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Linear programming with multiple objective functions: Step method (stem)

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Abstract

This paper describes a solution technique for Linear Programming problems with multiple objective functions. In this type of problem it is often necessary to replace the concept of “optimum” with that of “best compromise”. In contrast with methods dealing with a priori weighted sums of the objective functions, the method described here involves a sequential exploration of solutions. This exploration is guided to some extent by the decision maker who intervenes by means of defined responses to precise questions posed by the algorithm. Thus, in this man-model symbiosis, phases of computation alternate with phases of decision. The process allows the decision-maker to “learn” to recognize good solutions and the relative importance of the objectives. The final decision (best compromise) furnished by the man-model system is obtained after a small number of successive phases.

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References

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Authors and Affiliations

  1. SEMA (Metra International), Paris, France

    R. Benayoun, J. de Montgolfier & J. Tergny

  2. Institut d'Automatique et de Télémécanique, Moscow, USSR

    O. Laritchev

Authors
  1. R. Benayoun
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  2. J. de Montgolfier
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  3. J. Tergny
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  4. O. Laritchev
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Benayoun, R., de Montgolfier, J., Tergny, J. et al. Linear programming with multiple objective functions: Step method (stem). Mathematical Programming 1, 366–375 (1971). https://doi.org/10.1007/BF01584098

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  • DOI: https://doi.org/10.1007/BF01584098

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