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Aggregation and non aggregation techniques for large facility location problems - a survey

A facility location problem is concerned with determining the location of some useful facilities in such a way so to fulfil one or a few objective functions and constraints. We survey those problems where, in the presence of a large number of customers, some form of aggregation may be required. In addition, a review on conditional location problems where some (say q) facilities already exist in the study area is presented. | Yugoslav Journal of Operations Research 25 (2015), Number , 3, 313-341 DOI: 10.2298/YJOR140909001I AGGREGATION AND NON AGGREGATION TECHNIQUES FOR LARGE FACILITY LOCATION PROBLEMS - A SURVEY Chandra Ade IRAWAN Centre for Operational Research and Logistics, Department of Mathematics, University of Portsmouth, UK and Department of Industrial Engineering, Institut Teknologi Nasional, Bandung, Indonesia chandra.irawan@port.ac.uk Said SALHI Centre for Logistics and Heuristic Optimization (CLHO), Kent Business School, University of Kent S.Salhi@kent.ac.uk Received: September 2014 / Accepted: January 2015 Abstract: A facility location problem is concerned with determining the location of some useful facilities in such a way so to fulfil one or a few objective functions and constraints. We survey those problems where, in the presence of a large number of customers, some form of aggregation may be required. In addition, a review on conditional location problems where some (say q) facilities already exist in the study area is presented. Keywords: Large Location Problem, p-median and p-centre Problems, Point Representation, Aggregation. MSC: 90B06, 90C05, 90C08. 1. INTRODUCTION Research in location theory formally started in 1909 by Alfred Weber [110] known as the father of modern location theory (Eilon et al. [35]). He studied the problem of locating a single warehouse in order to minimise the total travel distance between the warehouse and a set of customers. Since then, many researchers 314 C.A. Irawan, S. Salhi / Large Facility Location Problems Survey have observed this problem in many different areas. These include Hotelling [65], who considered the problem of locating two competing vendors along a straight line. The first powerful iterative approach to deal with the single facility location problem in the plane so to minimise the sum of the weighted distances from a single facility to all the points (i.e., continuous space) is put forward by .