Question

2. You manage the inventory of Lenovo desktops in a distribution center. You face deterministic demand of 2,000 desktops per month and a monthly holding cost of S2 per desktop. You've been using EOQ to determine the optimal order quantity, and currently do not backorder any demand. However, you are considering allowing backorders, and you estimate a corresponding cost of $25 per unit per month in customer goodwill. (a) What would be the percentage of demand met from backorders if you optimize your reorder point with respect to holding and backorder costs, regardless of the order quantity? (b) Suppose you keep your current order quantity but optimize the reorder point with respect to holding and backorder cost. Excluding purchasing cost (i.e. variable order cost), what percentage would your monthly cost be of the order cost without backorders? percentage? larger or smaller? How much does the quantity change in terms of percentage? (c) Considering the same situation as in (b), how would your maximum inventory change, as a (d) Suppose you re-optimize the order quantity to consider backorders. Is your new quantity

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Answer 1

* Answer b and d are in the image and A and C are written here :

A. The fraction of demand met by back orders is given by = h/ (h +b) --> h = 2 , b = 25 ;

= 2/27 = 0.074 = 7.4 %

C. Note that our max inventory level when not allowing back orders was q. We keep ordering q units, but now that we allow back orders we know that our optimal max inventory level s*is given by :

s* = bq/(b+h) = 0.93 q

So,  our max inventory level would decrease by 7%.