Balancing manual mixed-model assembly lines using overtime work in a demand variation environment

This study deals with the balancing problem of a manual mixed-model assembly line, where the production volume or the product mix changes from shift to shift during the planning horizon. The unstable demand can be characterised by several representative scenarios, and the line uses overtime work to meet the demand variation. The balancing problem concerns how to assign assembly tasks to stations and determine the amount of overtime in each possible demand scenario. The objective is to satisfy the demand in each possible scenario with the minimum labour costs paid for both normal shifts and overtime work. A lower bound on the labour costs is proposed, and a heuristic algorithm is developed to quickly find a feasible solution. A branch, bound and remember (BB&R) algorithm is then proposed to find better solutions. These solution methods are tested on 765 instances. The BB&R algorithm obtains optimal solutions for 510 instances and gives high-quality solutions for the remaining 255 instances within 60 s. The experimental results show that the use of overtime work and adjustable cycle times significantly reduces the labour costs, especially when the demand or task processing time variations are large.