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Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables

Author

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  • Gabriel R. Bitran

    (Massachusetts Institute of Technology)

  • Arnoldo C. Hax

    (Massachusetts Institute of Technology)

Abstract

The allocation of a specific amount of a given resource among competitive alternatives can often be modelled as a knapsack problem. This model formulation is extremely efficient because it allows convex cost representation with bounded variables to be solved without great computational efforts. Practical applications of this problem abound in the fields of operations management, finance, manpower planning, marketing, etc. In particular, knapsack problems emerge in hierarchical planning systems when a first level of decisions need to be further allocated among specific activities which have been previously treated in an aggregate way. In this paper we provide a recursive procedure to solve such problems. The method differs from classical optimization algorithms of convex programming in that it determines at each iteration the optimal value of at least one variable. Applications and computational results are presented.

Suggested Citation

  • Gabriel R. Bitran & Arnoldo C. Hax, 1981. "Disaggregation and Resource Allocation Using Convex Knapsack Problems with Bounded Variables," Management Science, INFORMS, vol. 27(4), pages 431-441, April.
    • Handle: RePEc:inm:ormnsc:v:27:y:1981:i:4:p:431-441
    DOI: 10.1287/mnsc.27.4.431
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    Keywords

    programming: algorithms; knapsack problem;

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