Lagrangian Relaxation for Flow Shop Scheduling
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.
KeywordsTravel Salesman Problem Flow Shop Lagrangian Relaxation Lagrange Dual Integrality Property
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