Sequencing with limited flexibility

Maher Lahmar, Saif Benjaafar

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


We consider the problem of resequencing a set of prearranged jobs when there is limited resequencing flexibility and sequence-dependent changeover costs. Resequencing flexibility is limited by how far forward or backward a job can shift in the sequence relative to its original position. We show how the problem can be solved using dynamic programming in polynomial time with respect to the number of jobs. We also show how the same solution approach can be extended to problems where sequencing constraints are job specific and to problems where job features, which determine changeover costs, are jointly determined with the job sequence. We provide an integer programming formulation to the resequencing problem whose linear programming relaxation offers a useful lower bound. We also describe a family of decomposition heuristics that are easy to customize to provide desired levels of solution quality and solution time. We document the quality of the lower bound from the linear programming relaxation and the upper bound from the heuristic using numerical results. We also provide numerical results to support managerial insights regarding the value of flexibility. We show that the value of flexibility is of the diminishing kind with most of the benefit realized with relatively limited flexibility. We also show that a balanced allocation of flexibility among forward and backward position shifting is superior to an unbalanced one. More significantly, we show that forward and backward position shifting flexibility are complements with the value of one increasing in the amount of the other. Finally, we apply our solution approach to a real-world case from the automotive industry.

Original languageEnglish (US)
Pages (from-to)937-955
Number of pages19
JournalIIE Transactions (Institute of Industrial Engineers)
Issue number10
StatePublished - Oct 2007

Bibliographical note

Funding Information:
This research is supported by grants from the National Science Foundation and the Air Force Office of Scientific Research.


  • Automotive industry
  • Feature assignment
  • Flexibility
  • Sequencing
  • Traveling salesman problem


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