Mathematical Model and Evaluation Function for Conflict-Free Warranted Makespan Minimization of Mixed Blocking Constraint Job-Shop Problems

Abstract

In this paper, we consider a job-shop scheduling problem with mixed blocking constraints. Contrary to most previous studies, where no blocking or only one type of blocking constraint was used among successive operations, we assume that, generally, we may address several different blocking constraints in the same scheduling problem depending on the intermediate storage among machines, the characteristics of the machines, the technical constraints, and even the jobs. Our objective was to schedule a set of jobs to minimize the makespan. Thus, we propose, for the first time, a mathematical model of the job-shop problem taking into account the general case of mixed blocking constraints, and the results were obtained using Mosel Xpress software. Then, after explaining why and how groups of jobs have to be processed, a blocking constraint conflict-free warranted evaluation function is proposed and tested with the particle swarm optimization and genetic algorithm methods. The results prove that we obtained a near-optimal solution to this problem in a very short time.

A JSSP solution for production planning optimization combining industrial engineering and evolutionary algorithms

“…Many other subtypes exist, many of them extending the basic types with different constraints and Objective Functions, for instance, machine blocking constraints [17]. Recent research even covers the so-called "low-carbon" JSSPs by pursuing the goal to minimize the sum of completion time cost and energy consumption cost [18].…”

“…(16) where: (17) Variable stands for job completion time, stands for waiting (or IDLE) time of job at sequence and stands for the processing time for job on machine at sequence .…”

Two NEH Heuristic Improvements for Flowshop Scheduling Problem with Makespan Criterion

“…However, meta-heuristics correctly perform at continuous and binary problem resolutions. For scheduling problems, particle swarm optimization (PSO) algorithms [22,23], as well as genetic algorithms [24], continue to show good results. NEH is also useful for solving flowshop scheduling problems with objective functions different from the makespan, such as minimizing the core waiting time [25], total tardiness [26], total flowtime [27], or makespan [28] for the distributed permutation flowshop problem.…”