An Efficient Relax-and-Solve Heuristic for Open-Shop Scheduling Problem to Minimize Total Weighted Earliness-Tardiness

Abstract

An open-shop scheduling problem to minimize the total weighted earliness-tardiness of job-on-machine operations is studied. Each operation has its own due date, earliness weight and tardiness weight. An efficient relax-and-solve heuristic is developed. A feature that makes the proposed heuristic distinctive from the existing heuristics of this kind is that it operates by iterative relaxation and optimization of a series of sub-problems. Performance of the proposed heuristic is verified on a set of 72 benchmark instances with up to 200 operations, adapted from the literature on a similar job-shop scheduling problem. The heuristic delivers best solutions for nearly 71\% of the instances (i.e., 51 out of 72 instances), including the best solution for all instances with 150 and 200 operations. Its running time is around three minutes, while CLPEX was run for 30 minutes.