Minimizing the total tardiness and makespan in an open shop scheduling problem with sequence-dependent setup times

Samaneh Noori-Darvish,Reza Tavakkoli-Moghaddam

doi:10.1186/2251-712x-8-25

Abstract

We consider an open shop scheduling problem with setup and processing times separately such that not only the setup times are dependent on the machines, but also they are dependent on the sequence of jobs that should be processed on a machine. A novel bi-objective mathematical programming is designed in order to minimize the total tardiness and the makespan. Among several multi-objective decision making (MODM) methods, an interactive one, called the TH method is applied for solving small-sized instances optimally and obtaining Pareto-optimal solutions by the Lingo software. To achieve Pareto-optimal sets for medium to large-sized problems, an improved non-dominated sorting genetic algorithm II (NSGA-II) is presented that consists of a heuristic method for obtaining a good initial population. In addition, by using the design of experiments (DOE), the efficiency of the proposed improved NSGA-II is compared with the efficiency of a well-known multi-objective genetic algorithm, namely SPEAII. Finally, the performance of the improved NSGA-II is examined in a comparison with the performance of the traditional NSGA-II.

Highlights

An open shop scheduling problem (OSSP) is a kind of shop scheduling such that the operations can be executed in any order
The efficiency of this algorithm is first compared with the efficiency of a well-known multi-objective genetic algorithm, namely strength-Pareto evolutionary algorithm (SPEA)-II, by using the design of experiments (DOE)
The results have indicated the better performance of the improved non-dominated sorting genetic algorithm II (NSGA-II) based on three performance metrics

Summary

Introduction

An open shop scheduling problem (OSSP) is a kind of shop scheduling such that the operations can be executed in any order. The open shop allows much flexibility in scheduling, but it is difficult to develop rules that give an optimum sequence for every problem (Sule 1997). This problem is a class of NP-hard ones Setup times affect on the completion time of each job. Allahverdi et al (2008) surveyed the literature of setup times or costs in scheduling problems. They classified scheduling problems into those with batching and nonbatching considerations as well as sequence-independent and sequence-dependent setup times.

Methods

Results

Conclusion