Stochastic Multifacility Location Problem under Triangular Area Constraint with Euclidean Norm

The multifacility location issue is an augmentation of the single-location problem in which we might be keen on finding the location of various new facilities concerning different existing locations. In the present study, multifacility location under triangular zone limitation with probabilistic methodology for the weights considered in the objective function and the Euclidean distances between the locations has been presented. Scientific detailing and the explanatory arrangement have been acquired by utilizing Kuhn-Tucker conditions. The arrangement strategy has been represented with the assistance of a numerical illustration. Two sub-instances of the issue in each of which the new locations are to be situated in semi-open rectangular zone have likewise been talked about

A two-stage method for the capacitated multi-facility location-allocation problem

This is the author accepted manuscript. The final version is available from Inderscience via the DOI in this recordThis paper examines the capacitated planar multi-facility location-allocation problem, where the number of facilities to be located is specified and each of which has a capacity constraint. A two-stage method is put forward to deal with the problem where in the first stage a technique that discretises continuous space into discrete cells is used to generate a relatively good initial facility configurations. In stage 2, a variable neighbourhood search (VNS) is implemented to improve the quality of solution obtained by the previous stage. The performance of the proposed method is evaluated using benchmark datasets from the literature. The numerical experiments show that the proposed method yields competitive results when compared to the best known results from the literature. In addition, some future research avenues are also suggested

The continuous single source location problem with capacity and zone-dependent fixed cost: Models and solution approaches

The continuous capacitated single-source multi-facility Weber problem with the presence of facility fixed cost is investigated. A new mathematical model which incorporates multi-level type capacity (or design) and facility fixed cost that is capacity-based and zone-dependent is introduced. As no data set exists for this new location problem, a new data set based on convex polygons using triangular shape is constructed. A generalised two stage heuristic scheme that combines the concept of aggregation, an exact method, and an enhanced Cooper’s alternate location-allocation method is put forward. A framework that embeds Variable Neighbourhood Search is also proposed. Computational experiments show that these matheuristics produce encouraging results for this class of location problems. The proposed approaches are also easily adapted to cater for a recently studied variant namely the single-source capacitated multi-facility Weber problem where they outperform those recently published solution method

A review of network location theory and models

Cataloged from PDF version of article.In this study, we review the existing literature on network location problems. The study has a broad scope that includes problems featuring desirable and undesirable facilities, point facilities and extensive facilities, monopolistic and competitive markets, and single or multiple objectives. Deterministic and stochastic models as well as robust models are covered. Demand data aggregation is also discussed. More than 500 papers in this area are reviewed and critical issues, research directions, and problem extensions are emphasized.Erdoğan, Damla SelinM.S

Solution Methods for the \u3cem\u3ep\u3c/em\u3e-Median Problem: An Annotated Bibliography

The p-median problem is a graph theory problem that was originally designed for, and has been extensively applied to, facility location. In this bibliography, we summarize the literature on solution methods for the uncapacitated and capacitated p-median problem on a graph or network

The optimal location of facilities on a network

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An allocation based modeling and solution framework for location problems with dense demand /

In this thesis we present a unified framework for planar location-allocation problems with dense demand. Emergence of such information technologies as Geographical Information Systems (GIS) has enabled access to detailed demand information. This proliferation of demand data brings about serious computational challenges for traditional approaches which are based on discrete demand representation. Furthermore, traditional approaches model the problem in location variable space and decide on the allocation decisions optimally given the locations. This is equivalent to prioritizing location decisions. However, when allocation decisions are more decisive or choice of exact locations is a later stage decision, then we need to prioritize allocation decisions. Motivated by these trends and challenges, we herein adopt a modeling and solution approach in the allocation variable space.Our approach has two fundamental characteristics: Demand representation in the form of continuous density functions and allocation decisions in the form of service regions. Accordingly, our framework is based on continuous optimization models and solution methods. On a plane, service regions (allocation decisions) assume different shapes depending on the metric chosen. Hence, this thesis presents separate approaches for two-dimensional Euclidean-metric and Manhattan-metric based distance measures. Further, we can classify the solution approaches of this thesis as constructive and improvement-based procedures. We show that constructive solution approach, namely the shooting algorithm, is an efficient procedure for solving both the single dimensional n-facility and planar 2-facility problems. While constructive solution approach is analogous for both metric cases, improvement approach differs due to the shapes of the service regions. In the Euclidean-metric case, a pair of service regions is separated by a straight line, however, in the Manhattan metric, separation takes place in the shape of three (at most) line segments. For planar 2-facility Euclidean-metric problems, we show that shape preserving transformations (rotation and translation) of a line allows us to design improvement-based solution approaches. Furthermore, we extend this shape preserving transformation concept to n-facility case via vertex-iteration based improvement approach and design first-order and second-order solution methods. In the case of planar 2-facility Manhattan-metric problems, we adopt translation as the shape-preserving transformation for each line segment and develop an improvement-based solution approach. For n-facility case, we provide a hybrid algorithm. Lastly, we provide results of a computational study and complexity results of our vertex-based algorithm

ROLAND : a tool for the realistic optimisation of local access network design

Bibliography: p. 141-147.Investment in the local access network represents between 50% and 70% of capital investment of a telecommunications company. This thesis investigates algorithms that can be used to design economical access networks and presents ROLAND: a tool that incorporates several of these algorithms into an interactive environment. The software allows a network designer to explore different approaches to solving the problem, before adopting a particular one. The family of problems that are tackled by the algorithms included in ROLAND involve determining the most economical way of installing concentrators in an access network and connecting demand nodes such as distribution points to these concentrators. The Centre-of-Mass (COM) Algorithm identifies clusters of demand in the network and suggests good locations for concentrators to be installed. The problem of determining which concentrators in a set of potential sites to install is known as the concentrator location problem (CPL) and is an instance of the classical capacitated plant location problem. Linear programming techniques such as branch-and-bound can be used to find an optimal solution to this problem, but soon becomes infeasible as the network size increases. Some form of heuristic approach is needed, and ROLAND includes two such heuristics, namely the Add and Drop Heuristic. Determining the layout of multi-drop lines, which allow a number of demand nodes to share the same connection to a concentrator, is analogous to finding minimal spanning trees in a graph. Greedy approaches such as Kruskal's algorithm are not ideal however, and heuristics such as Esau-William's algorithm achieve better results. Kruskal's algorithm and Kershenbaum's Unified Algorithm (which encapsulates a number of heuristics) have been implemented and come bundled with ROLAND. ROLAND also includes an optimal terminal assignment algorithm for associating distribution points to concentrators. A description of ROLAND's architecture and GUI are provided. The graphical elements are kept separate from the algorithm implementations, and an interface class provides common data structures and routines for use by new algorithm implementations. A test data generator, able to create random or localized data, is also included. A new hybrid concentrator location algorithm, known as the Cluster-Add Heuristic is presented. The implementation of this algorithm is included in ROLAND, and demonstrates the ease with which new solution methods can be integrated into the tool's framework. Experimentation with the concentrator location algorithms is conducted to show the Cluster-Add Heuristic's relative performance

Development of transportation and supply chain problems with the combination of agent-based simulation and network optimization

Demand drives a different range of supply chain and logistics location decisions, and agent-based modeling (ABM) introduces innovative solutions to address supply chain and logistics problems. This dissertation focuses on an agent-based and network optimization approach to resolve those problems and features three research projects that cover prevalent supply chain management and logistics problems. The first case study evaluates demographic densities in Norway, Finland, and Sweden, and covers how distribution center (DC) locations can be established using a minimizing trip distance approach. Furthermore, traveling time maps are developed for each scenario. In addition, the Nordic area consisting of those three countries is analyzed and five DC location optimization results are presented. The second case study introduces transportation cost modelling in the process of collecting tree logs from several districts and transporting them to the nearest collection point. This research project presents agent-based modelling (ABM) that incorporates comprehensively the key elements of the pick-up and delivery supply chain model and designs the components as autonomous agents communicating with each other. The modelling merges various components such as GIS routing, potential facility locations, random tree log pickup locations, fleet sizing, trip distance, and truck and train transportation. The entire pick-up and delivery operation are modeled by ABM and modeling outcomes are provided by time series charts such as the number of trucks in use, facilities inventory and travel distance. In addition, various scenarios of simulation based on potential facility locations and truck numbers are evaluated and the optimal facility location and fleet size are identified. In the third case study, an agent-based modeling strategy is used to address the problem of vehicle scheduling and fleet optimization. The solution method is employed to data from a real-world organization, and a set of key performance indicators are created to assess the resolution's effectiveness. The ABM method, contrary to other modeling approaches, is a fully customized method that can incorporate extensively various processes and elements. ABM applying the autonomous agent concept can integrate various components that exist in the complex supply chain and create a similar system to assess the supply chain efficiency.Tuotteiden kysyntä ohjaa erilaisia toimitusketju- ja logistiikkasijaintipäätöksiä, ja agenttipohjainen mallinnusmenetelmä (ABM) tuo innovatiivisia ratkaisuja toimitusketjun ja logistiikan ongelmien ratkaisemiseen. Tämä väitöskirja keskittyy agenttipohjaiseen mallinnusmenetelmään ja verkon optimointiin tällaisten ongelmien ratkaisemiseksi, ja sisältää kolme tapaustutkimusta, jotka voidaan luokitella kuuluvan yleisiin toimitusketjun hallinta- ja logistiikkaongelmiin. Ensimmäinen tapaustutkimus esittelee kuinka käyttämällä väestötiheyksiä Norjassa, Suomessa ja Ruotsissa voidaan määrittää strategioita jakelukeskusten (DC) sijaintiin käyttämällä matkan etäisyyden minimoimista. Kullekin skenaariolle kehitetään matka-aikakartat. Lisäksi analysoidaan näistä kolmesta maasta koostuvaa pohjoismaista aluetta ja esitetään viisi mahdollista sijaintia optimointituloksena. Toinen tapaustutkimus esittelee kuljetuskustannusmallintamisen prosessissa, jossa puutavaraa kerätään useilta alueilta ja kuljetetaan lähimpään keräyspisteeseen. Tämä tutkimusprojekti esittelee agenttipohjaista mallinnusta (ABM), joka yhdistää kattavasti noudon ja toimituksen toimitusketjumallin keskeiset elementit ja suunnittelee komponentit keskenään kommunikoiviksi autonomisiksi agenteiksi. Mallinnuksessa yhdistetään erilaisia komponentteja, kuten GIS-reititys, mahdolliset tilojen sijainnit, satunnaiset puunhakupaikat, kaluston mitoitus, matkan pituus sekä monimuotokuljetukset. ABM:n avulla mallinnetaan noutojen ja toimituksien koko ketju ja tuloksena saadaan aikasarjoja kuvaamaan käytössä olevat kuorma-autot, sekä varastomäärät ja ajetut matkat. Lisäksi arvioidaan erilaisia simuloinnin skenaarioita mahdollisten laitosten sijainnista ja kuorma-autojen lukumäärästä sekä tunnistetaan optimaalinen toimipisteen sijainti ja tarvittava autojen määrä. Kolmannessa tapaustutkimuksessa agenttipohjaista mallinnusstrategiaa käytetään ratkaisemaan ajoneuvojen aikataulujen ja kaluston optimoinnin ongelma. Ratkaisumenetelmää käytetään dataan, joka on peräisin todellisesta organisaatiosta, ja ratkaisun tehokkuuden arvioimiseksi luodaan lukuisia keskeisiä suorituskykyindikaattoreita. ABM-menetelmä, toisin kuin monet muut mallintamismenetelmät, on täysin räätälöitävissä oleva menetelmä, joka voi sisältää laajasti erilaisia prosesseja ja elementtejä. Autonomisia agentteja soveltava ABM voi integroida erilaisia komponentteja, jotka ovat olemassa monimutkaisessa toimitusketjussa ja luoda vastaavan järjestelmän toimitusketjun tehokkuuden arvioimiseksi yksityiskohtaisesti.fi=vertaisarvioitu|en=peerReviewed

Hub Network Design and Discrete Location: Economies of Scale, Reliability and Service Level Considerations

In this thesis, we study three related decision problems in location theory. The first part of the dissertation presents solution algorithms for the cycle hub location problem (CHLP), which seeks to locate p-hub facilities that are connected by means of a cycle, and to assign non-hub nodes to hubs so as to minimize the total cost of routing flows through the network. This problem is useful in modeling applications in transportation and telecommunications systems, where large setup costs on the links and reliability requirements make cycle topologies a prominent network architecture. We present a branch and-cut algorithm that uses a flow-based formulation and two families of mixed-dicut inequalities as a lower bounding procedure at nodes of the enumeration tree. We also introduce a greedy randomized adaptive search algorithm that is used to obtain initial upper bounds for the exact algorithm and to obtain feasible solutions for large-scale instances of the CHLP. Numerical results on a set of benchmark instances with up to 100 nodes confirm the efficiency of the proposed solution algorithms. In the second part of this dissertation, we study the modular hub location problem, which explicitly models the flow-dependent transportation costs using modular arc costs. It neither assumes a full interconnection between hub nodes nor a particular topological structure, instead it considers link activation decisions as part of the design. We propose a branch-and-bound algorithm that uses a Lagrangean relaxation to obtain lower and upper bounds at the nodes of the enumeration tree. Numerical results are reported for benchmark instances with up to 75 nodes. In the last part of this dissertation we study the dynamic facility location problem with service level constraints (DFLPSL). The DFLPSL seeks to locate a set of facilities with sufficient capacities over a planning horizon to serve customers at minimum cost while a service level requirement is met. This problem captures two important sources of stochasticity in facility location by considering known probability distribution functions associated with processing and routing times. We present a nonlinear mixed integer programming formulation and provide feasible solutions using two heuristic approaches. We present the results of computational experiments to analyze the impact and potential benefits of explicitly considering service level constraints when designing distribution systems