Hybrid genetic algorithms with dispatching rules for unrelated parallel machine scheduling with setup time and production availability

https://doi.org/10.1016/j.cie.2015.02.029Get rights and content

Highlights

  • We study unrelated parallel machine scheduling with setup and production availability.

  • We derive a mixed integer programming model for the problem.

  • We propose hybrid genetic algorithms (HGAs) with three dispatching rules.

  • We evaluate the performances of the GAs using randomly generated examples.

Abstract

This article considers the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times and machine-dependent processing times. Furthermore, the machine has a production availability constraint to each job. The objective of this problem is to determine the allocation policy of jobs and the scheduling policy of machines to minimize the total completion time. To solve the problem, a mathematical model for the optimal solution is derived, and hybrid genetic algorithms with three dispatching rules are proposed for large-sized problems. To assess the performance of the algorithms, computational experiments are conducted and evaluated using several randomly generated examples.

Introduction

Companies that manufacture goods based on orders generally have several machine groups consisting of simple-purpose machines or general-purpose machines that are similar function but differ shape and performance. Therefore, each (ordering) job can or cannot be processed on a specific machine, and the processing time of the job depends upon the machine to which it is assigned. This physical limitation of machines is called production availability constraint of the machine. In the manufacturing companies, the consideration of setup times between jobs is dependent upon not only the sequence of jobs to be processed on a machine but also the machine to which the jobs are assigned. In this article, we consider unrelated parallel machine scheduling with sequence- and machine-dependent setup times, machine dependent processing times, and production availability constraints.

Several studies have investigated unrelated parallel machines without consideration of setup time. Rogendran and Subur (2004) proposed a tabu-search-based heuristic minimizing the total weighted tardiness in the unrelated parallel machine scheduling problem with job splitting and dynamic machine availability. Agarwal, Colak, Jacob, and Pirkul (2006) suggested 12 combinations of single-pass heuristics and a neural network approach for minimizing a makespan for non-identical parallel machines. Balin (2011) presented a genetic algorithm (GA) for non-identical parallel machine scheduling to minimize the makespan of the machines without having setup times, ready times, and due times. In this article, the authors propose a new crossover operator and a new optimality criterion in order to adapt GA to the non-identical parallel machine scheduling problem. Lin, Pfund, and Fowler (2011) also proposed a GA for unrelated parallel machine problem to minimize the total weighted tardiness. Lin, Lin, and Hsieh (2013) proposed ant colony optimization incorporating a number of new ideas such as heuristic initial solution, machine reselection step, and local search procedure to solve the problem of scheduling unrelated parallel machine to minimize total weighted tardiness. Rodriguez, Lozano, Blum, and Garcia-Martinez (2013) proposed an iterated greedy algorithm for the large-scale unrelated parallel machine scheduling problem without consideration of setup. They tested instances with up to 1000 jobs and 50 machines and showed relatively good performance compared to other meta-heuristics. Yang, 2013, Yang and Yang, 2013, Yang et al., 2013, Yang et al., 2014 consider unrelated parallel-machine scheduling with several maintenance activities and deterioration effects to minimize the total completion time without set-up consideration.

On the other hand, several studies have investigated unrelated parallel machine scheduling problems with consideration of setup time. Weng, Lu, and Ren (2001) presented seven constructive procedures for the unrelated parallel machine scheduling problem for minimizing total completion time and performed an experimental comparison between them. Vredeveld and Hurkens (2002) proposed two meta-heuristics based on local search. The local search procedures make use of two types of different neighborhood functions. Kim, Kim, Jang, and Chen (2002) presented a scheduling problem for unrelated parallel machines with sequence- and machine-dependent setup times to minimize total tardiness using simulated annealing (SA). Hop and Nagarur (2004) considered non-identical parallel machines with sequence-dependent times to minimize makespan in a printed-circuit board (PCB) production line. They developed a mathematical model and propose a genetic algorithm. Li and Yang (2009) considered non-identical parallel machine scheduling to minimize total weighted completion time. Tavakkoli-Moghaddam, Taheri, Bazzazi, Izadi, and Sassani (2009) proposed a genetic algorithm for minimizing the number of tardy jobs and the total completion time constrained by minimizing the number of tardy jobs for an unrelated parallel machine scheduling problem with sequence-dependent and machine-dependent setup times, ready times, and due-times. Chen and Chen (2009) presented a hybrid metaheuristic combining tabu search and variable neighborhood descent to minimize the total weighted tardiness on unrelated parallel machine. Gharehgozli, Tavakkoli-Moghaddam, and Zaerpour (2009) presented a new mixed-integer goal programming model to minimize the total weighted flow time and the total weighted tardiness simultaneously for a non-identical parallel machine scheduling problem with sequence-dependent setup times, ready times, and due-times. Ko, Kim, Kim, and Baek (2010) proposed a dispatching rule that guarantees a predetermined minimum quality level for non-identical parallel machines with multiple product types. They only considered sequence-dependent setup times between product types. Vallada and Ruiz (2011) presented hybrid genetic algorithms to minimize makespan including a fast local search and a local search enhanced crossover operator based on a two-dimensional representation of a chromosome for the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup time. Ruiz and Andres-Romano (2011) investigated the unrelated parallel machine problem with resource-assignable sequence and machine dependent setup times. Their new characteristic is that the amount of setup time depends not only upon the machine and job sequence but also upon the number of resources assigned. The objective function of the study is a linear combination of the total completion time and the number of human resources assigned to the setup. They developed a mixed-integer programming (MIP) model and proposed some fast dispatching heuristics. Lin and Lin (2013) considered an unrelated parallel scheduling problem with sequence- and machine-dependent setup times and release date for minimizing makespan, total weighted completion time, and total weighted tardiness. They developed a mixed-integer programming model for an optimal solution and proposed several dispatching rules to find good solutions quickly.

To the best of our knowledge, the unrelated parallel machine scheduling problem with sequence- and machine-dependent set-up time and production availability of machines constraints has not been considered previously in the literature. The remainder of this article is organized as follows. After a brief problem description, a mathematical model for finding an optimal solution is derived in Section 2. As the solution approaches, hybrid GAs are proposed with three dispatching rules for assigning jobs to machines in Section 3. Section 4 evaluates the performances of the GAs on the basis of computational experiments. Finally, Section 5 summarizes the study and discusses for further research.

Section snippets

Mathematical model

In this section, we propose an MIP model for the unrelated parallel machine scheduling problem with sequence and machine dependent setup times, machine dependent processing times, and machine availability constraints. The objective is to minimize the total completion time of all jobs within a given working horizon. The following notations are used for the MIP model:

Indices
SJ: set of jobs to be scheduled.
SM: set of machines.
h,i,j: job indices, where h,i,jSJ.
k: machine index, where kSM.

Genetic algorithms

The MIP model presented in the previous section is not tractable for the unrelated parallel machine scheduling problem because it is a typical combinatorial optimization problem. Furthermore, the simplification of this model, the problem P|Sj|C is already NP-hard (Webster, 1997). Thus, we focus on developing effective meta-heuristic approaches instead, and propose GAs.

In a GA, the representation of a solution, a chromosome, has a great influence on the performance of the algorithm. The

Computational results

We conducted computational experiments using randomly generated test problems to evaluate the performances of the GAs proposed in this article. Since the complexity of a problem is highly dependent on the number of jobs, two problem groups are randomly generated according to the number of jobs. A small sized problem group, involving problem instances with the number of machines being 2, 3, and 4 and the average number of jobs per machine being 2, 3, and 4, is for comparing solutions obtained by

Conclusions

In this article, the unrelated parallel machine scheduling problem with sequence- and machine-dependent setup times, machine-dependent processing times, and production availability constraints was considered. The objective of our article is to find a schedule that minimizes the total completion time while simultaneously determining the assignment of jobs to available machines and the sequencing of assigned jobs on each machine. A MIP model is derived to search for the optimal solution. While

Acknowledgment

This work was supported by the Incheon National University Research Grant in 2014 (Grant No.: 20141205).

References (27)

Cited by (0)

This manuscript was processed by Area Editor Mitsuo Gen.

View full text