A hybrid PSO algorithm for a multi-objective assembly line balancing problem with flexible operation times, sequence-dependent setup times and learning effect Nima Hamta a , S.M.T. Fatemi Ghomi a,n , F. Jolai b , M. Akbarpour Shirazi a a Department of Industrial Engineering, Amirkabir University of Technology, 424 Hafez Avenue, 1591634311, Tehran, Iran b Department of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran article info Article history: Received 4 October 2011 Accepted 9 March 2012 Available online 16 March 2012 Keywords: Assembly line balancing Multi-objective optimization Hybrid PSO Flexible operation times Learning effect Sequence-dependent setup times abstract This paper addresses multi-objective (MO) optimization of a single-model assembly line balancing problem (ALBP) where the operation times of tasks are unknown variables and the only known information is the lower and upper bounds for operation time of each task. Three objectives are simultaneously considered as follows: (1) minimizing the cycle time, (2) minimizing the total equipment cost, and (3) minimizing the smoothness index. In order to reflect the real industrial settings adequately, it is assumed that the task time is dependent on worker(s) (or machine(s)) learning for the same or similar activity and sequence-dependent setup time exists between tasks. Finding an optimal solution for this complicated problem especially for large-sized problems in reasonable computational time is cumbersome. Therefore, we propose a new solution method based on the combination of particle swarm optimization (PSO) algorithm with variable neighborhood search (VNS) to solve the problem. The performance of the proposed hybrid algorithm is examined over several test problems in terms of solution quality and running time. Comparison with an existing multi-objective evolutionary computation method in the literature shows the superior efficiency of our proposed PSO/VNS algorithm. & 2012 Elsevier B.V. All rights reserved. 1. Introduction Assembly line balancing problem (ALBP) has been studied for more than 50 years and different lines with various considera- tions have been investigated up to now. The balancing of assembly lines has significant effects on the performance and productivity of manufacturing systems and has been widely enriched over the past several decades. An assembly line contains a limited set of tasks, each having a certain operation time in the presence of a set of precedence relations. The purpose of the assembly line balancing problem is to assign these tasks to workstations in such a way that the precedence relations are not violated and some effectiveness measures (such as cycle time, number of workstations, line efficiency or idle time) are optimized (Erel and Sarin, 1998). The first scientific study in the ALBP was published by Salveson (1955). Since then, different approaches were proposed enriching the ALBP and many attempts were made to reduce the wide gap between the academic discussion and realistic situation. There are different published surveys on the ALBP in the literature (Ghosh and Gagnon, 1989; Becker and Scholl, 2006; Boysen et al., 2007; Boysen et al., 2008). Most of the researches assumed that the operation time of tasks is deterministic. However, in many real-world situations, tasks’ operation times are rarely fixed and may vary more or less. So in this paper, operation times of tasks are regarded as unknown variables while the only known information is the lower and upper bounds for the operation time of each task. Hamta et al. (2011) called this type of processing time as flexible operation time. In a similar mode, Allahverdi (2006) consi- dered all setup times and job processing times as unknown variables between lower and upper limits in the two-machine flow- shop scheduling problem. In this paper, we assume that compres- sing the operation times causes higher equipment cost due to cumulative wear, erosion, depreciation and so on. Following the classification of Boysen et al. (2007), ALBP can be classified into three groups in terms of the number of models: in single-model ALBP, only one product is manufactured in the lines; in mixed-model ALBP, varying models of one product are assembled on the same assembly processes; and multi-model ALBP considers manufacturing different products in batches. In the optimization of ALBPs, one or more objectives are considered to evaluate solutions. Recently, multi-objective (MO) optimization has attracted the research attention in comparison with single- objective problems (Nearchou, 2008; Cakir et al., 2011; Kara et al., 2011). The most well-known objective functions are minimizing the cycle time, minimizing the number of workstations, maximiz- ing the line efficiency (productive part of the line capacity) (Boysen Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics 0925-5273/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijpe.2012.03.013 n Corresponding author. Tel.: þ98 2164545381; fax: þ98 2166954569. E-mail address: fatemi@aut.ac.ir (S.M.T. Fatemi Ghomi). Int. J. Production Economics 141 (2013) 99–111