A Proposed Technique for Solving Scenario Based Multi-Period Stochastic Optimization Problems with Computer Application

Автор: Sajal Chakroborty, M. Babul Hasan

Журнал: International Journal of Mathematical Sciences and Computing(IJMSC) @ijmsc

Статья в выпуске: 4 vol.2, 2016 года.

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In this paper, we have presented a new technique for solving scenario based multi-period stochastic programming problems and presented a case study for the business policy of a super shop market in Bangladesh. We have developed our technique based on decomposition based pricing method which is the latest and faster decomposition technique in use. To our knowledge, this is the first work in the field of stochastic programming for solving multi-period stochastic optimization problems by using decomposition based pricing method. We have also developed a model by collecting data of a year from a super shop market of Bangladesh and analyzed their profit by dividing the whole year into four periods for different scenarios of an uncertainty. We have developed a computer code by using mathematical programming language AMPL and analyzed the model by using our developed technique.

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SP, DBP, Scenarios, AMPL, LP, Decomposition, Sub-problem, Master problem, Deterministic problem

Короткий адрес: https://sciup.org/15010289

IDR: 15010289

Список литературы A Proposed Technique for Solving Scenario Based Multi-Period Stochastic Optimization Problems with Computer Application

  • Brige, J. R. and Louveaux, F. (1997).Introduction to Stochastic Programming, Springer, Verlag, New York.
  • Benders, J.F. (1962). Partitioning Procedures for Solving Mixed Variables Programming Problems, Numerische Mathematik, 4(3):238-252.
  • Charnes, A. and Cooper, W. W. (1959). Chance-constrained Programming, Management Science, 6(1): 73-79.
  • Defourny, B., Ernst, D. and Wehenkel, L.(2013).Multi-Stage Stochastic Programming: A Scenario Tree Based Approach to Planning Under Uncertainty, INFORMS Journal on Computing, 25(3): 488-501.
  • Dantzig, G. B. and Wolfe, P. (1961). The Decomposition Algorithm for Linear Programming, Econometrica, 29(4):101-111.
  • Higel, J.L., and Sen, S. (1999). Statistical Approximations for Stochastic Linear Programs, Ann. Oper. Res., 85(1): 173-192.
  • Higel, J.L. and Sen, S. (1991). An Algorithm for Two Stage Linear Programs with Recourse, Mathematics of Operations Research, 16(3): 650-669.
  • Kall,P.(1997). Stochastic Linear Programming, Springer.
  • Mamer, J. W. and McBride, R. D. (2000). A Decomposition-based Pricing Procedure for Large-Scale Linear Programs: An application to the linear multi-commodity Flow Problem, 46(5), 693-709.
  • Messina, E. and Mitra, G. (1997). Modeling and Analysis of Multi Stage Stochastic Programming Problems: A Software Environment, Eurp. J. Oper. Res., 101(2): 343-359.
  • Ravindran, A., Philips, D. T., and Solberg, J. J. (2005) .Operations Research: Principles and Practice.
  • Slyke, R. V., and Wets, R. G. B. (1969). L-Shaped Programs with Applications to Control and Stochastic Programming, SIAM, J. on Applied Mathematics, 17 (4):638-663.
  • Topologlu, H. and Powell, W. B. (2006). Dynamic Programming Approximations for Stochastic, Time-Staged Integer Multi-Commodity Flow Problems, 18(1):31-42.
  • Weiner A. and Khan, H. (1967). The Year 2000: A Framework for Speculation on the next Thirty Three years, Macmillan, New York.
  • Winston, W.L. (1994).Linear Programming: Applications and Algorithm, Dunbury Press, Bellmont, California, U.S.A.
  • Wallace, S.W. and Ziemba, W. T. (2005).Applications of Stochastic Programming, Society of Industrial and Applied Mathematics.
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