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Direct solution to constrained tropical optimization problems with application to project scheduling

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  • Nikolai Krivulin

    (Saint Petersburg State University)

Abstract

We examine a new optimization problem formulated in the tropical mathematics setting as a further extension of certain known problems. The problem is to minimize a nonlinear objective function, which is defined on vectors over an idempotent semifield by using multiplicative conjugate transposition, subject to inequality constraints. As compared to the known problems, the new one has a more general objective function and additional constraints. We provide a complete solution in an explicit form to the problem by using an approach that introduces an auxiliary variable to represent the values of the objective function, and then reduces the initial problem to a parametrized vector inequality. The minimum of the objective function is evaluated by applying the existence conditions for the solution of this inequality. A complete solution to the problem is given by solving the parametrized inequality, provided the parameter is set to the minimum value. As a consequence, we obtain solutions to new special cases of the general problem. To illustrate the application of the results, we solve a real-world problem drawn from time-constrained project scheduling, and offer a representative numerical example.

Suggested Citation

  • Nikolai Krivulin, 2017. "Direct solution to constrained tropical optimization problems with application to project scheduling," Computational Management Science, Springer, vol. 14(1), pages 91-113, January.
    • Handle: RePEc:spr:comgts:v:14:y:2017:i:1:d:10.1007_s10287-016-0259-0
    DOI: 10.1007/s10287-016-0259-0
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    References listed on IDEAS

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    1. A. J. Hoffman, 1963. "On abstract dual linear programs," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 10(1), pages 369-373, March.
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    Cited by:

    1. Nikolai Krivulin, 2017. "Using tropical optimization to solve constrained minimax single-facility location problems with rectilinear distance," Computational Management Science, Springer, vol. 14(4), pages 493-518, October.
    2. Nikolai Krivulin, 2021. "Algebraic Solution to Constrained Bi-Criteria Decision Problem of Rating Alternatives through Pairwise Comparisons," Mathematics, MDPI, vol. 9(4), pages 1-22, February.

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    2. Nikolai Krivulin, 2020. "Tropical optimization technique in bi-objective project scheduling under temporal constraints," Computational Management Science, Springer, vol. 17(3), pages 437-464, October.

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