Multi-choice probabilistic linear programming problem

作     者：Pradhan, Avik Biswal, M. P. 

作者机构：Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India 

出 版 物：《OPSEARCH》 (运筹学；印度运筹学会志)

年 卷 期：2017年第54卷第1期

页      面：122-142页

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Chance-constrained programming Multi-choice programming Linear programming Probabilistic programming 

摘      要：In this paper, we present a linear programming model where the parameter space contains some multi-choice parameters. Alternative choices of multi-choice parameter are considered as random variables. Using interpolating polynomial for each multi-choice parameter, the model has been transformed into a non-linear mixed integer probabilistic programming problem. Then chance constrained programming technique is used to obtain an equivalent deterministic model of the transformed problem. To find the deterministic form of the objective function four different models namely, E-model, V-model, probability maximization model and fractile criterion model are used. Assuming the values of the multi-choice parameters as independent normal random variables, the methodology is presented. A numerical example is also presented to illustrate the methodology.