A Relax-and-Fix Heuristic for a Production Planning Problem with Order Acceptance and Flexible Due Dates

We present a new production planning problem which integrates order acceptance decisions with due date flexibility while taking into consideration realistic production capacity constraints. The problem consists of choosing among a set of customer orders which ones to accept based on the profit of the orders and the available resource capacity. Realistic capacities are considered by linking the lead times to the utilization and explicitly considering the work-inprocess inventory. Furthermore, due dates of customer orders are given as time intervals within which the order can be satisfied without penalty. A mixed integer linear programming formulation (MILP) is presented. The problem is solved using a two MILP heuristics: a reversals heuristic and a relax-and-fix heuristic. The performance of the heuristics is compared with that of a state-of-the-art commercial solver applied to the MILP formulation. The relaxand-fix heuristic outperforms the reversals heuristic and the solver solution as it yields the same integrality gaps for much less CPU effort. Furthermore, the performance of the heuristic can be adjusted using two parameters in such a way that one can sacrifice some CPU time to seek better solutions.