A line balancing problem with parallel workers and cycle time minimization

We study the problem of balancing assembly lines with parallel workers, motivated by features observed at a third-party logistics provider. The assembly line differs from the two known types of line balancing problems in the literature since it determines simultaneously the line cycle time and the number of workers per station. Furthermore, each station can be occupied by more than one worker and a restriction on the minimum number of stations is imposed. This new type of line balancing problem minimizes the line cycle time, where two types of decisions must be made: how to group the tasks into stations and how many workers to assign to each station. We adapt mathematical models based on assembly line balancing problems with parallel stations. Furthermore, we propose a new model based on network flow formulations for the special case of lines with a serial task structure, frequently observed at the company. We perform an extensive computational study with realistic instances in order to compare the speed of solving different formulations, which is important as such a problem is at the operational level. We also provide a sensitivity analysis of key parameters aiming to better understand the trade-offs and provide meaningful managerial insights.