An acceptability index based approach for solving shortest path problem on a network with interval weights

Department of Mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran

^* Corresponding author: a.ebrahimnejad@qaemiau.ac.ir, aemarzoun@gmail.com

Received: 7 May 2019
Accepted: 26 March 2020

Abstract

Based on the acceptability index for comparison of any two imprecise values, efficient algorithms have been proposed in the literature for solving shortest path (SP) problem when the weights of connected arcs in a transportation network are represented as interval numbers. In this study, a generalized Dijkstra algorithm is proposed to handle the SP problem with interval weights. Here it is shown that once the acceptability index is chosen, the interval SP problem is converted into crisp one, which is easily solved by the standard SP algorithms. The main contribution here is the reduction of the computational complexity of the existing algorithm for solving interval SP problem. To show the advantages of the proposed algorithm over existing algorithm the numerical example presented in literature is solved using the proposed algorithm and the obtained results are discussed. Moreover, an small sized telecommunication network is provided to illustrate the potential application of the proposed method. Finally, the practical relevance of the proposed algorithm is evaluated by means of a large scale pilot case where a pharmaceutical shipment between the cities in Iran should be transported.