Analysis of a parallel machine scheduling problem with sequence dependent setup times and job availability intervals

Abstract

In this study, we propose constraint programming (CP) model and logic-based Benders algorithms in order to make the best decisions for scheduling non-identical jobs with availability intervals and sequence dependent setup times on unrelated parallel machines in a fixed planning horizon. In this problem, each job has a profit, cost and must be assigned to at most one machine in such a way that total profit is maximized. In addition, the total cost has to be less than or equal to a budget level. Computational tests are performed on a real-life case study prepared in collaboration with the U.S. Army Corps of Engineers (USACE). Our initial investigations show that the pure CP model is very efficient in obtaining good quality feasible solutions but, fails to report the optimal solution for the majority of the problem instances. On the other hand, the two logic-based Benders decomposition algorithms are able to obtain near optimal solutions for 86 instances out of 90 examinees. For the remaining instances, they provide a feasible solution. Further investigations show the high quality of the solutions obtained by the pure CP model.

A survey of case studies in production scheduling: Analysis and perspectives

“…Particularly interesting, for example, is the explicit treatment of setup times, i.e. they are treated separately from the job processing times in quite a number of studies [82,46,86,70,84,59,78,9,41,26,16,45,27,81].…”

“…Rossi et al [68] developed a MILP model and constructive heuristics for a high-fashion industry. Gedik et al [27] proposed a constraint programming model and logic-based Benders algorithms to optimize the inland waterway infrastructure maintenance operations conducted by the U.S. Army Corps of Engineers. They take into account constraints such as environmental windows, dredge resource cost and availability, and sequence dependent travel times.…”

Design and analysis of bi-objective flexible job shop scheduling problem: A case study in construction equipment manufacturing industry

“…Abdeljaouad et al [13] develops a custom solution algorithm to minimize the maximum completion time of planned jobs. Gedik et al [14] presents a constraint programming optimization model with logic-based Benders decomposition algorithm that takes account of total profit maximization and reduction of machine setup times. Ozguven et al [15] designs two different mathematical models to minimize production completion time and to balance workloads of machines, and shares solution sets for both models.…”

Modeling and Solving Scheduling Problem with m Uniform Parallel Machines Subject to Unavailability Constraints

“…Furthermore, most research papers studied the case of identical parallel machines. For example, [9][10][11][12][13] studied various identical parallel machine problems allowing various types of unavailable intervals for machines.…”