Abstract
We propose a new approach to the formulation of models for solving problems of equitable distribution. Equity is achieved by the use of “proportional equity constraints” which require that each recipient must receive ashare of the total distribution which falls within a prespecified range. The algorithmic implications of this new approach are illustrated using two mathematical models. We consider the problem of maximizing total flow in a multiterminal network with proportional equity constraints. An efficient algorithm for solving this problem is provided. As a further application, we show that the introduction of such constraints still permits easy solutions for the linear knapsack problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
J.R. Brown, “The sharing problem,”Operations Research 27 (1979a) 324–340.
J.R. Brown, “The knapsack sharing problem,”Operations Research 27 (1979b) 341–355.
L.R. Ford, Jr. and D.R. Fulkerson,Flows in Networks (Princeton University Press, Princeton, NJ, 1962).
S. Fujishige, “Lexicographically optimal base of a polymatroid with respect to a weight vector,”Mathematics of Operations Research 5 (1980) 186–196.
G. Gallo, M.D. Grigoriadis and R.E. Tarjan, “A fast parametric maximum flow algorithm,”SIAM Journal on Computing 18 (1989) 30–55.
T. Ichimori, H. Ishii and T. Nishida, “Optimal sharing,”Mathematical Programming 23 (1982) 341–348.
S. Kaplan, “Application of programs with maximin objective functions to problems of optimal resource allocation,”Operations Research 22 (1974) 802–807.
V.M. Malhotra, M.P. Kumar and S.N. Maheshwari, “An O(|V|3) algorithm for finding maximum flows in networks,”Information Processing Letters 7 (1978) 277–278.
M. Minoux, “Flots equilibries et flots avec securité,”Informatique 1 (1976) 5–16.
J. Rawls,A Theory of Justice (Harvard University Press, Cambridge, MA, 1971).
U. Zimmerman, “Duality for balanced submodular flows,”Discrete Applied Mathematics 15 (1986) 365–376.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hall, N.G., Vohra, R.V. Towards equitable distribution via proportional equity constraints. Mathematical Programming 58, 287–294 (1993). https://doi.org/10.1007/BF01581272
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01581272