Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand

This study develops a mathematical model for a transportation problem consisting of a multi-objective environment with nonlinear cost and multi-choice demand. The objective functions of the proposed transportation problem are non-commensurable and conflict with each other. The focus of the paper is on objective functions of nonlinear type, which occur due to the extra cost of supplying goods remaining at their points of origin to various destinations, and on demand parameters that are considered to be of multi-choice type. Thus, the mathematical model is formulated by considering nonlinear cost and multi-choice demand. Multi-choice programming models cannot be solved directly. A general transformation technique is developed to make multi-choice demand tractable with the help of binary variables. Therefore, an equivalent multi-objective decision making model is established in order to find the optimal solution of the problem. The outcome from a numerical example demonstrates the feasibility of the proposed method.