# Assembly line balancing with task division

## TL;DR

This paper introduces the Task Division Assembly Line Balancing Problem (TDALBP), a new variant allowing limited task division with penalties, which can reduce the number of stations needed in assembly lines.

## Contribution

It proposes a mathematical model and exact solution method for TDALBP, demonstrating potential improvements over traditional SALBP solutions.

## Key findings

- Task division can reduce the number of stations needed.
- The proposed model effectively solves TDALBP instances.
- Significant performance improvements are possible with task division.

## Abstract

In a commonly-used version of the Simple Assembly Line Balancing Problem (SALBP-1) tasks are assigned to stations along an assembly line with a fixed cycle time in order to minimize the required number of stations. It has traditionally been assumed that the total work needed for each product unit has been partitioned into economically indivisible tasks. However, in practice, it is sometimes possible to divide particular tasks in limited ways at additional time penalty cost. Despite the penalties, task division where possible, now and then leads to a reduction in the minimum number of stations. Deciding which allowable tasks to divide creates a new assembly line balancing problem, TDALBP (Task Division Assembly Line Balancing Problem). We propose a mathematical model of the TDALBP, an exact solution procedure for it and present promising computational results for the adaptation of some classical SALBP instances from the research literature. The results demonstrate that the TDALBP sometimes has the potential to significantly improve assembly line performance.