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PROBLEM B: AN INVENTORY MANAGEMENT PROBLEM

In the following problem, find the best ordering policies:

Given that the information for demand is known in advance, the company can decide how many items to order from its supplier in which month. If the company orders Z items, it incurs a cost of K+iZ, where K=35 is the setup cost (transportation, administrative, etc) and i=4 is the incremental purchase cost per item ordered. (If Z=0, no cost is incurred.) When an order is placed, the time required for it to arrive (lead time) is 1 month. (Therefore, the order placed at t=1 will arrive at the beginning of t=2 ). The company cannot incur backlog, that is, it needs to make sure that there is always enough inventory to satisfy the demand the demanth occurs at the beginning of the month and that is the time when last month order arrives. There is holding costs for keeping inventory. Let I(t) be the inventory level at the end of month t [note that I(t) can be positive, or zero but not negative]. We assume the company incurs a holding cost of h=1 per item per month held in (positive) inventory for a month. Assume that the initial inventory level is I(0)=50 and that no order is outstanding. a) Determine the best ordering policy. b) Write a report explaining the steps you take in approaching the above problems