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Dynamic Programming Solution of Sequencing Problems with Precedence Constraints

Author

Listed:
  • Linus Schrage

    (University of Chicago, Chicago, Illinois)

  • Kenneth R. Baker

    (Duke University, Durham, North Carolina)

Abstract

Consider a set of tasks that are partially ordered by precedence constraints. A subset of tasks is called feasible if, for every task in the subset, all predecessors are also in the subset. The major results are (1) a method for enumerating all feasible subsets and (2) a method for assigning to each feasible subset an easily computed label that can be used as a physical address for storing information about the subset. These two results permit a very compact computer implementation of a dynamic programming algorithm for solving one-machine sequencing problems with precedence constraints. This algorithm appears to be much more efficient than previous ones for certain one-machine sequencing problems.

Suggested Citation

  • Linus Schrage & Kenneth R. Baker, 1978. "Dynamic Programming Solution of Sequencing Problems with Precedence Constraints," Operations Research, INFORMS, vol. 26(3), pages 444-449, June.
    • Handle: RePEc:inm:oropre:v:26:y:1978:i:3:p:444-449
    DOI: 10.1287/opre.26.3.444
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