Admission and inventory control of a single-component make-to-order production system with replenishment setup cost and lead time

• We study admission and inventory control for a make-to-order production system.
• We investigate the optimal policy under non-preemptive lead time and setup cost.
• We introduce sub- and supermodularity and convexity with step size of order size.
• We develop two types of simple and implementable heuristic policies.

We consider the admission control and inventory management problems of a single-component make-to-order production system. Components are purchased from suppliers in batches of fixed size subject to stochastic lead times and setup costs. A control policy specifies when a batch of components is purchased, and whether the demand for each MTO production is accepted upon arrival. We formulate the problem as a Markov decision process (MDP) model, and characterize the structure of optimal admission control and inventory replenishment policies. We show that a state dependent base-stock policy is optimal for the inventory replenishment, although the MDP value function is not necessarily convex. We also show that the optimal admission control can be identified as a lattice dependent policy. A sensitivity analysis is conducted to show how the optimal policy changes as a function of the system parameters. To effectively coordinate admission and inventory control decisions, we propose simple, implementable, and yet effective heuristic policies. Our extensive numerical results suggest that the proposed heuristics can greatly help firms to effectively coordinate their admission and inventory control activities.