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An interactive weight space reduction procedure for nonlinear multiple objective mathematical programming

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Abstract

To make a decision that is defined by multiple, conflicting objectives it is necessary to know the relative importance of the different objectives. In this paper we present an interactive method and the underlying theory for solving multiple objective mathematical programming problems defined by a convex feasible region and concave, continuously differentiable objective functions. The relative importance of the different objectives for a decision maker is elicited by using binary comparisons of objective function vectors. The method is cognitively easy to use and in test problems has rapidly converged to an optimal solution.

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Authors and Affiliations

  1. College of Business and Technology, Black Hills State University, 1200 University Street, Spearfish, SD, 57779, USA

    Patrick D. Mackin

  2. Department of Information Systems, Arizona State University, PO Box 874606, Tempe, AZ, 85287-4606, USA

    Asim Roy

  3. Department of Business Technology, Helsinki School of Economics, PO Box 1210, 00101, Helsinki, Finland

    Jyrki Wallenius

Authors
  1. Patrick D. Mackin
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  2. Asim Roy
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  3. Jyrki Wallenius
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Corresponding author

Correspondence to Jyrki Wallenius.

Additional information

This study was initiated while the third author was on sabbatical in the Industrial Engineering Department at Arizona State University. He appreciates the hospitality of the Industrial Engineering Department. Wallenius would also like to acknowledge the financial support of the Academy of Finland (grants no. 212767 and 200935) and the Foundation for Economic Education, Finland.

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Mackin, P.D., Roy, A. & Wallenius, J. An interactive weight space reduction procedure for nonlinear multiple objective mathematical programming. Math. Program. 127, 425–444 (2011). https://doi.org/10.1007/s10107-009-0293-6

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  • DOI: https://doi.org/10.1007/s10107-009-0293-6

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