A branch, price and remember algorithm for the U shaped assembly line balancing problem

TL;DR

This paper introduces a novel branch, price, and remember algorithm that effectively solves the U-shaped assembly line balancing problem by combining column generation with memory and a modified Hoffman algorithm, outperforming previous methods.

Contribution

The paper presents a new algorithm integrating column generation with memory and a modified Hoffman algorithm for improved solution quality and efficiency in U-shaped assembly line balancing.

Findings

Solved 255 of 269 benchmark problems optimally

Outperforms previous best algorithm ULINO on benchmark problems

Achieved 96.48% success rate on a new dataset

Abstract

In this paper we propose a branch, price and remember algorithm to solve the U shaped assembly line balancing problem. Our proposed algorithm uses a column generation approach to obtain tight lower bounds for this problem. It also stores generated columns in memory to enhance the speed of column generation approach. We also develop a modification of Hoffman algorithm to obtain high quality upper bounds. Our computational results show that our proposed algorithm is able to optimally solve 255 of Scholl's well-known 269 benchmark problems. Previous best known exact algorithm, ULINO, is able to solve 233 of the 269 benchmark problems. We also examined our algorithm on a new data set and the results show that our algorithm is able to solve 96.48 percent of all available benchmark problems.