Production planning with order acceptance and demand uncertainty

Traditional production planning models assume that all orders must be satisfied when capacity is available. In this paper, we analyze the value of providing decision makers with the flexibility to accept or reject orders, when order quantity is uncertain. We introduce this demand flexibility in two production planning problems. The first problem integrates order acceptance in the capacitated lot sizing problem, providing the option to reject an order if it requires a high setup cost and cannot be aggregated with additional orders to take advantage of economies of scale. The second problem integrates order acceptance in the order release planning problem with load-dependent lead times (LDLTs). This problem provides the option to reject an order if it increases the workload causing the delay of other orders due to congestion effects. Robust counterparts of both integrated problems are formulated as linear mixed integer programs (MIPs). The deterministic integrated problems and their robust counterparts are shown to be NP-hard and a two-stage MIP heuristic is proposed as a solution procedure. A relax and fix (RF) heuristic is adapted to efficiently construct feasible solutions to the robust problems, which are then improved by a fix and optimize (FO) heuristic. Numerical results show that the proposed heuristics give promising results in terms of solution quality and computation time. Simulation experiments are conducted to assess the value of demand flexibility and to study the effects of various parameters on economical performance.