Some exact algorithms for the knapsack sharing problem

European Journal of Operational Research

Volumn 106, Issue 1, 1998, Pages 177-183

  Yamada, Takeo ^a   Futakawa, Mayumi ^a   Kataoka, Seiji ^a  

^a NATIONAL DEFENSE ACADEMY   (Japan)

Author keywords

Binary search method; Combinatorial optimization; Knapsack sharing problem; Max min objective function

Indexed keywords

EID: 0010763990     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(97)00165-3     Document Type: Article

References (16)

1. Bellman, R., Dynamic Programming, Princeton University Press, Princeton, NJ, 1957.
2. Brown, J.R., The knapsack sharing problem, Operations Research 27 (1979) 341-355.
3. Brown, J.R., Bounded knapsack sharing, Mathematical Programming 67 (1994) 343-382.
4. Chvátal, V., Linear Programming, Freeman, New York, 1983.
5. Garey, M.R., Johnson, D.S., Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, New York, 1979.
6. Horowitz, E., Sahni, S., Computing partitions with applications to the knapsack problem, Journal of the ACM 21 (1974) 277-292.
7. Jacobsen, S., On marginal allocation in single constraint minmax problems, Management Science 17 (1971) 780-783.
8. Kaplan, S., Application of programs with maximin objective functions to problems of optimal resource allocation, Operations Research 22 (1974) 802-807.
9. Kuno, T., Konno, H., Zemel, E., A linear-time algorithm for solving continuous maximin knapsack problems. Operations Research Letters 10 (1991) 23-26.
10. Luss, H., A nonlinear minimax allocation problem with multiple knapsack constraints, Operations Research Letters 10 (1991) 183-187.
11. Luss, H., Minimax resource allocation problems: optimization and parametric analysis, European Journal of Operational Research 60 (1992) 76-86.
12. Martello, S., Toth, P., Knapsack Problems: Algorithms and Computer Implementations, Wiley, New York, 1990.
13. Nemhauser, G.L., Wolsey, L.A., Integer and Combinatorial Optimization, Wiley, New York, 1988.
14. Porteus, E.L., Yormark, J.S., More on min-max allocation, Management Science 18 (1972) 502-507.
15. Tang, C.S., A max-min allocation problem: its solutions and applications, Operations Research 36 (1988) 359-367.
16. Zeitlin, Z., Integer allocation problems of min-max type with quasiconvex separable functions, Operations Research 29 (1981) 207-211.