Mixed Integer Programming models for job shop scheduling: A computational analysis

Abstract

In both industry and the research literature, mixed integer programming (MIP) is often the default approach for solving scheduling problems. In this paper we present and evaluate four MIP formulations for the classical job shop scheduling problem (JSP). While MIP formulations for the JSP have existed since the 1960s, it appears that comprehensive computational studies have not been performed since then. Due to substantial improvements in MIP technology in recent years, it is of interest to compare the standard JSP models using modern optimization software. We perform a fully crossed empirical study of four MIP models using CPLEX, GUROBI and SCIP, focusing on both the number of instances that can be proved optimal and the solution quality over time. Our results demonstrate that modern MIP solvers are able to prove optimality for moderate-sized problems very quickly. Comparing the four MIP models, the disjunctive formulation proposed by Manne performs best on both performance measures. We also investigate the performance of MIP with multi-threading and parameter tuning using CPLEX. Noticeable performance gain is observed when compared to the results using only single thread and default parameter settings. Our results serve as a snapshot of the performance of modern MIP solvers for an important, well-studied scheduling problem. Finally, the results of MIP is compared to constraint programming (CP), another common approach for scheduling, and the best known complete algorithm to provide a broad view among different approaches.

Bi-Objective Dynamic Multiprocessor Open Shop Scheduling: An Exact Algorithm

“…On the other hand, for the flexible job shop scheduling problem, the computational experiments by Demir and Kürşat Işleyen [33] show that the disjunctive models provide quicker results. The same conclusion is confirmed by Ku and Beck [34] for the job shop scheduling problem. For the MOSP, Abdelmaguid [20] developed a disjunctive model for the objective of minimizing the makespan.…”

“…In the scheduling literature, comparisons of the different MILP models are provided for the flow shop scheduling problem [31], for the OSP [32], for the flexible job shop scheduling [33] and for the job shop scheduling problem [34]. The disjunctive MILP models have less size in terms of the number of decision variables and number of Constraints [32].…”

A Heuristic’s Job Order Gain in Pyramidal Preemptive Job Scheduling Problems for Total Weighted Completion Time Minimization

“…Most JSPs are solved by using heuristics because exact schedules are found intractably slow [6], [7]. When a JSP is given by job parts (or processing periods), release dates, and priority weights, without due dates or other constraining variables or parameters, it is effectively solved by the shortest processing period approach (SPPA) [5], [8].…”

“…Whichever subset E is, PPJSPs by AJOI are those that have condition (6). Consequently, PPJSPs by DJOI are those that have condition (7).…”

“…Consequently, PPJSPs by DJOI are those that have condition (7). Obviously, if this is AJOI by (6), then the volumes of those N jobs in vector (1) are non-decreasing. Inversely, the volumes in vector (1) are non-increasing for DJOI by (7).…”