Improved integer programming models for simple assembly line balancing and related problems

TL;DR

This paper introduces a stronger integer programming formulation for simple assembly line balancing that improves solution quality and can be applied to related problems like U-shaped line balancing and bin packing with precedence constraints.

Contribution

It proposes a new formulation with enhanced precedence constraints and station limits, outperforming previous models in solution quality and applicability.

Findings

Linear relaxation dominates previous formulations.

Produces significantly better solutions in practice.

Effective for related problems like U-shaped balancing and bin packing.

Abstract

We propose a stronger formulation of the precedence constraints and the station limits for the simple assembly line balancing problem. The linear relaxation of the improved integer program theoretically dominates all previous formulations using impulse variables, and produces solutions of significantly better quality in practice. The improved formulation can be used to strengthen related problems with similar restrictions. We demonstrate their effectiveness on the U-shaped assembly line balancing problem and on the bin packing problem with precedence constraints.