A simple and effective genetic algorithm for the two-stage capacitated facility location problem q Diogo R.M. Fernandes a , Caroline Rocha b , Daniel Aloise c,⇑ , Glaydston M. Ribeiro d , Enilson M. Santos e , Allyson Silva a a Department of Industrial Engineering, Federal University of Rio Grande do Norte, Brazil b School of Sciences and Technology, Federal University of Rio Grande do Norte, Brazil c Department of Computer Engineering and Automation, Federal University of Rio Grande do Norte, Brazil d Department of Transport Engineering, COPPE-Graduate School and Research in Engineering, Brazil e Department of Civil Engineering, Federal University of Rio Grande do Norte, Brazil article info Article history: Received 17 October 2013 Received in revised form 9 April 2014 Accepted 31 May 2014 Available online 5 July 2014 Keywords: Two-stage facility location Genetic algorithm Multi-stage transportation systems abstract This paper presents a simple and effective Genetic Algorithm (GA) for the two-stage capacitated facility location problem (TSCFLP). The TSCFLP is a typical location problem which arises in freight transporta- tion. In this problem, a single product must be transported from a set of plants to meet customers demands, passing out by intermediate depots. The objective is to minimize the operation costs of the underlying two-stage transportation system thereby satisfying demand and capacity constraints of its agents. For this purpose, a GA is proposed and computational results are reported comparing the heuristic results with those obtained by two state-of-the-art Lagrangian heuristics proposed in the literature for the problem. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Location Analysis is one of the most active fields in Operations Research and Industrial Engineering. It deals with the decision of optimally placing facilities in order to minimize operational costs (Nickel & Puerto, 2005; Daskin, 1995; Drezner & Hamacher, 2004). Although solved in several practical situations by intuitive methods, optimal facility location decisions usually demand more in-depth studies. Regardless of the type of business in which the company/industry is involved, the decisions about location are strategic and belong to the core of any planning and/or management process. Furthermore, these decisions lead to long term commitments due to high costs involved in installing location facilities. The choice of the location may have influence over the relations between the company and its clients. If the client must be physically joined in the process, it is unlikely that a location is acceptable if the travel time or distance between the provider and the client is relatively large. Many different facility location models have been proposed in order to cope with the large spectrum of real-world applications (see Klose & Drexl (2005) for a survey). Multi-stage modeling consists in finding the optimal placement for facilities on several hierarchically layered levels. They are traditionally solved sequentially providing, in some cases, infeasible or less profitable solutions (Guyonnet, Grant, & Bagajewicz, 2009). Particularly, the two-stage capacitated facility location problem (TSCFLP) is a typi- cal problem which arises in freight transportation. In this problem, a single product must be transported from a set of plants to meet customers demands. However, the transportation is not performed directly; the plants send the product to a set of depots which perform the delivery to customers. Then, there are two transporta- tion flows: between plants and depots, and between depots and customers. The TSCFLP includes capacities for plants and depots, fixed and variable costs. The fixed costs are assigned to opening of plants and depots and the variables costs are assigned to trans- portation flows. So, we need to identify which plants and depots should be opened to serve all customers, at a minimal total cost. The TSCFLP has some variants. For instance, Tragantalerngsak, Holt, and Ronnqvist (2000) approached a TSCFLP where depots are load with goods from a single plant and a customer is served by just one depot. Klose (2000), Keskin and Íster (2007) approach the TSCFLP on locating only the depots, i.e., the location of the http://dx.doi.org/10.1016/j.cie.2014.05.023 0360-8352/Ó 2014 Elsevier Ltd. All rights reserved. q This manuscript was processed by Area Editor Qiuhong Zhao. ⇑ Corresponding author. Tel.: +55 8499069268. E-mail addresses: diogorobson@hotmail.com (D.R.M. Fernandes), caroline. rocha@ect.ufrn.br (C. Rocha), aloise@dca.ufrn.br (D. Aloise), glaydston@pet.coppe. ufrj.br (G.M. Ribeiro), enilson@interjato.com.br (E.M. Santos), allysonfcs@gmail.com (A. Silva). Computers & Industrial Engineering 75 (2014) 200–208 Contents lists available at ScienceDirect Computers & Industrial Engineering journal homepage: www.elsevier.com/locate/caie