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 $ per unit or $ 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.