Mathematical Problems in Engineering

Volume 2016 (2016), Article ID 9315024, 20 pages

http://dx.doi.org/10.1155/2016/9315024

## Balancing Lexicographic Multi-Objective Assembly Lines with Multi-Manned Stations

Industrial Engineering Department, Engineering Faculty, Gazi University, Maltepe, 06570 Ankara, Turkey

Received 21 October 2015; Accepted 7 March 2016

Academic Editor: Martin J. Geiger

Copyright © 2016 Talip Kellegöz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In a multi-manned assembly line, tasks of the same workpiece can be executed simultaneously by different workers working in the same station. This line has significant advantages over a simple assembly line such as shorter line length, less work-in-process, smaller installation space, and less product flow time. In many realistic line balancing situations, there are usually more than one objective conflicting with each other. This paper presents a preemptive goal programming model and some heuristic methods based on variable neighborhood search approach for multi-objective assembly line balancing problems with multi-manned stations. Three different objectives are considered, minimizing the total number of multi-manned stations as the primary objective, minimizing the total number of workers as the secondary objective, and smoothing the number of workers at stations as the tertiary objective. A set of test instances taken from the literature is solved to compare the performance of all methods, and results are presented.

#### 1. Introduction

Assembly lines are mostly installed for producing products in high volumes and usually include automatic material handling system [1], tools, workers, and more than one workpiece. Therefore, in fact, assembly lines are designed by arranging all of their components. One of most important problems in this arrangement is to group tasks into stations. In this problem, there are some constraints, such as precedence restrictions between task pairs and cycle time constraints for stations. This grouping process is carried out for optimizing some objectives by fulfilling all of restrictions. The optimization problem of this process is called assembly line balancing problem (ALBP).

ALBPs which are strongly NP-hard [2] can be classified based on different criteria, such as line layout (straight lines, U lines, etc.), the number of models produced (single model, multimodel, mixed model, etc.), duration of tasks (deterministic, stochastic, etc.), the number of workers for each station (traditional lines, two sided lines, multi-manned lines, etc.), and the number of objectives considered (single objective, multi-objective, etc.). The reader is referred to the recent paper by Sivasankaran and Shahabudeen [3] for a comprehensive survey and classification of line balancing problems. Also, other well-crafted surveys can be found in papers by Lusa [4], Becker and Scholl [5], and Erel and Sarin [6].

In practice, products produced in assembly lines have different characteristics based on size, the number of tasks, demand structure, duration of tasks, and so forth. Therefore, different products may require different line structures which are briefly mentioned above. For example, consider the assembly processes of a computer keyboard and a bus. It is obvious that the production of the computer keyboard requires less number of tasks than the one of bus. Also, based on sum of task times, the keyboard has smaller flow time than the bus. On the other hand, more than one worker can perform tasks on the same bus workpiece while only one worker is usually allowed to perform tasks on the same keyboard workpiece. Therefore, for decreasing the flow time, tool cost, work-in-process cost, space used for the assembly line, and so forth, assembly lines with multi-manned workstations may be more suitable to produce large size products like bus in practice. Consider the problem with cycle time and precedence diagram given in Figure 1. By using the sum of task times , the lower bound value for the total number of stations for simple assembly line [15] and also for the total number of workers for multi-manned assembly line [7, 8] can be calculated as follows:For simple assembly line balancing problem with minimizing the number of stations (SALBP1), the optimum solution is given in Figure 2(a). As is seen from this figure, at least 5 stations are required to produce the goods with desired properties. There are 5 workpieces (and workers) in the line since there is a workpiece (a worker) at each one of these stations. For multi-manned assembly line balancing problem (MALBP) with minimizing the number of stations, the optimum solution is presented in Figure 2(b). In MALBP, determining a station for each task is necessary but not sufficient. To address a MALBP solution, a worker for each task and a sequence of tasks for each worker must also be obtained. As is seen from Figure 2, the multi-manned line requires less number of stations than the simple line. Hence, in multi-manned lines, same products may be produced by using less layout space, work-in-process, flow time, and so forth.