Problem # 4 Suppose the unit cost is about to rise from UC to a new level NUC (i.e., UC < NUC), and the new economic order quantity becomes Qo.

If we place a single large order of Q using UC (assuming there is no stock remaining) the stock pattern can be described as below: A reasonable objective would be to order an amount which minimizes costs over some long period. We could look at the total costs over some time horizon TH. During this time there will be: A single special cycle of length T, corresponding to the single order for Q units. A number of ordinary cycles with total length TH - T, corresponding to the regular orders of size Qo. It is assumed that the fixed customer demand rate is D (unit per unit time) for TH, and the holding costs for T and TH - T are given by Ix UC and I x NUC, respectively, where I is the proportion factor to calculate the hold cost. Therefore, the cost function during T is simply defined as \mathrm{UC} \cdot \mathrm{Q}+\mathrm{RC}+\frac{\mathrm{I} \cdot \mathrm{UC} \cdot \mathrm{Q} \cdot \mathrm{T}}{2} which is the total cost function of EOQ.