Integrating order acceptance decisions with flexible due dates in a production planning model with load-dependent lead times

We consider a tactical planning problem, which integrates production planning decisions together with order acceptance decisions, while taking into account the dependency between workload and lead times. The proposed model determines which orders to accept and in which period they should be produced, so that they can be delivered to the customer within the acceptable flexible due dates. When the number of accepted orders increases, the workload and production lead time also increase, and this may result in the possibility of missing customer due dates. This problem is formulated as a mixed integer linear programme for which two relax-and-fix heuristic solution methods are proposed. The first one decomposes the problem based on time periods, while the second decomposes it based on orders. The performances of these heuristics are compared with that of a state-of-the-art commercial solver. Our results show that the time-based relax-and-fix heuristic outperforms the order-based relax-and-fix heuristic, and the solver solution as it yields better integrality gaps for much less CPU effort.