A mathematical model and a genetic algorithm for two-sided assembly line balancing
Introduction
Assembly line balancing (ALB) is the problem of assigning tasks to the workstations (stations, hereafter), while optimizing one or more objectives without violating restrictions imposed on the line. This paper considers two-sided ALB (two-ALB) problems, as shown in Fig. 1. Different assembly tasks on the same product item can be performed in parallel at both sides of the line. Such two-sided assembly lines are typically found in the production of large products, such as trucks and buses. A pair of two directly facing stations, such as station (1, 1) and (1, 2), is called a mated-station, and one of them calls the other a companion. A two-sided assembly line in practice can provide the following advantages over a one-sided assembly line: shorter line length, reduced throughput time, lower cost of tools and fixtures, and less material handling [1].
Two-ALB differs from traditional one-sided ALB (one-ALB), often called simple ALB problem, in that tasks have restrictions on the operation directions. Some assembly operations prefer one of the two sides, while others can be performed at either side of the line. That is, the tasks are classified into three types: L (left), R (right), and E (either) -type tasks. For example, in a truck assembly line of an automotive plant, such tasks as installing fuel tanks, air filters, and tool boxes are L-type tasks since these can be more easily performed at the left-hand side of the line, while mounting batteries, air tanks, and mufflers are R-type tasks. E-type tasks include assembling axles, propeller shafts, and radiators that do not have any preferred operation directions. Considering the operation directions is important to maximize the productivity of the assembly line since it can reduce material handling, workers movement, and set-up time.
The consideration of operation directions changes the way of handling precedence and cycle time restrictions. Idle time is sometimes unavoidable even between tasks assigned to the same mated-station [1]. Consider, for example, two tasks i and p such that p is an immediate predecessor of i. Suppose that i be assigned to station j and p to the companion of j. A worker at j cannot begin to work on task i unless task p is completed. Therefore, balancing the line needs to take into account the sequence-dependent finish time of tasks [2], unlike a one-sided assembly line. The sequence dependency influences cycle time. In this paper, the objective of two-ALB is to minimize the cycle time for a given number of mated-stations.
A large number of methods for solving ALB have been studied, including heuristic procedures [3], [4], [5], [6] and exact algorithms [5], [7], [8], [9]. Most of the methods have involved one-sided assembly lines. Although two-ALB problems are often encountered in the real world, little attention has been paid to these problems. As far as we know, Bartholdi [1] was the first to address two-ALB problems. He suggested a simple assignment rule, and developed an interactive program assisting humans to build solutions quickly and incrementally. Thereafter, a few studies on two-ALB [2], [10], [11], [12] were performed. A genetic algorithm (GA) [2] and an ant-colony-based heuristic [13] were suggested to solve two-ALB problems. Hu et al. [10] proposed an enumerative algorithm that is integrated with the Hoffmann heuristic [14]. Lee et al. [11] addressed the problem of maximizing work relatedness and slackness in balancing the line and presented a procedure for the problem. Lapierre and Ruiz [12] dealt with the problem of balancing a two-sided assembly line with two different heights and solved it with a priority-based heuristic.
The purpose of this paper is twofold: (1) to present a mathematical formulation for two-ALB problems with the objective of minimizing the cycle time for a given number of mated-stations, and (2) to develop a GA to efficiently solve the problem considered here. To the best of our knowledge, no mathematical formulation for two-ALB problems has yet been reported. Kim et al. [2] proposed a GA for two-ALB, but in this paper we use the distinct main framework of GA to improve the search capability and deal with the different ALB type in order to minimize the cycle time, not to minimize the number of stations. In the GA proposed in this paper, genetic encoding and decoding schemes, and genetic operators suitable for the problem addressed in this paper are devised. The proposed algorithm is compared with the GA with the same framework used in Kim et al. [2] as well as the assignment procedure based on the rule proposed by Bartholdi [1] in terms of solution quality and convergence speed. Extensive experiments are performed to verify the efficacy of the proposed algorithm.
The remainder of this paper is organized as follows. The mathematical formulation for two-ALB is presented in Section 2, the proposed algorithm in Section 3, and the experimental design and results in Section 4. Concluding remarks follow in Section 5.
Section snippets
Notation
The notation used in this paper follows the convention in Baybars [7]:
- I:
set of tasks; .
- J:
set of mated-stations; .
- :
a station of mated-station j and its operation direction is k.
- :
set of tasks which should be performed at a left station; .
- :
set of tasks which should be performed at a right station; .
- :
set of tasks which can be performed at either a left or a right station; . , and are mutually
Genetic algorithm
A GA is presented here to solve the two-ALB. The algorithm is a stochastic procedure that imitates the biological evolutionary process of genetic inheritance and the survival of the fittest. In the algorithm, we adopt the strategy of localized evolution that we expect can promote population diversity and search efficiency. The population forms a two-dimensional structure of toroidal grids. The structure of a neighborhood is used here for the localized evolution. Let denote the
Test-bed problems and parameter setting
The search capability of the GA proposed in this paper (n-GA) was analyzed with six test-bed problems: three small-sized problems, P12, P16, and P24; and three relatively large-sized problems, P65, P148, and P205. P12, P16, and P24 are shown in Figs. 2 and 4(a) and (b), respectively. P65 and P205 are formulated by the authors for a truck assembly line of AAA automotive company. The problems can be found in Lee et al. [11]. P148 is constructed by Bartholdi [1]. In P148, the processing times of
Summary and conclusion
This paper has addressed two-ALB with the objective of minimizing cycle time for a fixed number of mated-stations. A mathematical model for two-ALB has been presented. While modelling the problems, we tried to reduce the number of constraints, in order to produce a more compact MIP. A GA is also proposed to efficiently solve two-ALB within a reasonable computational time. In the algorithm, we adopt the strategy of localized evolution and steady-state reproduction to promote population diversity
References (21)
- et al.
State-of-the art exact and heuristic solution procedures for simple assembly line balancing
European Journal of Operational Research
(2006) - et al.
Balancing assembly lines with tabu search
European Journal of Operational Research
(2006) - et al.
Maximizing the production rate in simple assembly line balancing—a branch and bound procedure
European Journal of Operational Research
(1996) - et al.
A station-oriented enumerative algorithm for two-sided assembly line balancing
European Journal of Operational Research
(2008) - et al.
Two-sided assembly line balancing to maximize work relatedness and slackness
Computers & Industrial Engineering
(2001) - et al.
An enumerative heuristic and reduction methods for the assembly line balancing problem
European Journal of Operational Research
(2003) - et al.
A symbiotic evolutionary algorithm for the integration of process planning and job shop scheduling
Computers & Operations Research
(2003) A study of reproduction in generational and steady-state genetic algorithms
Balancing two-sided assembly lines: a case study
International Journal of Production Research
(1993)- et al.
Two-sided assembly line balancing: a genetic algorithm approach
Production Planning and Control
(2000)
Cited by (180)
Multi-manned assembly line balancing problem with dependent task times: a heuristic based on solving a partition problem with constraints
2022, European Journal of Operational ResearchAssembly line balancing: What happened in the last fifteen years?
2022, European Journal of Operational ResearchHarmonizing ergonomics and economics of assembly lines using collaborative robots and exoskeletons
2022, Journal of Manufacturing SystemsAn exact solution method for multi-manned disassembly line design with AND/OR precedence relations
2021, Applied Mathematical ModellingLoad Balancing of Two-Sided Assembly Line Based on Deep Reinforcement Learning
2023, Applied Sciences (Switzerland)