A Metaheuristic Approach to Solve the Alternative Subgraphs Assembly Line Balancing Problem

Abstract

Nowadays, assembly line balancing problems are commonly found in most manufacturing and production systems. In its basic form, an assembly line balancing problem consists of finding an assignment of tasks to a group of workstations in such a way that the precedence constraints among the tasks are maintained and the sum of the times of the task assigned to each workstation does not exceed the maximum workstation time (i.e. the cycle time). According to the objective considered, two variants of the problem are distinguished: (1) the problem aims at minimizing the number of workstations for a given cycle time and (2), given the number of workstations, the problem seeks to minimize the cycle time. Over the last years a significant amount of research work has been done towards solving assembly line balancing problems efficiently. Finding the best solution is a crucial task for maintaining the competitive advantage of industries and, in some cases, for their survival. Falkenauer (2005), pg. 360, argues that the efficiency difference between an optimal and a sub-optimal assignment can yield economies reaching millions of dollars per year. However, solving real life problems is a very difficult task for decision makers and practitioners since even the simple case is NP-hard by nature. For this reason, most assembly line balancing problems involve only a few aspects of the real systems (see, for example, (Becker & Scholl, 2006)). In order to deal with the complexity of industrial problems, a great variety of problem definitions (i.e. generalized assembly line balancing problems) have arisen, which consider other restrictions apart from the technological ones. Most common, these include mixed models, multiple products, different line layouts, parallel workstations and multiple objectives. However, real problems require tackling many of those generalizations simultaneously (Falkenauer, 2005). Such a consideration must also be taken into account when alternatives processes are involved. Alternatives may appear when, for example, new technologies are taking place in a production system, in which different procedures are available to complete a production unit, or when the processing order affects the processing times of certain tasks; i.e., the realization of one task facilitates, or makes more difficult, the completion of other tasks (see, for example, (Scholl et al., 2008) and (Das & Nagendra, 1997)).