Inventory rationing, admission control, and production capacity allocation in a make‐to‐stock/make‐to‐order manufacturing system

This paper considers a manufacturing system in which products are produced in both make‐to‐stock (MTS) and make‐to‐order (MTO) modes. Production of MTS and MTO products is done in batches, incurs a setup cost, and is non‐preemptive. The inventory of MTS products fulfills the demand of multiple classes, and each class demand can be satisfied or rejected. Customer orders for MTO production can be accepted or rejected, and their size is the same as the production batch. The primary goal of this paper is to study a policy that coordinates inventory rationing, admission control, and production capacity allocation to maximize the system's profit. We formulate the problem as a Markov decision process model and identify the structure of optimal control policies. We investigate the effect of inventory rationing on the profit by comparing its performance to that of the system with a first‐come‐ first‐serve policy to allocate inventory to multiple demand classes and study the extent to which the benefit of inventory rationing can be affected by system parameter changes. We also propose a heuristic that manages control decisions from linear threshold functions. Our test results from numerical examples show that the average percentage difference between the optimal and heuristic policies is within 1.2%.