Solving a class of two-resource allocation problem by equivalent load method

Journal of the Operational Research Society

Volumn 48, Issue 8, 1997, Pages 818-825

  Armstrong, R ^a   Gu, S ^a   Lei, L ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Efficient algorithm; Equivalent load method; Series parallel graphs; Two resource allocation

Indexed keywords

ALGORITHMS; GRAPH THEORY; MATHEMATICAL MODELS; PROBLEM SOLVING; RESOURCE ALLOCATION;

EQUIVALENT LOAD METHOD; SERIES PARALLEL GRAPHS;

OPERATIONS RESEARCH;

EID: 0031199114     PISSN: 01605682     EISSN: 14769360     Source Type: Journal    
DOI: 10.1057/palgrave.jors.2600387     Document Type: Article

References (20)

1. Monma, C.L., Schrijver, A., Todd, M.J., Wei, V.K., (1990). Convex resource allocation problems on directed acyclic graphic: Duality, complexity, special cases, and extensions, Math Opns Res 15: 736-748.
2. Luss, H., Gupta, S.K., (1975). Allocation of effort resources among competing activities, Opns Res 23: 360-366.
3. Einbu, J.M., (1978). Optimal allocations of continuous resources to several activities with a concave return function—some theoretical results, Math Opns Res 3: 82-88.
4. Einbu, J.M., (1981). Extension of the Luss-Gupta resource allocation algorithm by means of first order approximation techniques, Opns Res 29: 621-626.
5. Einbu, J.M., (1984). A finite method for the solution of a multiresource allocation problem with concave return functions, Math Opns Res 9: 232-243.
6. Eibu, J.M., (1985). Addendum: a finite algorithm for solving nonlinear allocation problems, Math Opns Res 10: 154-157.
7. Megiddo, N., Ichimori T (1985). A two-resource allocation problem solvable in linear time, Math Opns Res 10: 7-16.
8. Mjelde, K.M., (1977). Properties of optimal allocations of resources, Opl Res Q 28: 735-737.
9. Mjelde, K.M., (1982). The allocation of linear resources to concave activities—a finite algorithm with a polynomial time bound, J Opl Res Soc 33: 1045-1046.
10. Luss, H., (1991). A nonlinear min-max allocation problem with multiple knapsack constraints, Opns Res Lett 10: 183-187.
11. Luss, H., (1992). Minimax resource allocation problems: optimization and parametric analysis, Eur J Opl Res 5: 227-231.
12. Luss, H., Smith, D.R., (1986). Resource allocation among competing activities: a lexicographic minimax approach, Opns Res Lett 5: 227-231.
13. Klein, R., Luss, H., (1991). Minimax resource allocation with tree structured substitutable resources, Opns Res 39: 285-295.
14. Pang, J.S., Yu, C.S., (1989). A min-max resource allocation problem with substitutions, Eur J Opl Res 41: 218-223.
15. Ibaraki, T., Katoh, N., (1988). Resource Allocation Problems: Algorithmic Approaches. The MIT Press: Cambridge, Massachusetts.
16. Mjelde, K.M., (1983). Methods of the Allocation of Limited Resources. John Wiley & Sons: New York.
17. Armstrong, R., Gu, S., Lei, L., (1995). An 0(N log(1/e)) algorithm for the two-resource allocation problem with a nondifferentiable convex objective function, J Opl Res Soc 46: 116-122.
18. Matousek, J., Thomas, R., (1991). Algorithms finding tree- decompositions of graphs, J Algorithms 12: 1-22.
19. Valdes, J.R., Tarjan, E., Lawler, E.L., (1979). The recognition of series parallel digraphs, Proc Sympos Theory Comp 11: 1-12.
20. Golub, G.H., Ortega, J.M., (1992). Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Academic Press, Inc.: Country, pp. 150-151.