A MILP model for the Accessibility Windows Assembly Line Balancing Problem (AWALBP)

Abstract

This work studies a novel assembly line balancing problem that has recently appeared in the literature, which we name Accessibility Windows Assembly Line Balancing Problem (AWALBP). AWALBP is a real-world industrial problem that arises in those assembly lines where, as opposed to the most common ones, the length of the workpiece is larger than the widths of the workstation. This means that, at any time, a workstation cannot access one whole workpiece, but only a restricted portion of one or two consecutive workpiece. In our problem the cycle decomposes into stationary stages separated by forward steps, according to a cyclic movement scheme. The aim of this paper is (i) to formalise the AWALBP and its variants, and (ii) to propose a Mixed Integer Linear Programming (MILP) model using two alternative formulations to solve the variant AWALBP-L2. This variant involves solving the task assignment and the movement scheme sub-problems (with the objective of minimising the cycle time). An extensive computational experiment is carried out to study the behaviour of the proposed model for different instance sizes. To the best of our knowledge, this is the first work in the literature which provides optimal solutions for AWALBP-L2. In addition, a set of benchmark instances is provided, which can be further used by the research community.

Keywords:

• assembly line balancing
• accessibility windows