Solving Non-Permutation Flow Shop Scheduling Problem with Time Couplings

Radosław Idzikowski,Andrzej Gnatowski,Jarosław Rudy

doi:10.3390/app11104425

Radosław Idzikowski, Andrzej Gnatowski + Show 1 more

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https://doi.org/10.3390/app11104425

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Abstract

In this paper, a non-permutation variant of the Flow Shop Scheduling Problem with Time Couplings and makespan minimization is considered. Time couplings are defined as machine minimum and maximum idle time allowed. The problem is inspired by the concreting process encountered in industry. The mathematical model of the problem and solution graph representation are presented. Several problem properties are formulated, including the time complexity of the goal function computation and block elimination property. Three solving methods, an exact Branch and Bound algorithm, the Tabu Search metaheuristic, and a baseline Genetic Algorithm metaheuristic, are proposed. Experiments using Taillard-based problem instances are performed. Results show that, for the Tabu Search method, the neighborhood based on the proposed block property outperforms other neighborhoods and the Genetic Algorithm under the same time limit. Moreover, the Tabu Search method provided high quality solutions, with the gap to the optimal solution for the smaller instances not exceeding 2.3%.

Highlights

IntroductionThe Flow Shop Scheduling Problem (or FSSP), formulated in both permutation and non-permutation variants [1], remains one of the most well-known optimization problems in operations research
We considered the non-permutation Flow Shop Scheduling Problem with Time Couplings and makespan criterion, based on a real-life concreting process in industry
We presented a mathematical model and formulated several problem properties based on the graph representation, including the computation of the goal function and its complexity

Summary

Introduction

The Flow Shop Scheduling Problem (or FSSP), formulated in both permutation and non-permutation variants [1], remains one of the most well-known optimization problems in operations research. It is widely used for modeling theoretical and real-life problems in manufacturing and production planning [2]. In this problem, a number of jobs and machines are given. The objective is to determine a production schedule such that each job is processed on each machine in the same fixed order (given by the technological process) and the given criterion, usually the completion time of all jobs, is minimized

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