“Properties of Pareto Optimal Allocations of Resources to Activities”

Authors: Kåre M. Mjelde,
Affiliation: Det Norske Veritas (DNV)
Reference: 1983, Vol 4, No 3, pp. 167-173.

Keywords: Resource allocation, Pareto-optimality

Abstract: A linear multi-objective decision problem is considered, of the maximization of the effect of allocations of resources to activities. Necessary and sufficient conditions for a feasible solution to the problem to be Pareto-optimal are derived, in terms of properties of the allocation matrix and a certain matrix of efficiency coefficients of the allocations. A condition is given for all optimal solutions to be simple in the sense that they contain a small number of non-zero allocations. A feasible change of the positive allocations of an optimal solution produces a new optimal solution.

PDF PDF (383 Kb)        DOI: 10.4173/mic.1983.3.3

DOI forward links to this article:
[1] Kåre M. Mjelde (1986), doi:10.4173/mic.1986.3.4
[2] Waldemar Czuchra (1988), doi:10.1016/0377-2217(88)90458-4
[3] Ephraim Zehavi, Amir Leshem, Ronny Levanda and Zhu Han (2013), doi:10.1109/TSP.2013.2262278
[4] Ephraim Zehavi and Amir Leshem (2017), doi:10.1007/s10614-017-9673-9
[1] DANSKIN, F.M. (1967). The theory of max-min, Pp. 85-100..Berlin : Springer-Verlag.
[2] EINBU, J.M. (1978). Optimal allocation of continuous resources to several activities with a concave return function - some theoretical results, Math. Opns. Res., 3, 82-88 doi:10.1287/moor.3.1.82
[3] GAL, T., LEBERLING, H. (1981). Relaxation analysis in linear vector values maximization, EJOR, 8, 274-282 doi:10.1016/0377-2217(81)90176-4
[4] LUSS, H., GUPTA, S. (1975). Allocation of effort resources among competing activities, Opts. Res., 23, 360-366 doi:10.1287/opre.23.2.360
[5] MJELDE, K.M. (1977). Properties of optimal allocations of resources, Opt Res. Q., 28, 735-737 doi:10.1057/jors.1977.149
[6] MJELDE, K.M. (1981). Properties of optimal allocations of resources according to a fractional objective, Opl. Res. Q., 32, 405-408 doi:10.1057/jors.1981.78
[7] MJELDE, K. M. (1983). Methods of the allocation of limited resources, Chichester. New York: John Wiley and Sons.
[8] ROY, B., VINCKE, P. (1981). Multicriteria analysis: survey and new directions, EJOR, 8, 207-218 doi:10.1016/0377-2217(81)90168-5
[9] ZIONTS, S., WALLENIUS, J. (1980). Identifying efficient vectors: some theory and computational results, Opns. Res., 28, 785-793 doi:10.1287/opre.28.3.785

  title={{Properties of Pareto Optimal Allocations of Resources to Activities}},
  author={Mjelde, Kåre M.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}