Title: An O(m² + mn²) algorithm for the bi-objective location problem on a network with mixed metrics

Authors: Emanuel Melachrinoudis; Emre Yavuz; Ruhollah Heydari

Addresses: Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA ' Arcelik-LG Klima San. ve Tic. A.Ş., Gebze Organize Sanayi Bölgesi, 139 Ihsan Dede Cad., Gebze/Kocaeli 41480, Turkey ' Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA

Abstract: In this paper, we formulate the Euclidean maximin with the network minisum bi-objective location model for a semi-obnoxious facility on a transportation network that is embedded into the Euclidean plane. The Euclidean distance metric is used in modelling the undesirable characteristics of the facility, using the maximin objective, while the network shortest path distance metric is used for modelling the transportation cost to these facilities using the minisum objective. After identifying the problem properties, we develop an O(m² + mn²) algorithm for generating the efficient set and implement this algorithm in a realistic example involving the location of a semi-obnoxious facility in the province of Bursa in Turkey.

Keywords: semi-obnoxious facility; bi-objective location; Euclidean maximin; minisum; transport networks; modelling; transports costs; Turkey.

DOI: 10.1504/IJOR.2015.070144

International Journal of Operational Research, 2015 Vol.23 No.4, pp.427 - 450

Received: 22 Jun 2013
Accepted: 05 Aug 2013
Published online: 28 Jun 2015 *

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