On the max-min 0-1 knapsack problem with robust optimization applications

Operations Research

Volumn 44, Issue 2, 1996, Pages 407-415

  Yu, Gang ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; HEURISTIC PROGRAMMING; INTEGER PROGRAMMING; LARGE SCALE SYSTEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; ROBUSTNESS (CONTROL SYSTEMS); STATISTICAL METHODS;

BRANCH AND BOUND ALGORITHMS; MAXMIN KNAPSACK (MNK) PROBLEMS;

OPTIMIZATION;

EID: 0030092483     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.44.2.407     Document Type: Article

References (34)

1. AGASI, E., R. I. BECKER AND Y. PERL. 1993. A Shifting Algorithm for Constrained Min-max Partition on Trees. Discr. Appl. Math. 45, 1-28.
2. AHUJA, R. K. 1985. Minimax Linear Programming Problem. O.K. Letts. 4, 131-134.
3. BAZARAA, M. S., AND J. J. GOODE. 1982. An Algorithm for Solving Linearly Constrained Minimax Problems. Eur. J. Opnl. Res. 11, 158-166.
4. BROWN, J. R. 1979a. The Sharing Problem. Opns. Res. 27, 325-340.
5. BROWN, J. R. 1979b. The Knapsack Sharing Problem. Opns. Res. 27, 341-355.
6. CZUCHRA, W. 1986. A Graphical Method to Solve a Maximin Allocation Problem. Eur. J. Opnl. Res. 26, 259-261.
7. DREZNER, Z., AND G. O. WESOLOWSKY. 1980. A Maximin Location Problem With Maximum Distance Constraints. IIE Trans. 12, 249-252.
8. DUTTA, R. S. K., AND M. VIDYASAGAR. 1977. New Algorithm for Constrained Minimax Optimization. Math. Prog. 13, 140-155.
9. EISELT, H. A. 1986. Continuous Maximin Knapsack Problems With GLB Constraints. Math. Prog. 36, 114-121.
10. FISHER, M. L. 1981. The Lagrangian Relaxation Method for Solving Integer Programming Problems. Mgmt. Sci. 27, 1-18.
11. GAREY, M. R., AND D. S. JOHNSON. 1979. Computers and Intractability. W.H. Freeman, San Francisco.
12. GLOVER, F. 1975. Surrogate Constraint Duality in Mathematical Programming. Opns. Res. 23, 434-451.
13. GUPTA, S. K., AND J. ROSENHEAD. 1972. Robustness in Sequential Investment Decisions. Mgmt. Sci. 15, 18-29.
14. ICHIMORI, T. 1984. On Min-Max Integer Allocation Problems. Opns. Res. 32, 449-450.
15. ICHIMORI, T., H. ISHII AND T. NISHIDA. 1982. Optimal Sharing. Math. Prog. 23, 341-348.
16. JACOBSEN, S. 1971. On Marginal Allocation in Single Constraint Min-Max Problems. Mgmt. Sci. 17, 780-783.
17. KAPLAN, S. 1974. Application of Programs With Maximin Objective Functions to Problems of Optimal Resource Allocation. Opns. Res. 22, 802-807.
18. KLEIN, R. S., H. LUSS AND U. G. ROTHBLUM. 1993. Minimax Resource Allocation Problems With Resource-Substitutions Represented by Graphs. Opns. Res. 41, 959-971.
19. KOUVELIS, P., AND G. Yu. 1993. Robust Discrete Optimization and Its Application. Working Paper, Graduate School of Business, The University of Texas at Austin.
20. LEMARECHAL, C. 1989. Nondifferentiable Optimization. In Handbooks in Operations Research and Management Science, Vol. 1, G. L. Nemhauser, A. H. G. Rinnooy Kan and M. J. Todd (eds.). Elsevier Science Publishers, 529-572.
21. LUSS, H. 1987. An Algorithm for Separable Nonlinear Minimax Problems. O.R. Letts. 6, 159-162.
22. LUSS, H., AND D. R. SMITH. 1986. Resource Allocation Among Competing Activities: A Lexicographic Minimax Approach. O.R. Letts. 5, 227-231.
23. MADSEN, K., AND H. SCHJAER-JACOBSEN. 1978. Linearly Constrained Minimax Optimization. Math. Prog. 14, 208-223.
24. MARTELLO, S., AND P. TOTH. 1990. Knapsack Problems: Algorithms and Computer Implementations. John Wiley, New York.
25. PANG, J. S., AND C. S. Yu. 1989. A Min-Max Resource Allocation Problem With Substitutions. Eur. J. Opnl. Res. 41, 218-223.
26. POSNER, M. E., AND C. T. Wu. 1981. Linear Max-Min Programming. Math. Prog. 20, 166-172.
27. PORTEUS, E. L., AND J. S. YORMARK. 1972. More on the Min-Max Allocation. Mgmt. Sci. 18, 520-527.
28. RANGAN, C. P., AND R. GOVINDAN. 1992. An O(n log n) Algorithm for a Maxmin Location Problem. Discr. Appl. Math. 36, 203-205.
29. ROSENHEAD, J., M. ELTON AND S. K. GUPTA. 1972. Robustness and Optimality as Criteria for Strategic Decisions. Opnl. Res. Quart. 23(4), 413-430.
30. SENGUPTA, J. K. 1991. Robust Decisions in Economic Models. Comput. and Opns. Res. 18(2), 221-232.
31. TANG, C. S. 1988. A Max-Min Allocation Problem: Its Solutions and Applications. Opns. Res. 36, 359-367.
32. VINCENT, T. L., B. S. GOH AND K. L. TEO. 1992. Trajectory-Following Algorithms for Min-Max Optimization Problems. J. Optim. Theory and Applic. 75(3), 501-519.
33. YU, G., AND P. KOUVELIS. 1993. Complexity Results for a Class of Min-Max Problems With Robust Optimization Applications. In Complexity in Numerical Optimization, P. M. Pardalos (ed.). World Scientific Publishing, 503-511.
34. ZIMMERMANN, U. 1986. Linear and Combinatorial Sharing Problems. Discr. Appl. Math. 15, 85-104.