Zone design of specific sizes using adaptive additively weighted voronoi diagrams

Territory or zone design processes entail partitioning a geographic space, organized as a set of areal units, into different regions or zones according to a specific set of criteria that are dependent on the application context. In most cases, the aim is to create zones of approximately equal sizes (zones with equal numbers of inhabitants, same average sales, etc.). However, some of the new applications that have emerged, particularly in the context of sustainable development policies, are aimed at defining zones of a predetermined, though not necessarily similar, size. In addition, the zones should be built around a given set of seeds. This type of partitioning has not been sufficiently researched; therefore, there are no known approaches for automated zone delimitation. This study proposes a new method based on a discrete version of the adaptive additively weighted Voronoi diagram that makes it possible to partition a two-dimensional space into zones of specific sizes, taking both the position and the weight of each seed into account. The method consists of repeatedly solving a traditional additively weighted Voronoi diagram, so that each seed?s weight is updated at every iteration. The zones are geographically connected using a metric based on the shortest path. Tests conducted on the extensive farming system of three municipalities in Castile-La Mancha (Spain) have established that the proposed heuristic procedure is valid for solving this type of partitioning problem. Nevertheless, these tests confirmed that the given seed position determines the spatial configuration the method must solve and this may have a great impact on the resulting partition

Improved instance generation for kidney exchange programmes

Kidney exchange programmes increase the rate of living donor kidney transplants, and operations research techniques are vital to such programmes. These techniques, as well as changes to policy regarding kidney exchange programmes, are often tested using random instances created by a Saidman generator. We show that instances produced by such a generator differ from real-world instances across a number of important parameters, including the average number of recipients that are compatible with a certain donor. We exploit these differences to devise powerful upper and lower bounds and we demonstrate their effectiveness by optimally solving a benchmark set of Saidman instances in seconds; this set could not be solved in under thirty minutes with previous algorithms. We then present new techniques for generating random kidney exchange instances that are far more consistent with real-world instances from the UK kidney exchange programme. This new process for generating random instances provides a more accurate base for comparisons of algorithms and models, and gives policy-makers a better understanding of potential changes to policy leading to an improved decision-making process

Police districting problem: literature review and annotated bibliography

The police districting problem concerns the efficient and effective design of patrol sectors in terms of performance attributes. Effectiveness is particularly important as it directly influences the ability of police agencies to stop and prevent crime. However, in this problem, a homogeneous distribution of workload is also desirable to guarantee fairness to the police agents and an increase in their satisfaction. This chapter provides a systematic review of the literature related to the police districting problem, whose history dates back to almost 50 years ago. Contributions are categorized in terms of attributes and solution methodology adopted. Also, an annotated bibliography that presents the most relevant elements of each research is given

A generic geometric approach to territory design and districting

Territory design and districting may be viewed as the problem of grouping small geographic areas into larger geographic clusters called territories in such a way that the latter are acceptable according to relevant planning criteria. The availability of GIS on computers and the growing interest in Geo-Marketing leads to an increasing importance of this area. Despite the wide range of applications for territory design problems, when taking a closer look at the models proposed in the literature, a lot of similarities can be noticed. Indeed, the models are many times very similar and can often be, more or less directly, carried over to other applications. Therefore, our aim is to provide a generic application-independent model and present efficient solution techniques. We introduce a basic model that covers aspects common to most applications. Moreover, we present a method for solving the general model which is based on ideas from the field of computational geometry. Theoretical as well as computational results underlining the efficiency of the new approach will be given. Finally, we show how to extend the model and solution algorithm to make it applicable for a broader range of applications and how to integrate the presented techniques into a GIS

Towards a Unified Territory Design Approach – Applications, Algorithms and GIS Integration

Territory design may be viewed as the problem of grouping small geographic areas into larger geographic clusters called territories in such a way that the latter are acceptable according to relevant planning criteria. In this paper we review the existing literature for applications of territory design problems and solution approaches for solving these types of problems. After identifying features common to all applications we introduce a basic territory design model and present in detail two approaches for solving this model: a classical location–allocation approach combined with optimal split resolution techniques and a newly developed computational geometry based method. We present computational results indicating the efficiency and suitability of the latter method for solving large–scale practical problems in an interactive environment. Furthermore, we discuss extensions to the basic model and its integration into Geographic Information Systems

A novel territory design model arising in the implementation of the WEEE-Directive

The problem discussed in this paper is motivated by the new recycling directiveWEEE of the EC. The core of this law is, that each company which sells electrical or electronic equipment in a European country has the obligation to recollect and recycle an amount of returned items which is proportional to its market share. To assign collection stations to companies, in Germany for one product type a territory design approach is planned. However, in contrast to classical territory design, the territories should be geographically as dispersed as possible to avoid that a company, resp. its logistics provider responsible for the recollection, gains a monopoly in some region. First, we identify an appropriate measure for the dispersion of a territory. Afterwards, we present a first mathematical programming model for this new problem as well as a solution method based on the GRASP methodology. Extensive computational results illustrate the suitability of the model and assess the effectiveness of the heuristic

A two-stage approach for improving service management in retail banking

Bu çalışma, Eylül 05-07, 2007 tarihleri arasında Saarbrucken [Almanya]’da düzenlenen Annual International Conference of the German-Operations-Research-Society’da bildiri olarak sunulmuştur.Efficiency analysis is a survival tool for bank managers due to severe competition in retail banking industry. Certainly, it is important to identify the inefficient branches of a bank in building better service management and marketing strategies. The problem here is to eliminate the causes of their inefficiencies in order to improve the inefficient branches. In this study, a two-stage methodology consisting of Data Envelopment Analysis (DEA) and data mining is proposed for solving the problem. Firstly, DEA is used for measuring the relative efficiencies of a bank's branches. Secondly, data mining is used to extract useful information from given data consisting of the characteristics of bank branches, thus allowing bank managers to identify the underlying causes of inefficiencies and helping them to improve their service management. The approach is used in the valuation of the one's branches of the biggest banks in Turkey.German Operat Res So

Multifacility ordered median problems on networks: a further analysis

We address the ordered p-median problem, which includes as special cases most of the classical multifacility location problems discussed in the literature. Finite dominating sets (FDS) are known for particular instances of this problem: p-median, p-center, and p-centdian. We find an FDS for the ordered p-median problem. This set allows us to gain a better insight into the general FDS structure of network location problems. This FDS is later used to present the first polynomial time algorithm for p-facility ordered median problems on tree networks. This result is combined with some approximation algorithms to give an O(log M log log M) approximate solution of these problems on general networks, where M is the number of vertices