Consider the Economic Order Quanity (EOQ) problem, with all of the assumptions discussed in class. However, instead of a continuously depleting demand, suppose that the demand is now discrete (and periodic), with d units being demanded at times t,2t,3t,..., where d = λt, in order to make the average slope the same as in the EOQ case. Also, assume that an order arrives at the beginning of the period for which it is ordered. (And, for points of time when both a demand occurs and an order arrives, assume that the demand is taken instantaneously before the order arrives. This is the scenario we examined in class.) Assuming the same quantity Q = Q_EOQ is ordered at the same times in both cases, let Id and Ic be the annual inventory costs for the discrete and continuous scenarios, respectively. Also, assume that Q_EOQ = nd for some integer n.
(a) (Id−Ic)/Ic is the percent increase of the discrete scenario inventory cost over that of the continuous scenario. Determine this value as simply as possible, in terms of the parameters Q,λ,h, and n. [Note: This quantity may be independent of some of these parameters.]
(b) Determine the optimal order quantity in terms of K, λ, h, and d.