Abstract
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.
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References
J. Adams, E. Balas, and D. Zawack, 1988, The Shifting Bottleneck Procedure for Job Shop Scheduling, Management Science, 34, 391–401.
R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, 1993, Network Flows: Theory, Algorithms, and Complexity, Prentice-Hall, Englewood Cliffs, New Jersey.
K. R. Baker, 1992, Elements of Sequencing and Scheduling, Hanover, New Hampshire.
E. Balas, J. K. Lenstra, and A. Vazacopoulos, 1995, The One-machine Problem with Delayed Precedence Constraints and Its Use in Job Shop Scheduling, Management Science, 41, 94–109.
E. Balas and A. Vazacopoulos, 1996, Efficient Search Procedures Combining Different Neighborhood Structures, 1996 MSOM Conference, Hanover, New Hampshire.
J. Carlier and E. Pinson, 1989, An Algorithm for Solving the Job-Shop Problem, Management Science, 35, 164–176.
H. Fisher and G. L. Thompson, 1963, Probabilistic Learning Combinations of Local Job-Shop Scheduling Rules, in J. F. Muth and G. L. Thompson, (Eds.), Industrial Scheduling, Prentice-Hall, Englewood Cliffs, NJ.
M. R. Garey and D.S. Johnson, 1979, Computers and Intractability, W.H. Freeman and Co., San Francisco, CA.
A. M. Geoffrion, 1974, Lagrangian Relaxations Approaches for Integer Programming, Mathematical Programming Study, 2, 82–114.
K. Holmberg, 1990, On the Convergence of Cross Decomposition, Mathematical Programming, 47, 269–296.
G. L. Nemhauser and L.A. Wolsey, 1988, Integer Programming and Combinatorial Optimization, John Wiley and Sons, New York, NY.
B. Neureuther, G. Polak, and N. Sanders, 1996, A Hierarchical Production Plan for Steel Fabricating. Presentation, Winter Conference, Cincinnati/Dayton INFORMS, Dayton, Ohio.
S. Sevast’janov, 1995, Mathematics of Operations Research, 20, 90–103.
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© 1998 Springer Science+Business Media Dordrecht
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Polak, G.G. (1998). Lagrangian Relaxation for Flow Shop Scheduling. In: Yu, G. (eds) Industrial Applications of Combinatorial Optimization. Applied Optimization, vol 16. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-2876-7_11
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DOI: https://doi.org/10.1007/978-1-4757-2876-7_11
Publisher Name: Springer, Boston, MA
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