Solving probabilistic programming problems involving multi-choice parameters

Abstract

Probabilistic programming is used in some optimization problems where some or all parameters are considered as random variables, in order to deal with uncertainty, which is an inherent feature of the system. The situation of multiple parameters may exist in a decision making problem in our real life. The multi-choice programming can not only avoid the underestimation of parameters, but also can decide the appropriate parameter from multiple parameters. This paper deals with a probabilistic linear programming problem, where the right hand side parameters of probabilistic constraints are multi-choice in nature and rest of the parameters are independent random variables. In this paper the probabilistic programming problem is converted to an equivalent deterministic mathematical programming model. The resulting model is then solved by standard linear or non-linear programming techniques. A numerical example is presented to illustrate the methodology.