A two-stage data envelopment analysis approach to solve extended transportation problem with non-homogenous costs

The transportation problem is a particular type of linear programming problem in which the main objective is to minimize the cost. In marked contrast to the classical real-world transportation model, shipping supplies from one source to a destination cause several costs and benefits, each of which is incomparable to another. The extended transportation problem was first introduced in a study conducted by Amirteimoori [1]. In contrast, many important questions regarding the production possibility set, the place of costs, the benefits, and the essence of these costs were not fully addressed yet. Therefore, this paper focuses on transportation models that do not provide explicit output. This method is helpful because it is designed for a specific purpose: to send goods and supply-demand at the lowest cost and decision-maker; does not suffer from the confusion of costs and the various consequences of placing them costs and outputs. Furthermore, this model improves the contradiction between the essence of the problem and the input/output-oriented data envelopment analysis. In this paper, previous models that can not incorporate all the sources of inefficiency have been solved. We apply the slack-based measure(SBM) to calculate all identified inefficiency sources. A numerical example is considered to show the approach's applicability, as mentioned above, to actual life situations. As a result, the optimal costs achieved via the proposed method are more realistic and accurate by obtaining a more representative efficiency assessment. This example proved our proposed approach's efficiency, providing a more efficient solution by corporate all sources inefficiency and presenting efficient costs for each path.