal Stocking Quantity Essay example

957 Words Oct 1st, 2012 4 Pages
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
So when the transfer price is raised Armentrout would stock more and the fill rate would increase but at the same time Sheen’s profit would decrease and she would also put less effort in paper. e. Channel effort and stocking level will be lower in a differentiated channel than in an integrated one because of the splitting of the margins.

Problem #4 a. Armentrout’s optimal stocking quantity is 516. b. His stocking level is different because his underage cost has changed significantly because of customer’s willingness to replace Express with Private when Armentrout has stock out. New overage cost = \$0.20 – 40% * \$0.40 = \$0.16 c. In this case Armentrout’s real cost for each paper is \$0.80 + \$0.03 = \$0.83 so now his underage cost his would very low \$0.17 (margin on Express) - \$0.16 (margin from Private) = \$0.01 but overstocking cost would be much higher \$0.83. So [pic] which reduces his stocking level a lot.

Problem #5 a. By introducing the buy-back price concept Sheen reduces Armentrout’s overage cost and thus increases his optimal stocking level. Setting the buyback price at \$0.75 maximized channel profit. Armentrout’s optimal stocking quantity would be 659. (Either use newsvendor solution or Solver add-in in Excel) b. Though not requested in the question it is interesting to check how we obtain the Buy-Back Price as a function of the Transfer Price. Assume that the Transfer price is T then the system works as

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