In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and generalized Tchebycheff norm then use it to obtain some equivalent characterizations (weakly, strictly, properly) efficient solutions adjusting range parameters. These results do not need any convexity assumption conditions object...

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 app...