Optimal production-inventory policy for make-to-order versus make-to-stock based on the M/Er/1 queuing model

Abstract

This paper analyzes a multi-product production / inventory system where demands for each item arrive according to a Poisson process and the production time for each product has an Erlang distribution. The paper proposes an optimality condition that specifies whether each product should be produced make-to-stock or make-to-order. In the event a product should be produced make-to-stock, an approach for computing the optimal base-stock level is proposed. Numerical examples are given for illustrative purpose.