Optimal Inventory Policies When Ordering Prices are Random

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Abstract
We consider a single-item inventory model with deterministic demands. At the beginning of each period, a random ordering price is received according to a known distribution function. A decision must be made as to how much (if any) of the item to order in each period so as to minimize total expected costs while satisfying all demands. We show that, in each period, a sequence of critical price levels determines the optimal ordering strategy, so that it is optimal to satisfy the demands of the next n periods if and only if the random price falls between the nth and the n+ 1st levels. We derive recursive expressions that describe the critical price numbers, and demonstrate the relationship of these expressions to minimal expected cost. We study finite horizon as well as infinite horizon models and show that the critical number strategy is also average-cost optimal.

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