ASALBP: the alternative subgraphs assembly line balancing problem

Abstract

Assembly line balancing problems basically consist in assigning a set of tasks to a group of workstations while maintaining the tasks' precedence relations, which are represented by a predetermined precedence graph. However, one or more parts of a product's assembly process may admit alternative precedence subgraphs, which represent possible assembly variants. In general, because of the great difficulty of the problem and the impossibility of representing alternative subgraphs in a precedence graph, the system designer will decide to select, a priori, one of such alternative subgraphs. This paper presents, characterizes and formulates a new general assembly line balancing problem with practical relevance: the Alternative Subgraphs Assembly Line Balancing Problem (ASALBP). Its novel characteristic is that it considers the possibility of having alternative assembly subgraphs, with the processing times and/or the precedence relations of certain tasks dependent on the assembly subgraph selected. Therefore, solving this problem implies simultaneously selecting an assembly subgraph for each part of the assembly that allows alternatives and balancing the line. The potentially positive effects of this on the solution of the problem are shown in a numerical example. Finally, a simple mathematical programming model is described and the results of a brief computational experiment are presented.

Optimally solving the alternative subgraphs assembly line balancing problem

“…The new problem ASALBP, introduced by Capacho and Pastor (2005), overcomes this drawback as it considers processing alternatives within the precedence graph such that selecting the processes and assigning tasks to stations is done simultaneously. Up to now, the problem has been defined and modelled in a restricted version (Capacho and Pastor 2005) and an extended version Pastor 2006, 2007).…”

“…Of course, this approach can be rather inefficient, because SALBP is an NP-hard problem itself and PN might be very large as it requires completely combining all possible subgraphs. Facing this fact, Capacho and Pastor (2005) take it for granted that solving ASALBP by iteratively solving the underlying SALBP instances is not useful at all. This assumption might be justified for the just mentioned uninformed solution approach.…”

“…Up to now, the problem has been defined and modelled in a restricted version (Capacho and Pastor 2005) and an extended version Pastor 2006, 2007). Furthermore, constructive heuristic methods have been developed and tested comprehensively by .…”

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

“…When the production alternative has been selected (i.e., the complete assembly process has been defined) and a single precedence graph is available, the problem is then balanced in a second stage. (Capacho & Pastor, 2008) illustrated, by means of numerical examples, how by selecting a priory an alternative, it cannot be guaranteed that an optimal solution of the global problem will be obtained, because the best solution of a problem can be discarded if it does not meet the selection criteria. For instance, it was shown that the alternative assembly variant with the longest processing time required the smallest number of workstations for a given cycle time.…”

The ASALB Problem with Processing Alternatives Involving Different Tasks: Definition, Formalization and Resolution

“…The Alternative Subgraphs Assembly Line Balancing Problem (ASALBP) considers assembly alternatives that determine task processing times and/or precedence relations among the tasks. Capacho and Pastor [3] formalized this problem and developed a mathematical programming model (MILP) in which the assembly alternatives are determined by combining all available processing alternatives of each existing sub-assembly. In this paper an extended definition of the ASALBP is presented in which assembly subprocesses involving different tasks are also considered.…”