MIP formulations for flowshop scheduling with limited buffers

  • Authors:

  • Janick V. Frasch;Sven Oliver Krumke;Stephan Westphal

  • Affiliations:

  • Interdisciplinary Center for Scientific Computing, University of Heidelberg, Heidelberg, Germany and Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany;Institute for Numerical and Applied Mathematics, Georg-August University, Göttingen, Germany

  • Venue:
  • TAPAS'11 Proceedings of the First international ICST conference on Theory and practice of algorithms in (computer) systems
  • Year:
  • 2011

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Abstract

We focus on MIP-formulations for flowshop scheduling problems of the kind Fm|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.