tailieunhanh - 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: 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 Said SALHI Centre for Logistics and Heuristic Optimization (CLHO), Kent Business School, University of Kent 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 . 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 (., continuous space) is put forward by .