A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

  • Authors:

  • Gabriella Stecco;Jean-François Cordeau;Elena Moretti

  • Affiliations:

  • Department of Applied Mathematics, University Ca' Foscari of Venice, Dorsoduro n. 3825/E, 30123 Venice, Italy;Canada Research Chair in Logistics and Transportation, HEC Montréal 3000 chemin de la Côte-Sainte-Catherine, Montréal, Canada H3T 2A7;Department of Applied Mathematics, University Ca' Foscari of Venice, Dorsoduro n. 3825/E, 30123 Venice, Italy

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2008

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Abstract

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.