INVENTORY MODEL WITH FULL LOAD ORDERING

Consideration is given to a discrete review, single product, dynamic inventory model with stochastic demands. The ordering cost is assumed to consist of a linear purchase cost and a cost K for each vehicle used. The authors examine the simple policy: ″If the stock level at the beginning of period n does not exceed some critical number T//n, order the smallest number of full vehicle loads which will raise the inventory level just above T//n. If the stock level is above T//n do not order.″ Conditions ensuring that this full load ordering rule minimizes total expected cost are given. It is proven that the sequence of critical numbers T//1, T//2, . . . is bounded and nondecreasing and the authors find a limiting value T that characterizes an optimal infinite horizon policy. The conditions include typical assumptions, such as the covexity and differentiability of the expected one period holding and shortage cost. The most interesting condition involves the variation in the demand distribution over intervals of length equal to the vehicle capacity. As one would expect, it is satisfied if capacity is small or K is large.