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Interval linear systems and optimization problems over max-algebras

In: Linear Optimization Problems with Inexact Data

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  • K. Zimmermann

Abstract

6.8 Conclusion The results obtained in this chapter extend the possibility of applications of the (⊕, ⊗)-linear systems and optimization problems to cases in which the data of the problems are inexact and the inexactness is expressed by replacing the exact coefficients of the (⊕, ⊗)-linear functions involved with interval coefficients. Such problems occur, e.g., in scheduling problems with inexact processing times, reliability problems with inexact failure probabilities and others. As we have already mentioned, only problems with variables on one side of the constraints were considered here. Problems with variables on both sides of (⊕, ⊗)-linear constraints may become the subject of further research.

Suggested Citation

  • K. Zimmermann, 2006. "Interval linear systems and optimization problems over max-algebras," Springer Books, in: Linear Optimization Problems with Inexact Data, chapter 6, pages 165-193, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-32698-6_6
    DOI: 10.1007/0-387-32698-7_6
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