On equitable approaches to resource allocation problems: the conditional minimax solutions

Authors

DOI:

https://doi.org/10.26636/jtit.2002.3.134

Keywords:

telecommunication networks, resource allocation, equity, min-max

Abstract

In this paper we introduce and analyze a solution concept of the conditional minimax as a generalization of the minimax solution concept extended to take into account the number of services (the portion of demand) related to the worst performances. Namely, for a specified portion of demand we take into account the corresponding portion of the maximum results and we consider their average as the worst conditional mean to be minimized. We show that, similar to the standard minimax approach, the minimization of the worst conditional mean can be defined by a linear objective and a number of auxiliary linear inequalities. We report some results of initial computational experience with the new solution concept.

Downloads

Download data is not yet available.

References

[1] J. F. Campbell, "Hub location and the p-hub median problem", Oper. Res., vol. 44, pp. 923-935, 1996.
View in Google Scholar

[2] D. W. Corne, M. J. Oates, and G. D. Smith, Eds., Telecommunications Optimization: Heuristics and Adaptive Techniques. New York: Wiley, 2000.
View in Google Scholar

[3] S. Cosares, D. N. Deutsch, I. Saniee, and O. J. Wasem, "SONET toolkit: a decision support system for designing robust and cost-effective fiber-optic networks", Interfaces, vol. 25, pp. 20-40, 1995.
View in Google Scholar

[4] E. Gourdin, "Optimizing Internet networks", OR/MS Today, vol. 28, pp. 46-49, 2001.
View in Google Scholar

[5] ILOG Inc., Using the CPLEX Callable Library. Incline Village: ILOG Inc., CPLEX Division, 1997.
View in Google Scholar

[6] J. G. Klincewicz, "Hub location in backbone/tributary network design: a review", Loc. Sci., vol. 6, pp. 307-335, 1998.
View in Google Scholar

[7] M. M. Kostreva and W. Ogryczak, "Linear optimization with multiple equitable criteria", RAIRO Oper. Res., vol. 33, pp. 275-297, 1999.
View in Google Scholar

[8] H. Luss, "On equitable resource allocation problems: a lexicographic minimax approach", Oper. Res., vol. 47, pp. 361-378, 1999.
View in Google Scholar

[9] W. Ogryczak, "On the lexicographic minimax approach to location problems", Eur. J. Oper. Res., vol. 100, pp. 566-585, 1997.
View in Google Scholar

[10] W. Ogryczak, "Inequality measures and equitable approaches to location problems", Eur. J. Oper. Res., vol. 122, pp. 374-391, 2000.
View in Google Scholar

[11] J. Rawls, The Theory of Justice. Cambridge: Harvard University Press, 1971.
View in Google Scholar

[12] A. Sen, On Economic Inequality. Oxford: Clarendon Press, 1973.
View in Google Scholar

Downloads

Submitted

2023-04-07

Published

2002-09-30

Issue

Section

ARTICLES FROM THIS ISSUE

How to Cite

[1]
W. Ogryczak and T. Śliwiński, “On equitable approaches to resource allocation problems: the conditional minimax solutions”, JTIT, vol. 9, no. 3, pp. 40–48, Sep. 2002, doi: 10.26636/jtit.2002.3.134.

Most read articles by the same author(s)