SALSA: Combining branch-and-bound with dynamic programming to smoothen workloads in simple assembly line balancing

Abstract We consider a version of the well-known simple assembly line balancing problem (called SALBP-SX) where, given the cycle time and the number of stations, the workloads of the stations are to be leveled according to an adequately defined smoothness index SX. Our index SX involves for each station the quadratic deviation of its workload from the average (or ideal) workload and is therefore closely related to the variance, which is a common measure of dispersion in statistics. Contrary to the existing literature on workload smoothing in ALB, which often treats the optimization of a prespecified smoothness index as a secondary objective, we consider our SX-objective as the single one in order to account for the practical relevance of fair workload distributions and avoiding overloaded bottleneck stations. To optimally solve SALBP-SX, we develop a tailored branch-and-bound procedure. It contains a new station-oriented branching scheme, new lower bound arguments, logical tests and, in particular, a dynamic programming scheme for the pre-calculation of potential workloads, which accelerates the procedure greatly. In comprehensive computational experiments, we show that our method clearly outperforms a class of recently developed task-oriented branch-and-bound procedures and also the mathematical programming solver Gurobi.