Contemporary Engineering Sciences, Vol. 3, 2010, no. 2, 53 - 62 DEA and Multi-Objective Shortest Path Problems Mir Mozaffar Masoumi, Farhad Hosseinzadeh Lotfi and Amir Mohammad Mobasseri* Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Abstract In this paper we are concerned with a particular multi-criteria optimal path problem, known as the multi-objective shortest path problem. The purpose of this paper is to study a data envelopment analysis (DEA) model that allows us to determine the set of all non-dominated paths on a network. We prove that the non- dominated path in multi-objective shortest path problem is equivalent to corresponding strongly efficient unit in its DEA model without output with actually observed units. Mathematics Subject Classification: 90C29, 90C35, 52B05, 05C20 Keywords: Multi-objective Shortest Path Problem, Data Envelopment Analysis, Free Disposal Hull, Efficiency, Non-dominated Path 1 Introduction The optimal solution of the classic shortest path problem with a Min-Sum objective function is a single shortest route in a directed graph. This problem may be solved by a label-correcting algorithm [14] or for non-negative costs solved by a label-setting algorithm such as Dijkstra’s algorithm [6]. We can also consider several other objective functions such as Max-Sum, Max-Production or Max-Min function (See Ahuja et al. [15]). However, considering one objective function such as minimizing the sum of the arcs’ costs of the path may not be sufficient to describe real world problems. Suppose that each of the arcs of the graph has a number of both kinds of criteria, costs and benefits. In general, no single route * Corresponding author. E-mail address: Amir.mobasseri@gmail.com (A. M. Mobasseri)