A survey on Benders Decomposition methods applied to Assembly Line Balancing Problems

Abstract

The assembly line balancing problem (ALBP) assigns tasks to (work)stations to manufacture products. It divides the station loads as evenly as possible since any bottleneck defines the production rate of a flow shop system. The sum of task processing times represents the station load in the classical Simple Assembly Line Balancing Problem (SALBP). Thus, the most loaded station imposes a lower bound on the line's cycle time. However, the simple sum of processing times is only valid under several assumptions. For instance, more realistic ALBPs may contain stochastic data, multiple workers per station, or depend on the production sequence. Hence, the station load computation involves further scheduling decisions for this latter class of problems. In order to tackle these ALBPs with practical extensions, several literature contributions have recently employed Benders decomposition (BD) algorithms. The BD structure allows a division of the formulation into two or more levels. More specifically, this framework permits the decoupling of task assignment decisions and cycle time assessments. In the field of ALBPs, various stochastic and sequence-dependent problems have successfully applied this approach. This paper provides a literature review of these methods, the different formulations, implementation details, and improvement ideas.