Bilevel stochastic transportation problem with exponentially distributed demand

Yıl 2012, Cilt: 2 Sayı: 1, 32 - 37, 23.06.2012

Hande Günay Akdemir , Fatma Tiryaki

https://doi.org/10.17678/beuscitech.47150

Cited By: 2

Öz

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

Anahtar Kelimeler

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

Kaynakça

• Akdemir GH, Tiryaki F (2011). İki seviyeli kesikli stokastik taşıma problemi. Electron J Vocat Coll 1, 198-210.
• Bard JF, Moore JT (1990). A branch and bound algorithm for the bilevel programming problem. SIAM J Sci Stat Comput 11, 281–292.
• 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.
• Colson B, Marcotte P, Savard G (2005b). Bilevel programming: A survey. 4OR: Q J Oper Res 3, 87-107.
• 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.
• Dempe S (2003). Bilevel programming A survey. Technical Report TU 2003-11, Bergakademie Freiberg.
• Frank M, Wolfe P (1956). An algorithm for quadratic programming. Nav Res Log Q 3, 95–110.
• Holmberg K (1984). Separable programming applied to the stochastic transportation problem. Research Report Mathematics, Linkoping Institute of Technology, Sweden. Department of
• Holmberg K, Jörnsten K (1984). Cross decomposition applied to the stochastic transportation problem. Eur J Oper Res 17, 361-368.
• Holmberg K (1992). Linear mean value cross decomposition: A generalization of the Konai-Liptak method. Eur J Oper Res 62, 55–73.
• Holmberg K, Tuy H (1999). A production-transportation problem with stochastic demand and concave production costs. Math Prog 85, 157–179.
• 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.
• 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.
• 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
• Law AM, Kelton WD (1991). Simulation modeling and analysis. (2nd ed.). New York: McGraw-Hill Inc.
• 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
• Patriksson M, Wynter L (1999). Stochastic mathematical programs with equilibrium constraints. Oper Res Lett 25, 159-167.
• Ross, S. M. (2003). Introduction to probability models (8th Edition), International Edition, Academic Press.
• Qi L (1985). Forest iteration method for stochastic transportation problem. Math Prog Study 25, 142-163.
• Roghanian E, Sadjadi SJ, Aryanezhad MB (2007). A probabilistic programming problem to supply chain planning. Appl Math Comput 188, 786-800. linear multi-objective
• Ryu JH, Dua V, Pistikopoulos EN (2004). A bilevel programming framework for enterprise-wide process networks under uncertainty. Comput Chem Eng 28, 1121-1129.
• Sonia KA, Puri MC (2008). Bilevel time minimizing transportation problem. Discrete Optim 5, 714-723.
• 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
• Williams AC (1963). A stochastic transportation problem. Oper Res 11, 759-770.