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In this paper, a new mixed integer mathematical programme is proposed for the application of Hub Location Problems (HLP) in public transport planning. This model is among the few existing ones for this application. Some classes of valid inequalities are proposed yielding a very tight model. To solve instances of this problem where existing standard solvers fail, two approaches are proposed. The first one is an exact accelerated Benders decomposition algorithm and the latter a greedy neighborhood search. The computational results substantiate the superiority of our solution approaches to existing standard MIP solvers like CPLEX, both in terms of computational time and problem instance size that can be solved. The greedy neighborhood search heuristic is shown to be extremely efficient.
In this paper, we are going to propose the first mathematical model for Multi- Period Hub Location Problems (MPHLP). We apply this mixed integer program- ming model on public transport planning and call it Multi-Period Hub Location Problem for Public Transport (MPHLPPT). In fact, HLPPT model proposed earlier by the authors is extended to include more facts and features of the real-life application. In order to solve instances of this problem where existing standard solvers fail, a solution approach based on a greedy neighborhood search is developed. The computational results substantiate the efficiency of our solution approach to solve instances of MPHLPPT.
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.
The capacitated single-allocation hub location problem revisited: A note on a classical formulation
(2009)
Denote by G = (N;A) a complete graph where N is the set of nodes and A is the set of edges. Assume that a °ow wij should be sent from each node i to each node j (i; j 2 N). One possibility is to send these °ows directly between the corresponding pairs of nodes. However, in practice this is often neither e±cient nor costly attractive because it would imply that a link was built between each pair of nodes. An alternative is to select some nodes to become hubs and use them as consolidation and redistribution points that altogether process more e±ciently the flow in the network. Accordingly, hubs are nodes in the graph that receive tra±c (mail, phone calls, passengers, etc) from di®erent origins (nodes) and redirect this tra±c directly to the destination nodes (when a link exists) or else to other hubs. The concentration of tra±c in the hubs and its shipment to other hubs lead to a natural decrease in the overall cost due to economies of scale.
Home Health Care (HHC) services are becoming increasingly important in Europe’s aging societies. Elderly people have varying degrees of need for assistance and medical treatment. It is advantageous to allow them to live in their own homes as long as possible, since a long-term stay in a nursing home can be much more costly for the social insurance system than a treatment at home providing assistance to the required level. Therefore, HHC services are a cost-effective and flexible instrument in the social system. In Germany, organizations providing HHC services are generally either larger charities with countrywide operations or small private companies offering services only in a city or a rural area. While the former have a hierarchical organizational structure and a large number of employees, the latter typically only have some ten to twenty nurses under contract. The relationship to the patients (“customers”) is often long-term and can last for several years. Therefore acquiring and keeping satisfied customers is crucial for HHC service providers and intensive competition among them is observed.
In this paper we focus on the strategic design of supply chain networks. We propose a mathematical modeling framework that captures many practical aspects of network design problems simultaneously but which have not received adequate attention in the literature. The aspects considered include: dynamic planning horizon, generic supply chain network structure, external supply of materials, inventory opportunities for goods, distribution of commodities, facility configuration, availability of capital for investments, and storage limitations. Moreover, network configuration decisions concerning the gradual relocation of facilities over the planning horizon are considered. To cope with fluctuating demands, capacity expansion and reduction scenarios are also analyzed as well as modular capacity shifts. The relation of the proposed modeling framework with existing models is discussed. For problems of reasonable size we report on our computational experience with standard mathematical programming software. In particular, useful insights on the impact of various factors on network design decisions are provided.
In this paper we consider short term storage systems. We analyze presorting strategies to improve the effiency of these storage systems. The presorting task is called Batch PreSorting Problem (BPSP). The BPSP is a variation of an assigment problem, i.e., it has an assigment problem kernel and some additional constraints. We present different types of these presorting problems, introduce mathematical programming formulations and prove the NP-completeness for one type of the BPSP. Experiments are carried out in order to compare the different model formulations and to investigate the behavior of these models.
In this article, we consider the problem of planning inspections and other tasks within a software development (SD) project with respect to the objectives quality (no. of defects), project duration, and costs. Based on a discrete-event simulation model of SD processes comprising the phases coding, inspection, test, and rework, we present a simplified formulation of the problem as a multiobjective optimization problem. For solving the problem (i.e. finding an approximation of the efficient set) we develop a multiobjective evolutionary algorithm. Details of the algorithm are discussed as well as results of its application to sample problems.
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.
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.