Enumeration of Pareto Optima for a Flowshop Scheduling Problem with Two Criteria

We consider a two–machine flowshop–scheduling problem with an unknown common due date where the objective is minimization of both the number of tardy jobs and the unknown common due date. We show that the problem is NP–hard in the ordinary sense and present a pseudopolynomial dynamic program for its solution. Then, we propose an exact ϵ–constraint approach based on the optimal solution of a related single–machine problem. For this latter problem a compact ILP formulation is explored: a powerful variable–fixing technique is presented and several logic cuts are considered. Computational results indicate that, with the proposed approach, the pareto optima can be computed, in reasonable time, for instances with up to 500 jobs.