Recoverable robust knapsacks: The discrete scenario case

Optimization Letters

Volumn 5, Issue 3, 2011, Pages 379-392

  Büsing, Christina ^a   Koster, Arie M C A ^b   Kutschka, Manuel ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b RWTH AACHEN UNIVERSITY   (Germany)

Author keywords

Extended cover inequalities; Knapsack; Recoverable robustness

Indexed keywords

BANDWIDTH RESTRICTIONS; COMPLEX PROBLEMS; COMPUTATIONAL STUDIES; EXTENDED COVER INEQUALITIES; HIGH-RISK SITUATIONS; KNAPSACK; KNAPSACK PROBLEMS; PRODUCTION PLANNING; REAL-WORLD APPLICATION; RECOVERABLE ROBUSTNESS; ROBUST APPROACHES; ROBUST OPTIMIZATION; TELECOMMUNICATION NETWORK DESIGN; UNCERTAIN PARAMETERS; VALID INEQUALITY;

BANDWIDTH; COMBINATORIAL OPTIMIZATION; INTEGER PROGRAMMING; OPTIMIZATION; PRODUCTION CONTROL; PROFITABILITY; TELECOMMUNICATION NETWORKS; TELECOMMUNICATION SYSTEMS;

UNCERTAINTY ANALYSIS;

EID: 79960123816     PISSN: 18624472     EISSN: 18624480     Source Type: Journal    
DOI: 10.1007/s11590-011-0307-1     Document Type: Article

References (23)

1. Achterberg T.: SCIP: solving constraint integer programs. Math. Prog. Comp 1(1), 1-42 (2009).
2. Aissi, H., Bazgan, C., Vanderpooten, D.: Min-max and min-max regret versions of some combinatorial optimization problems: a survey. http://hal. archives-ouvertes. fr/docs/00/15/86/52/PDF/AN7LAMSADE_1-32. pdf (2007)
3. Balas E.: Facets of the knapsack polytope. Math. Prog 8, 146-164 (1975).
4. Beasley, J. E.: OR-Library: distributing test problems by electronic mail. J. of the OR Society 41: 1069-1072. http://people. brunel. ac. uk/~mastjjb/jeb/ (1990).
5. Bellman R.: Notes on the theory of dynamic programming iv-maximization over discrete sets. Naval Res. Logist. Quart. 3, 67-70 (1956).
6. Bertimas D., Sim M.: Robust discrete optimization and network flows. Math. Prog. Ser. B 98, 49-71 (2003).
7. Bertimas D., Sim M.: The price of robustness. Oper. Res 52, 35-53 (2004).
8. Büsing, C., Koster, A. M. C. A., Kutschka M.: Recoverable robust knapsacks: the discrete scenario case. Technical Report 018-2010, TU Berlin. http://www. math. tu-berlin. de/coga/publications/techreports/2010/ (2010).
9. Crowder H., Johnson E., Padberg M.: Large-scale zero-one linear programming problems. Oper. Res. 31, 803-834 (1983).
10. Cicerone S., D'Angelo G. D., Di Stefano G., Frigioni D., Navarra A., Schachtebeck M., Schöbel A.: Recoverable robustness in shunting and timetabling Robust and Online Large-Scale Optimization, vol. 5868 of LNCS, 28-60. Springer, Berlin (2009).
11. Fischetti M., Lodi A., Salvagnin D.: Just MIP it!. Ann. Inf. Syst. 10, 39-70 (2009).
12. Gabrel V., Minoux M.: A scheme for exact separation of extended cover inequalities and application to multidimensional knapsack problems. OR Lett. 30, 252-264 (2002).
13. Iida H.: A note on the max-min 0-1 knapsack problem. J. Comb. Opt. 3, 89-94 (1999).
14. Kalai, R., Vanderpooten, D.: Lexicographic α-robust knapsack problems: complexity results. IEEE International Conference on Services Systems and Service Managment 1103-1107 (2006).
15. Kaparis K., Letchford A.: Separation algorithms for 0-1 knapsack polytopes. Math. Prog. 124(1-2), 69-91 (2010).
16. Karp, R.: Reducibility among combinatorial problems. Complexity of Computer Computations. 85-103 (1972).
17. Kellerer H., Pferschy U., Pisinger D.: Knapsack Problems. Springer, (2004).
18. Klopfenstein, O., Nace, D.: Valid inequalities for a robust knapsack polyhedron-Application to the robust bandwidth packing problem. Networks Special Issue, Network Optimization (INOC 2009) (to appear).
19. Liebchen C., Lübbecke M. E., Möhring R. H., Stiller S.: The concept of recoverable robustness, linear programming recovery, and railway applications Robust and Online Large-Scale Optimization, vol 5868 of LNCS, 1-27. Springer, Berlin (2009).
20. Martello, S., Toth, P.: Knapsack problems: algorithms and computer implementations. Wiley (1990).
21. Weismantel R.: On the 0-1 knapsack polytope. Math. Prog. 77, 49-68 (1997).
22. Wolsey L.: Faces for a linear inequality in 0-1 variables. Math. Prog. 8, 165-178 (1975).
23. Yu G.: On the max- min 0-1 knapsack problem with robust optimization applications. Oper. Res. 44, 407-415 (1996).