Solving chance-constrained combinatorial problems to optimality

Computational Optimization and Applications

Volumn 45, Issue 3, 2010, Pages 607-638

  Klopfenstein, Olivier ^a,b  

^a ORANGE LABS   (France)

^b UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

Chance constrained programming; Integer linear programming

Indexed keywords

BRANCH-AND-CUT ALGORITHMS; CHANCE-CONSTRAINED; CHANCE-CONSTRAINED PROGRAMMING; COMBINATORIAL PROBLEM; INTEGER LINEAR PROGRAMMING; INTEGER LINEAR PROGRAMS; LINEAR INEQUALITIES; LINEAR RELAXATIONS; NEW EFFICIENT METHOD; NUMERICAL TESTS; OPTIMALITY;

COMBINATORIAL MATHEMATICS; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; LINEARIZATION;

INTEGER PROGRAMMING;

EID: 77950517984     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-008-9177-6     Document Type: Article

References (26)

1. Aringheri, R.: A tabu search algorithm for solving chance-constrained programs. Note del polo 73, DTI-University of Milano (2005). http://www.crema.unimi.it/Biblioteca/SchedaNota.asp?Nota=92
2. A. Ben-Tal A. Nemirovski 2000 Robust solutions of linear programming problems contamined with uncertain data Math. Program. (Ser. A) 88 411 424 0964.90025 10.1007/PL00011380 1782149
3. P. Beraldi A. Ruszczyński 2002 A branch and bound method for stochastic integer problems under probabilistic constraints Optim. Methods Softw. 17 359 382 1064.90030 10.1080/1055678021000033937 1944287 (Pubitemid 35242089)
4. D. Bertsimas M. Sim 2004 The price of robustness Oper. Res. 52 1 35 53 1165.90565 10.1287/opre.1030.0065 2066239 (Pubitemid 40000812)
5. Bianchi, L., Dorigo, M., Gambardella, L., Gutjahr, W.: Metaheuristics in stochastic combinatorial optimization: a survey. Technical Report idsia-08-06, IDSIA (2006). www.idsia.ch/idsiareport/IDSIA-08-06.pdf
6. Birge, J., Louveaux, F.: Introduction to Stochastic Programming. Springer, Berlin (1997)
7. D. Bradley R. Gupta 2002 On the distribution of the sum of non-identically distributed uniform random variables Ann. Inst. Stat. Math. 54 3 689 700 1014.62011 10.1023/A:1022483715767 1932412
8. G. Calafiore M. Campi 2005 Uncertain convex programs: randomized solutions and confidence levels Math. Program. (Ser. A) 102 25 46 1177.90317 10.1007/s10107-003-0499-y 2115479 (Pubitemid 40134690)
9. G. Calafiore L.E. Ghaoui 2006 Distributionally robust chance-constrained linear programs with applications J. Optim. Theory Appl. 130 1 1 22 1143.90021 10.1007/s10957-006-9084-x 2275351 (Pubitemid 44951197)
10. A. Charnes W. Cooper 1959 Chance-constrained programming Manage. Sci. 5 73 79 10.1287/mnsc.6.1.73 148478
11. E. Erdoǧan G. Iyengar 2006 Ambiguous chance constrained problems and robust optimization Math. Program. (Ser. B) 107 1-2 37 61 1134.90028 10.1007/s10107-005-0678-0 (Pubitemid 43334013)
12. Grinstead, C., Snell, J.: Introduction to Probability, 2nd edn. American Mathematical Society, Providence (1997)
13. W.K. Haneveld M. van der Vlerk 1999 Stochastic integer programming: general models and algorithms Ann. Oper. Res. 85 39 57 0920.90110 10.1023/A:1018930113099 1685596
14. F. Hillier 1967 Chance-constrained programming with 0-1 or bounded continuous decision variables Manage. Sci. 14 1 34 57 0155.28201 10.1287/mnsc.14.1.34 241112
15. Kall, P., Mayer, J.: Stochastic Linear Programming. Springer, Berlin (2005)
16. Kall, P., Wallace, S.: Stochastic Programming. Wiley, New York (1994)
17. Klopfenstein, O.: Tractable algorithms for chance-constrained combinatorial problems. www.optimization-online.org (2007)
18. Klopfenstein, O., Nace, D.: A robust approach to the chance-constrained knapsack problem. www.optimization-online.org (2006)
19. Nemirovski, A., Shapiro, A.: Scenario approximations of chance constraints. In: Calafiore, G., Dabbene, F. (eds.) Probabilistic and Randomized Methods for Design under Uncertainty, pp. 3-48. Springer, London (2005)
20. A. Nemirovski A. Shapiro 2006 Convex approximations of chance constrained programs SIAM J. Optim. 17 969 996 1126.90056 10.1137/050622328 2274500 (Pubitemid 350121950)
21. Prékopa, A.: Stochastic Programming. Kluwer Academic, Dordrecht (1995)
22. Prékopa, A.: Probabilistic programming. In: Ruszczynski, A., Shapiro, A. (eds.) Stochastic Programming. Handbooks in OR&MS, vol. 10. Elsevier, Amsterdam (2003)
23. Ross, S.: Initiation aux Probabilité. Presses Polytechniques Romandes, Lausanne (1987)
24. Y. Seppälä T. Orpana 1984 Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm Eur. J. Oper. Res. 16 345 357 0532.90079 10.1016/0377-2217(84)90289-3 (Pubitemid 14583788)
25. S. Tayur R. Thomas N. Natraj 1995 An algebraic geometry algorithm for scheduling in the presence of setups and correlated demands Math. Program. 69 3 369 401 10.1007/BF01585566 1355695
26. A. Weintraub J. Vera 1991 A cutting plane approach for chance constrained linear programs Oper. Res. 39 5 776 785 0744.90065 10.1287/opre.39.5.776 1132382