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This paper studies the joint stock and production capacity rationing polices for a make-to-stock system with two partially substitutable products manufactured at two factories, respectively. Customers are classified into three types with each type further segmented into multiple classes. Type I and Type II customers are selective and accept their favorite products only. Type III accepts either of the two products and hence its demand is regarded as the flexible demand. The management has to decide whether to run or stop production and whether the various classes of demand for each type of customers have to be satisfied from available inventory or not — in which case demand is lost — in order to minimize the firm’s inventory and production costs. We formulate the problem as a make-to-stock queue system and characterize the optimal joint stock and production rationing policies as monotone switching curves. Numerical examples are given to illustrate the optimal policies and demonstrate the value of flexible demand. Moreover, we develop a simple heuristic policy and compare the costs associated with the optimal and heuristic policies for different parameters.

The Joint Stock and Capacity Rationings of a Make-To-Stock System with Flexible Demand