Joint admission, production sequencing, and production rate control for a two-class make-to-order manufacturing system

Abstract

Today's manufacturing industry faces a number of challenges related to the rapid delivery of products with a high degree of variety. Striking a balance between the effectiveness in capacity utilization and the rapidness in order-fulfillment is a substantial challenge for manufacturing companies. This work aims to provide a theoretical basis from which to address this practical question. To this end, we address the problem of coordinating the admission, production sequencing, and production rate controls for a two-class make-to-order manufacturing system. Formulating the problem as a Markov decision process model, we identify the structural properties of optimal control policies under both discounted and average profit criteria. We show that the cμ rule is optimal for production sequencing and the optimal admission and production rate control policies can be characterized by the state-dependent threshold levels, provided that the production times are not associated with customer class. We also show that the optimal production rates are monotone in the system state, as in the case of a single class queueing system, and that the lower priority class can be preferred to the higher priority class in order admission under a certain condition on the system parameters. Our numerical study demonstrates that a considerable economic benefit can be achieved if the production rate is dynamically controlled between the minimum and maximum rates rather than fixed to the mean rate of these values. Finally, we present a heuristic policy that is described by linear switching functions for the control of order admission and a selection rule for the control of production rate. We compare the performance of our heuristic to the optimal policy using a numerical experiment, revealing that the heuristic provides near optimal solutions to test example problems and is robust to the system parameters.