Two branch-and-bound algorithms for the robust parallel machine scheduling problem

  • Authors:

  • Mohammad Ranjbar;Morteza Davari;Roel Leus

  • Affiliations:

  • Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;Department of Industrial Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, Iran;Research group ORSTAT, Faculty of Business and Economics, KULeuven, Belgium

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2012

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Abstract

Uncertainty is an inevitable element in many practical production planning and scheduling environments. When a due date is predetermined for performing a set of jobs for a customer, production managers are often concerned with establishing a schedule with the highest possible confidence of meeting the due date. In this paper, we study the problem of scheduling a given number of jobs on a specified number of identical parallel machines when the processing time of each job is stochastic. Our goal is to find a robust schedule that maximizes the customer service level, which is the probability of the makespan not exceeding the due date. We develop two branch-and-bound algorithms for finding an optimal solution; the two algorithms differ mainly in their branching scheme. We generate a set of benchmark instances and compare the performance of the algorithms based on this dataset.