Production planning problems with joint service-level guarantee: a computational study

We consider a class of single-stage multi-period production planning problems under demand uncertainty. The main feature of our paper is to incorporate a joint service-level constraint to restrict the joint probability of having backorders in any period. This is motivated by manufacturing and retailing applications, in which firms need to decide the production quantities ex ante, and also have stringent service-level agreements. The inflexibility of dynamically altering the pre-determined production schedule may be due to contractual agreement with external suppliers or other economic factors such as enormously large fixed costs and long lead time. We focus on two stochastic variants of this problem, with or without pricing decisions, both subject to a joint service-level guarantee. The demand distribution could be nonstationary and correlated across different periods. Using the sample average approximation (SAA) approach for solving chance-constrained programs, we reformulate the two variants as mixed-integer linear programs (MILPs). Via computations of diverse instances, we demonstrate the effectiveness of the SAA approach, analyse the solution feasibility and objective bounds, and conduct sensitivity analysis for the two MILPs. The approaches can be generalised to a wide variety of production planning problems, and the resulting MILPs can be efficiently computed by commercial solvers.