Adjustment strategies for a fixed delivery contract

We consider a long term contractual agreement between buyer and seller in w hich 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 per iod. In order to manage the inventory, the buyer has the option of adjustin g the delivery quantity upwards just prior to a delivery, but must pay a pr emium to do so. Demand is assumed random. and we model the system in a cont inuous review setting. We show that the equations one must solve to find op timal adjustment strategies are intractable. A diffusion approximation is d eveloped which when coupled with the solution to an even simpler determinis tic version of the problem yields very simple but effective approximations. Extensive computations are included to compare the performance of the opti mal and approximate policies. We also empirically derive a formula for comp uting Q whose accuracy is established computationally. We prove that the fi xed delivery contract results in lower variance of orders to the seller. We also include a computational study to find the unit cost discount that equ alizes the expected costs for the fixed delivery contract and the base stoc k contract for a large parameter set.