Effects of Probability Function on the Performance of Stochastic Programming

Journal of Optimization in Industrial Engineering

مقاله 5، دوره 11، شماره 1 - شماره پیاپی 23، خرداد 2018، صفحه 67-76   

نوع مقاله: Original Manuscript

شناسه دیجیتال (DOI): 10.22094/joie.2017.567.63

نویسندگان

Mohammad Ebrahim Karbaschi¹؛ Mohammad Reza Banan^{* 2}

¹Ph.D. Candidate in Structural Eengineering, Shiraz University, Shiraz, Iran.

²Associate Professor, Department of Civil and Environment Engineering, Shiraz University, Shiraz, Iran.

چکیده

Stochastic programming is a valuable optimization tool where used when some or all of the design parameters of an optimization problem are defined by stochastic variables rather than by deterministic quantities. Depending on the nature of equations involved in the problem, a stochastic optimization problem is called a stochastic linear or nonlinear programming problem. In this paper,a stochastic optimization problem is transformed intoan equivalent deterministic problem,which can be solved byany known classical methods (interior penalty method is applied here).The paper mainly focuseson investigatingthe effect of applying various probability functions distributions(normal, gamma, and exponential) for design variables. The following basic required equations to solve nonlinear stochastic problems with various probability functionsfor random variables are derived and sensitivity analyses to studythe effects of distribution function typesand input parameterson the optimum solution are presented as graphs and in tables by studyingtwoconsidered test problems. It is concluded that thedifference between probabilistic and deterministic solutions toa problem, when the normal distribution ofrandom variables isused, is very different fromthe results when gamma and exponential distribution functions are used. Finally, it is shownthat the rate of solution convergence tothe normal distribution is faster than the other distributions.

کلیدواژه‌ها

Stochastic programming؛ Sensitivity analysis؛ linear programming؛ Nonlinear Programming؛ Exponential, Gamma and normal probability functions