Multi-Choice Linear Programming Models and It's Engineering Applications

Abstract

In some optimization problems, one parameter or more may have a multiple choices. These multi-choice values of the parameters are considered by the experts or decision makers. In this case, the optimization problem is called a multi- choice problem. To solve this type of problem, there is no direct method even in the case of a medium size problem involving multi- choice parameter is computationally expensive to obtain an optimal solution. Therefore, to develop a methodology that optimizes objective function and selects an appropriate multi- choice parameter, is one of the challenging problem in multi-choice programming problem. Keeping this in mind the core of the thesis is concentrated in building up solution procedures for multi- choice problem that can be implemented also to probabilistic and fuzzy programming problems involving multi- choice type parameters. Several parameters, namely cost coefficients, technical coefficients, resource limits may be taken into consideration when formulating a multi- choice programming problem. The thesis highlights the treatment of multi-choice problem considering the resource limits as multi- choice type parameters. It covers a detailed description of transformation techniques with the help of some variables known as binary variables to solve a multi- choice problem. It also describes the application of some numerical methods, namely interpolating polynomial methods for multi-choice parameters with the intention of avoiding the difficulties that arises during the usage of binary variables for transformation of multi- choice Linear programming (LP) problem to an equivalent multi- choice problem.