Solving multi‐choice linear programming problems by interpolating polynomials

Multi‐choice programming solves some optimization problems where multiple information exists for a parameter. The aim of this paper is to select an appropriate parameter from a set of multiple choices, which optimizes the objective function. We consider a linear programming problem where the right hand side parameters are multi‐choice in nature. In this paper, the multiple choices of a parameter are considered as functional values of an affine function at some non‐negative integer nodes. An interpolating polynomial is formulated using functional values at non‐negative integer nodes to take care of any multi‐choice parameter. After establishing interpolating polynomials of all multi‐choice parameters, a mathematical programming problem is formulated. The formulated problem is treated as a nonlinear programming problem involving mixed integer type variables. It can be solved by using standard nonlinear programming software. Finally, a numerical example is presented to illustrate the solution procedure.