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It is the practice in some industries, as well as within multiplant organizations, to specify bounds on the range of allowable order values. That is, the buyer contracts to place an order within a small range in a future period. The specification of the range protects the supplier against large variations in the order at short notice, although it reduces the flexibility of the buyer to respond to demand changes in his own market. Hence, in exchange, the supplier is willing to reduce the price of the component to the buyer. This paper examines the implications of this specification for the production/inventory decisions. The optimal contract is determined from the structure of the solution to the production/inventory problem.
Kumar et al. (Thu,) studied this question.