MIP Formulations for Flowshop Scheduling with Limited Buffers

Abstract

We focus on MIP-formulations for flowshop scheduling problems of the kind F _m | lwt | γ, with the restriction lwt indicating that jobs are allowed to wait on a fixed limited number of buffers between machine levels. Most of the models discussed in literature only consider permutation schedules, i.e., schedules in which jobs are processed in identical order on all machines. As these are not necessarily optimal in the general case, there is a need for models which are not restricted in this way. In this paper, we try to fill this gap by presenting a new model which allows overtaking of jobs between different machine levels. We introduce position-tracking variables, variables that describe the paths of the jobs between the positions on succeeding machine levels, and allow for a special branching strategy exploiting the particular structure of this model.

In order to exemplify our model’s applicability to various objectives, we consider three different objective functions. In particular, we discuss the minimization of the makespan, the sum of completion times, and the number of strand interruptions, an objective function which is highly important in steel industry. For all of these we present specific improvements to the formulation, yielding reasonable computation times on instances of practically relevant size and setting.