Optimal Control of a Make-to-Stock System with Outsourced Production and Price-Sensitive Demand

Abstract

We consider a make-to-stock system with controllable demand rate (by varying product selling price) and adjustable service rate (by outsourcing production). With one outsourcing alternative and a choice of either high or low price, the system decides at any point in time whether to produce or even outsource for additional capacity as well as which price to sell the product at. We show in the paper that the optimal control policy is of dynamic threshold type: all decisions are based on the product inventory position which represents the state of the system; there is a state dependent base stock level to decide on production and a higher level on outsourcing; and there is a state dependent threshold which divides the choice of high and low prices.