Lagrangian Relaxation for Flow Shop Scheduling

  • George G. Polak
Part of the Applied Optimization book series (APOP, volume 16)


Job shop scheduling encompasses combinatorial problems of extraordinary difficulty. The special structure of a flow shop, in which the machines can be ordered in series, offers some advantages. Employing the disjunctive graph as a model of a flow shop, we proceed to formulate a mixed integer model for the problem of minimizing the makespan. By decomposing the model into unlinked one-machine sequencings without due dates, Lagrangian relaxation introduces subproblems amenable to the greedy algorithm. Moreover, since the subproblems do not have the integrality property, the Lagrangian bound can be stronger than the LP bound.


Travel Salesman Problem Flow Shop Lagrangian Relaxation Lagrange Dual Integrality Property 
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Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • George G. Polak
    • 1
  1. 1.Department of Management Science and Information SystemsWright State UniversityDaytonUSA

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