# An Entropy-based Mathematical Formulation for Straight Assembly Line Balancing Problem

DOI: 10.4018/IJSDS.2016040104
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## Abstract

This paper focuses on formulating a typical simple assembly line balancing problem. A new objective function based on a nonlinear entropy function is considered for the simple assembly line balancing problem for the first time. This objective function force the stations to have more similar total task processing time, so that the workers of the stations will have similar work load. Using a bounded variable approach, the nonlinear objective function is converted to an approximated linear objective function. Finally, efficiency of the linearized formulation of the entropy-based assembly line balancing problem is tested by a numerical example.
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## 1. Introduction

Assembly lines play a critical role is productions systems. Automobile manufacturing industries, electronic devices assembly lines, home appliances production systems, etc. are some instances of the production systems which are based on assembly lines (Kumar et al., 2015). An assembly line contains a series of stations which each one includes one or several assembly activities (tasks). The initial parts of products of the line are given to the beginning of the line and go over the line’s stations to be converted to the final product after passing the last station. In order to complete a product on the assembly line, some related tasks must be performed according to their precedence relationships, therefore, the precedence graph of the tasks would be of the most important limitations that is considered to assign the tasks to the stations. In other words, a task must not be assigned to a station that is placed earlier than the station of its predecessors. The assembly line also should be run by an acceptable speed to be able to produce an amount of product which responds the annual demand of the product. Therefore, all the stations of the line should perform their jobs in a given time which is called “cycle time” of the line. The cycle time of the line is an upper bound for total task time of each of the stations. The problem of assigning the tasks to the stations is named assembly line balancing problem (ALBP) which is a crucial stage in designing an effective production assembly line.

Baybars (1986), categorized ALBPs into two main types as simple assembly line balancing problem (SALBP) and generalized assembly line balancing problem (GALBP). In the SALBP (see Scholl and Becker, 2006), the task times are deterministic and certain and also the total task time of each station should not exceed the cycle time of the line. It is supposed that all stations use the same tools and the same number of workers (manning level), therefore, it is possible to do a task in any station. The tasks should not be assigned to more than one station and a task cannot be divided over the stations. The constraints to be respected are only the precedence relationships of the tasks and the cycle time of the line. On the other hand, GALBPs (see Becker and Scholl, 2006), consider more limitations on the balancing problem e.g. physical shape of the line, physical limitations of the floor, variable cycle time, using parallel stations, etc. In ALBPs, the common objective functions are minimization of the number of stations, minimization of idle time of the stations, minimization of the cycle time, etc. Of course, these objectives may be combined and even in some studies the number of stations assumed to be predetermined.

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