Rolling-horizon lot-sizing when set-up times are sequence-dependent

The challenging problem of efficient lot sizing on parallel machines with s equence-dependent set-up times is modelled using a new mixed integer progra mming (MIP) formulation that permits multiple set-ups per planning period. The resulting model is generally too large to solve optimally and, given th at it will be used on a rolling horizon basis with imperfect demand forecas ts, approximate models that only generate exact schedules for the immediate periods are developed. Both static and rolling horizon snapshot tests are carried out. The approximate models are tested and found to be practical ro lling horizon proxies for the exact model, reducing the dimensionality of t he problem and allowing for faster solution by MIP and metaheuristic method s. However, for large problems the approximate models can also consume an i mpractical amount of computing time and so a rapid solution approach is pre sented to generate schedules by solving a succession of fast MIP models. Te sts show that this approach is able to produce good solutions quickly.