Order acceptance and scheduling policies for a make-to-order environment with family-dependent lead and batch setup times

In many make-to-order production situations with batch setup times, customer orders are grouped into family-dependent batches to limit the loss of capacity due to setups. These batches, however, cannot be too large, since the make-to-order character requires that orders have to be produced in time. This trade-off between setup time efficiency and due-date adherence creates a challenging scheduling problem referred to in the literature as the Customised Stochastic Lot Scheduling Problem. Typically, suppliers reduce the complexity of the production problem by quoting lead times that are equal for all customer families. This choice, however, is in many cases too restrictive. In this paper, we show quantitatively by means of Markov decision processes (MDPs) that using family-dependent lead times can result in a significant gain in profit as compared with using standard lead times. We develop a simple heuristic acceptance/scheduling policy, and demonstrate that this heuristic performs very well compared with the optimal policy of the MDP for a wide range of parameters.