Adjustment Strategies for a Fixed Delivery Contract

Abstract

We consider a long term contractual agreement between buyer and seller in which Q units are delivered to the buyer at regular time intervals. It must be true that the delivery quantity, Q, is less than the mean demand per period. In order to manage the inventory, the buyer has the option of adjusting the delivery quantity upwards just prior to a delivery, but must pay a premium to do so. Demand is assumed random, and we model the system in a continuous review setting. We show that the equations one must solve to find optimal adjustment strategies are intractable. A diffusion approximation is developed which when coupled with the solution to an even simpler deterministic version of the problem yields very simple but effective approximations. Extensive computations are included to compare the performance of the optimal and approximate policies. We also empirically derive a formula for computing Q whose accuracy is established computationally. We prove that the fixed delivery contract results in lower variance of orders to the seller. We also include a computational study to find the unit cost discount that equalizes the expected costs for the fixed delivery contract and the base stock contract for a large parameter set.

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