Make-to-order versus make-to-stock in a production–inventory system with general production times

We study the optimality of make-to-order (MTO) versus make-to-stock (MTS) policies for a company producing multiple heterogeneous products at a shared manufacturing facility. Manufacturing times are general i.i.d. random variables, and different products may have different manufacturing-time distributions. Demands for the products are independent Poisson processes with different arrival rates. The costs of managing the production–inventory system are stationary and include inventory holding and backordering costs. Backordering costs may be dollars-per-unit or dollars-per-unit-per-unit-time. We derive optimality conditions for MTO and MTS policies. We also study the impact of several managerial considerations on the MTO versus MTS decision.