Matheuristic Algorithm for Job-Shop Scheduling Problem Using a Disjunctive Mathematical Model

Eduardo Guzman,Raul Poler,Beatriz Andres

doi:10.3390/computers11010001

Abstract

This paper focuses on the investigation of a new efficient method for solving machine scheduling and sequencing problems. The complexity of production systems significantly affects companies, especially small- and medium-sized enterprises (SMEs), which need to reduce costs and, at the same time, become more competitive and increase their productivity by optimizing their production processes to make manufacturing processes more efficient. From a mathematical point of view, most real-world machine scheduling and sequencing problems are classified as NP-hard problems. Different algorithms have been developed to solve scheduling and sequencing problems in the last few decades. Thus, heuristic and metaheuristic techniques are widely used, as are commercial solvers. In this paper, we propose a matheuristic algorithm to optimize the job-shop problem which combines a genetic algorithm with a disjunctive mathematical model, and the Coin-OR Branch & Cut open-source solver is employed. The matheuristic algorithm allows efficient solutions to be found, and cuts computational times by using an open-source solver combined with a genetic algorithm. This provides companies with an easy-to-use tool and does not incur costs associated with expensive commercial software licenses.

Highlights

Research Centre on Production Management and Engineering (CIGIP), Universitat Politècnica de València (UPV), Abstract: This paper focuses on the investigation of a new efficient method for solving machine scheduling and sequencing problems
This review revealed that the most widely used metaheuristics are led by genetic algorithms and tabu search algorithms
Step 1: set the input parameters of the matheuristic (GA-linear programming (LP)); Step 2: generate the initial population: generate individuals using dispatching heuristic rules and generate individuals randomly; Step 3: evaluate whether the individuals forming the initial population are feasible; Step 4: eliminate nonviable individuals and insert the feasible ones into the population; Step 5: convert the integer chromosome generated by the genetic algorithm (GA) into a binary chromosome; Step 6: evaluate binary individuals using the LP model; Step 7: normalize individuals’ fitness; Step 8: select two individuals from the population and use genetic operators; Step 9 evaluate the chromosomes of the offspring and check if chromosomes are feasible

Summary

Introduction

Research Centre on Production Management and Engineering (CIGIP), Universitat Politècnica de València (UPV), Abstract: This paper focuses on the investigation of a new efficient method for solving machine scheduling and sequencing problems. The matheuristic algorithm allows efficient solutions to be found, and cuts computational times by using an open-source solver combined with a genetic algorithm. This provides companies with an easy-to-use tool and does not incur costs associated with expensive commercial software licenses. Researchers are showing much interest in improving the performance of enterprises and SC to generally cope with these dynamic environments by devising mechanisms and techniques that provide SMEs with affordable tools in cost, easy-to-use and computational efficiency terms. The search for solutions for company scheduling problems, such as jobshop scheduling problems (JSP), remains a relevant research topic [3] This is because most of these real-world scheduling problems are too complex to be optimally solved and are often NP-hard. This means that exact techniques and some algorithms cannot solve them

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