On Allocation of Tasks with Different Learning Slopes to Stations in Assembly Line for Lots

This paper addresses the problem of allocating work elements with various learning slopes to stations to minimize the makespan of many products produced in an assembly line for lots. The lots are characterized by a low overall demand for each product. There is no buffer permitted in between the stations, and the line operates under learning. Due to the nature of work, station's learning slopes can be different. We propose a two stage optimization methodology: the first stage is an optimization based on a non-linear formulation for work allocation with some constraints relaxation; the second stage drops the relaxations and finds a solution that is the closest to the unconstrained solution found in the first stage. We show that in the presence of learning, the optimal makespan requires assigning different work loads to different stations. This difference depends on the number of cycles in the lot, the station's learning slope, and the station's location along the line. The savings in the optimal makespan value due to the imbalanced loading of work over the balanced loading case are demonstrated.