Optimal and heuristic solutions for a scheduling problem arising in a foundry

A scheduling problem for an engineer-to-order foundry that manufactures propeller blades for ships is outlined. The main objective for the foundry is to find an efficient production plan that minimizes the total number of days orders are late. This has to be done subject to a set of relatively common constraints related to the scheduling of the present jobs and resources. The constraints on the resources are quantified by a capacity matrix. A mixed integer programming formulation for the scheduling problem is proposed together with a set of corresponding heuristic strategies. The heuristic strategies perform very well compared to previous scheduling policies used in the company, and in comparison to optimal solutions where they can be found. Numerical results are presented to demonstrate the performance of these strategies.