Bilevel stochastic transportation problem with exponentially distributed demand

Abstract

In this paper, we consider a bilevel stochastic transportation problem (BSTP) which is a two level hierarchical program to determine optimal transportation plan assuming that customers’ demands are stochastic, in particular, exponentially distributed

Keywords

• Bilevel programming, stochastic programming, stochastic transportation problem, exponentially distributed demand

References

1. Akdemir GH, Tiryaki F (2011). İki seviyeli kesikli stokastik taşıma problemi. Electron J Vocat Coll 1, 198-210.
2. Bard JF, Moore JT (1990). A branch and bound algorithm for the bilevel programming problem. SIAM J Sci Stat Comput 11, 281–292.
3. Colson B, Marcotte P, Savard G (2005a). A trust-region method for nonlinear bilevel programming: algorithm and computational experience. Comput Optim Appl 30, 211-227.
4. Colson B, Marcotte P, Savard G (2005b). Bilevel programming: A survey. 4OR: Q J Oper Res 3, 87-107.
5. Daneva M, Larsson T, Patriksson M, Rydergren C (2010). A comparison of feasible direction methods for the stochastic transportation problem. Comput Optim Appl 46, 451-466.
6. Dempe S (2003). Bilevel programming A survey. Technical Report TU 2003-11, Bergakademie Freiberg.
7. Frank M, Wolfe P (1956). An algorithm for quadratic programming. Nav Res Log Q 3, 95–110.
8. Holmberg K (1984). Separable programming applied to the stochastic transportation problem. Research Report Mathematics, Linkoping Institute of Technology, Sweden. Department of

9. Holmberg K, Jörnsten K (1984). Cross decomposition applied to the stochastic transportation problem. Eur J Oper Res 17, 361-368.
10. Holmberg K (1992). Linear mean value cross decomposition: A generalization of the Konai-Liptak method. Eur J Oper Res 62, 55–73.
11. Holmberg K, Tuy H (1999). A production-transportation problem with stochastic demand and concave production costs. Math Prog 85, 157–179.
12. Kalashnikov VV, Pérez-Valdés GA, Tomasgard A, Kalashnykova NI (2010). Natural gas cash-out problem: bilevel stochastic optimization approach. Eur J Oper Res 206, 18-33.
13. Katagiri H, Ichiro N, Sakawa M, Kato K (2007). Stackelberg solutions to stochastic two-level linear programming problems. Proceedings of the 2007 IEEE Symposium on Computational Intelligence in Multicriteria Decision Making (MCMD’07), Hawaii, 240-244.
14. Kato K, Katagiri H, Sakawa M, Wang J (2006). Interactive fuzzy programming based on a probability maximization model for two-level stochastic linear programming Communications in Japan (Part III: Fundamental Electron Sci 89, 33-42. Electronics and
15. Law AM, Kelton WD (1991). Simulation modeling and analysis. (2nd ed.). New York: McGraw-Hill Inc.
16. Lin GH, Chen X, Fukushima M (2009). Solving stochastic mathematical programs with equilibrium constraints via programming with penalization. Math Program Ser B, 116, 343–368. smoothing implicit
17. Patriksson M, Wynter L (1999). Stochastic mathematical programs with equilibrium constraints. Oper Res Lett 25, 159-167.
18. Ross, S. M. (2003). Introduction to probability models (8th Edition), International Edition, Academic Press.
19. Qi L (1985). Forest iteration method for stochastic transportation problem. Math Prog Study 25, 142-163.
20. Roghanian E, Sadjadi SJ, Aryanezhad MB (2007). A probabilistic programming problem to supply chain planning. Appl Math Comput 188, 786-800. linear multi-objective
21. Ryu JH, Dua V, Pistikopoulos EN (2004). A bilevel programming framework for enterprise-wide process networks under uncertainty. Comput Chem Eng 28, 1121-1129.
22. Sonia KA, Puri MC (2008). Bilevel time minimizing transportation problem. Discrete Optim 5, 714-723.
23. Werner AS (2005). Bilevel stochastic programming problems: telecommunications. University of Science and Technology, Faculty of Social Sciences and Technology Management, Trondheim, Norway. and application to PhD Thesis, Norwegian
24. Williams AC (1963). A stochastic transportation problem. Oper Res 11, 759-770.