Approximations for multiproduct contracts with stochastic demands and business volume discounts: Single supplier case

In this paper we analyze contracts for multiple products when the supplier offers business volume discounts. The contract takes the form of price discounts for total minimum dollar volume commitments over the horizon with flexibility to adjust the total purchases upwards by a fixed percentage about this minimum commitment. The optimal policy could be complex since it involves the solution of a constrained multi-period multi-product dynamic program. We suggest approximations that give us an upper bound. To develop this upper bound, we present the optimal policy for a similar contract for a single product problem. We then develop a lower bound for the multiproduct problem and show, numerically, that the gap is small. Given the approximations standard single period resource allocation algorithms can be used to solve the problem. The resulting solution methodology is fast and permits evaluation of various what-if scenarios.