Probabilistic programming with discrete distributions and precedence constrained knapsack polyhedra

Mathematical Programming, Series B

Volumn 93, Issue 2, 2002, Pages 195-215

  Ruszczyński, Andrzej ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Integer programming; Stochastic programming; Valid inequalities

Indexed keywords

CONSTRAINT THEORY; INTEGER PROGRAMMING; ITERATIVE METHODS; PROBABILISTIC LOGICS; PROBLEM SOLVING;

ITERATIVE ALGORITHMS; PROBABILISTIC PROGRAMMING; PROBABILISTICALLY CONSTRAINED PROBLEMS; VALID INEQUALITIES;

STOCHASTIC PROGRAMMING;

EID: 10044271668     PISSN: 00255610     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10107-002-0337-7     Document Type: Article

References (22)

1. E. Balas, Facets of the knapsack polytope, Mathematical Programming 8 (1975) 146-164.
2. P. Beraldi and A. Ruszczyński, The probabilistic set covering problem, Operations Research, in press.
3. P. Beraldi and A. Ruszczyński, A branch and bound method for stochastic integer problems under probabilistic constraints, Optimization Methods and Software, in press.
4. J.R. Birge and F. Louveaux, Introduction to Stochastic Programming, Springer-Verlag, New York, NY, 1997.
5. E. Boros and A. Prékopa, Closed form two-sided bounds for probabilities that at least r and exactly r out of n events occur, Mathematics of Operations Research 14 (1989) 317-342.
6. E.A. Boyd, Polyhedral results for the precedence constrained knapsack problem, Discrete Applied Mathematics 41(1993) 185-201.
7. A. Charnes, WAV. Cooper and G.H. Symonds, Cost horizons and certainty equivalents: an approach to stochastic programming of heating oil, Management Science 4 (1958) 235-263.
8. D. Dentcheva, A. Prékopa and A. Ruszczyński, Concavity and efficient points of discrete distributions in probabilistic programming, Mathematical Programming 89 (2000) 55-77.
9. D. Dentcheva, A. Prékopa and A. Ruszczyński, On convex probabilistic programming with discrete distributions, Nonlinear Analysis 47 (2001) 1997-2009.
10. D. Dentcheva, A. Prékopa and A. Ruszczyński, Bounds for probabilistic integer programming problems, Discrete Applied Mathematics, in press.
11. R. Fourer, D.M. Gay and B.W. Kernighan, AMPL: A Modeling Language For Mathematical Programming Scientific Press, 1993.
12. M. Gendreau, G. Laporte and R. Séguin, Stochastic vehicle routing, European Journal of Operational Research 88 (1996) 3-12.
13. G. Laporte, F.V. Louveaux and H. Mercure, Models and Exact Solutions for a Class of Stochastic Location-Routing Problems, European Journal of Operational Research 39 (1989) 71-78.
14. R.L.M.J. van de Leensel, C.P.M. van Hoesel and J.J. van de Klundert, Lifting valid inequalities for the precedence constrained knapsack problem, Mathematical Programming 86 (1999) 161-185.
15. L.B. Miller and H.Wagner, Chance-constrained programming with joint constraints, Operations Research 13 (1965) 930-945.
16. G.L. Nemhauser and L.A. Wolsey, Integer and Combinatorial Optimization, John Wiley & Sons, New York, 1988.
17. K. Park and S. Park, Lifting cover inequalities for the precedence constrained knapsack problem, Discrete Applied Mathematics 72(1997) 219-241.
18. A. Prékopa, On probabilistic constrained programming, Proceedings of the Princeton Symposium on Mathematical Programming. Princeton University Press, 1970, pp. 113-138.
19. A. Prékopa, Boole-Bonferroni inequalities and linear programming. Operations Research 36 (1988) 145-162.
20. A. Prékopa, Stochastic Programming, Kluwer, Dordrecht, Boston, 1995.
21. S. Sen, Relaxations for the probabilistically constrained programs with discrete random variables. Operations Research Letters 11 (1992) 81-86.
22. L.A. Wolsey, Integer Programming, John Wiley & Sons, New York, 1998.