Detecting All Non-Dominated Points for Multi-Objective Multi-Index Transportation Problems

Multi-dimensional transportation problems denoted as multi-index are considered the extension of classical and appropriate practical modeling for solving real–world with multiple supply, demand, well different modes demands or delivering kinds commodities. This paper presents a method detecting complete nondominated set (efficient solutions) multi-objective four-index problems. The proposed approach implements weighted sum to convert problem into single objective problem, that can then be decomposed two-index sub-problems. For each sub-problem, parametric analysis was investigated determine range weights values keep efficient solution unchanged, which enable decision maker detect all solutions original also find stability first kind solution. Finally, an illustrative example is presented illustrate efficiency robustness approach. results demonstrate effectiveness solutions.