Corresponding author: George P. Alexandris , Ph.D., Lecturer Department of Mathematics and Science Engineering Hellenic Military University An Object Oriented Approach for the Discertization Process GEORGE P. ALEXANDRIS, NIKOLAOS V. KARADIMAS, NIKOLAOS DOUKAS Informatics and Computer Engineering LAB, Sector of Mathematics and Engineering Sciences Department of Military Sciences Hellenic Military University – Hellenic Army Academy Vari-Koropi Ave, 16673, Vari GREECE gpa@aueb.gr, nkaradimas@sse.gr, doukasn@sse.gr Abstract: - The representation of demand is a key issue which can significantly affect results in several demand covering models. In this paper we concentrate on the well known Maximal Coverage Location Problem and introduce a new parametrical object oriented approach for the discretization process so as to demonstrate that alternative representations of the demand space during the discertization process may lead to largely fluctuating as well as misleading results which seriously overestimate or underestimate the real coverage achieved by a specified number of servers. The new parametrical object oriented approach is based on the notions of data abstraction, encapsulation, polymorphism and inheritance and exploits the capabilities of Geographic Information Systems so as to create flexibility during the representation of demand. Furthermore we modify MCLP so as to work more efficiently with the new discertization process using exclusively objects and not characteristics like distance. Results of an empirical study indicate that the combination of the new object oriented approach with the modified MCLP is an alternative way so as not to create overestimation or underestimation and that there is absolutely no difference between the real (actual) coverage that can be verified using ArcGIS tools and the reported coverage, given by the solution of each integer problem. Key words: Object Oriented, Parametrical discertization Process, Demand Covering, Geographic Information Systems (GIS), Location Analysis 1 Introduction Demand covering problems constitute an extensive set of problems in location analysis with numerous applications ranging from crew scheduling to cytological screening tests (PAP tests) for cervical cancer [1]. They deal with the proper location of servers (facilities) such that a given demand set is appropriately covered. Coverage is achieved when the service provided by a server is available to any point within the demand area within some predetermined distance or time. In most practical applications of these models, both the demand area and the feasible locations of the servers are described by discrete sets. In cases where one (or both) set is continuous, a common approach is to transform this set (or sets) into a discrete one. One way to do this is by superimposing a grid of blocks over the continuous area and specifying a single point within each block as a representative of that block. Another way, is to use aggregate zones so as to present Geographic information of some spatial phenomena and a point within each zone as a representative. The problem is then stated as a discrete covering problem and is solved using one of the classical techniques. Although this discertization process results in a much simpler calculation of coverage, it introduces some error into the objective function and, in turn, to the optimal solution. The sources and the magnitude of this error have been studied extensively by various researchers. In fact, a number of different errors have been identified [2]. Error type A is the most common [3]. This error occurs when points in the demand area, different from the aggregated demand points, are not covered but considered as covered. Generally speaking the aggregation of demand points usually leads to suboptimal solutions. Goodchild [4] examined primarily the effects of different aggregations on the p-median problem and secondary on coverage and min-max problems. Moreover, Goodchild noticed that ‘solutions using aggregated data are open to extensive manipulation and in fact cast some degree of doubt on the usefulness of some location – allocation models’. McKnew [5] developed a simple regression model to estimate the number of servers required to cover a region and study the error involved. Daskin [6], Hodgson and Neuman [7] and Current and Shilling [3] made an extensive analysis of the error introduced into location-allocation models by transforming a continuous surface to a Recent Researches in Applications of Electrical and Computer Engineering ISBN: 978-1-61804-074-9 125