Mathematical formulations for the optimal sequencing and lot sizing in multiproduct synchronous assembly lines

The study of multiproduct assembly lines producing several models in a series of runs or campaigns is of special interest to modern industries. Assuming that the assembly line makes synchronous movements between workstations, it is particularly important to determine the best sequence and size of lots that permit to fulfill product demands at minimum total cost. Different products usually have different cycle times yielding productivity reductions during transition periods. This work presents an optimization approach based on a mixed-integer nonlinear mathematical programming (MINLP) model aiming at optimizing the operational cost of multi-product synchronous assembly lines. The formulation provides a detailed representation of the production steps, accounting for the cycle time of every unit moving along the assembly line. It can also be applied to mixed model assembly lines, with no changeovers. We propose a two-stage solution strategy involving a preliminary estimation of the lot sizes followed by a detailed representation of the production cycles, whose convergence is improved by adding efficient integer cuts. This model overcomes the shortcomings of previous approaches based on the representation of production campaigns over continuous domains. We assess the effectiveness of the solution strategies by solving a variety of real sized problems.