Approximations for Multiproduct Contracts with Stochastic
Demands and Business Volume Discounts: Single Supplier Case
R. Anupindi and Y. Bassok
*** Abstract ****
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 programm. 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.