A constraint programming-based lower bounding procedure for the job shop scheduling problem

Abstract

This paper presents a novel Constraint Programming (CP) approach to obtain strong lower bounds for the Job Shop Scheduling Problem (JSSP) under the makespan criterion. Our approach comprises two phases. In the first phase, a relaxation of the original problem is solved, while in the second phase, this relaxation is iteratively tightened until a time limit is reached or no better bounds are found. We tested our procedure with 80 JSSP open instances, and the results validated our approach as we were able to find 7 new lower bounds and prove optimality in one instance.