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1

Facility location problem mathematical models - supply chain perspective

Redmer Adam

LogForum

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2022

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Vol. 18, no. 4

379--395

EN

Background: Supply chains are the networks linking sources of supply with demand points and composed of so-called actors, i.e., producers, distributors/wholesalers, retailers, and customers/consumers. As in every network, supply chains contain vertices and arcs, the former represented by factories and warehouses (including distribution centers). Such facilities cause long-term and expensive investments. As a result, decisions on location and number of them belong to the strategic level of management and require quantitative analysis. To do this, mathematical models of the Facility Location Problem (FLP) are constructed to allow an application of optimization methods. Methods: Mathematical optimization or programming is the selection of the best solution, with regard to some criterion, from a set of feasible alternatives. The fundamental of mathematical optimization is the formulation of mathematical models of analyzed problems. Mathematical models are composed of objective function, decision variables, constraints, and parameters. These components are presented and compared in the paper concerning FLP from a supply chain perspective. Results: The ten mathematical models of the FLP are presented, including the two original ones. The models are classified according to such features as facility type they concern, including the desirable, neutral, and undesirable ones. The models and their components are characterized. In addition, their applicability and elasticity are analyzed. Finally, the models are compared and discussed from the supply chain point of view. Conclusions: However, the FLP mathematical models are relatively similar; the most important element of them for supply chain appropriate representation is an objective function. It strongly influences the possible applicability of FLP models and their solutions, as well. The objective functions having broader applicability turned out to be the maximized number of supply/demand points covered by facilities and the minimized number of facilities necessary to cover supply/demand points. However, not to locate all allowed facilities (use all the location sites) or as many as supply/demand points, but an appropriate number of them, it is necessary to take into account facility fixed costs. Thus, when locating logistics facilities, the minimized total cost of serving supply/demand points is the most appropriate objective function.

2

Planning the location of facilities in the supply chain using the firefly meta-innovation algorithm

Shayannia Sayed Ahmad

Foundations of Computing and Decision Sciences

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2022

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Vol. 47, No. 4

433--454

EN

Analysis of supply chain location issues and decision-making regarding the location of facilities in the supply chain is one of the most important issues in the decision-making of governments, organizations and companies. Undoubtedly, the correct location of facilities has very important effects on economic benefits, providing appropriate services and customer satisfaction. Supply chain issue is one of the most widely used issues in today's competitive world and location issues are among the most used issues in designing supply chain networks to improve and reduce costs and increase competitiveness. The facilities under consideration include warehouses and distribution centers, which have been solved with the aim of reducing transportation costs. And then the two methods are compared. The problem is solved in small, medium and large dimensions and finally it was concluded that the firefly algorithm had a better performance than the genetic algorithm.

3

Modeling the designs in terms of logistics service center placement: a case study

Stopka Ondrej, Droździel Paweł, L'upták Vladimir

Archives of Transport

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2022

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Vol. 64, iss. 4

59--71

EN

Suggesting the proper location for logistics facility can be considered as a decision making problem, wherein the final solution/decision is affected by multiple external or even internal circumstances. In order to address the decision making issues, various multi-criteria decision making (MCDM) techniques may be implemented; and hence, they can be applied even when making a decision about an adequate logistics service center (LSC) placement in an examined territory (i.e., national logistics network of the selected territory), which is an aim of this manuscript. Following the statements above, as for the individual instruments of MCDM to be implemented in terms of the crucial objective of this research, the definite decision making process will be carried out by applying the Analytic Hierarchy Process (AHP) followed by the Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS), on the basis of criteria weights defined by the Saaty pairwise comparison method. The methods used appear to be ideal instruments towards decision making on the most suit-able location which is represented by the region in our case. Subsequently, these will be ordered from the most preferred to least one by using a preference ranking. As a result of the application of AHP and TOPSIS approaches, based on the conducted calculations in regard to decision making on identifying the proper LSC location out of eight selected regions, one specific region will be defined as the most suitable (so-called compromise) scenario. Individual tools allow for reducing the number of assigned criteria that are taken into account in searching process for individual solutions. In order to objectify the entire decision making procedure, ten topic-involved experts having practical experience with a subject of logistics object allocation will be asked to participate in the process. Preferences differ from one decision maker (expert) to another; hence, the outcome depends on who is making decisions and what their goals and preferences are.

4

Inventory management and logistics optimization: a data mining practical approach

Granillo-Macías Rafael

LogForum

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2020

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Vol. 16, no. 4

535--547

EN

Background: In the current economic scenarios, characterized by high competitiveness and disruption in supply chains, the latent need to optimize costs and customer service has been promoted, placing inventories as a critical area with high potential to implement improvements in companies. Appropriate inventory management leads to positive effects on logistics performance indices. In economic terms, about 15% of logistics costs are attributed to warehousing operations. With a practical approach, using a case study in a company in the food sector, this article proposes an inventory classification method with qualitative and quantitative variables, using data mining techniques, categorizing the materials using variables such as picking frequency, consumption rates and qualitative characteristics regarding their handling in the warehouse. The proposed model also integrates the classification of materials with techniques for locating facilities, to support decision-making on inventory management and storage operations. Methods: This article uses a method based on the Partitioning Around Medoids algorithm that includes, in an innovative way, the application of a strategy for the location of the optimal picking point based on the cluster classification considering the qualitative and quantitative factors that represent the most significant impact or priority for inventory management in the company. Results: The results obtained with this model, improve the routes of distributed materials based on the identification of their characteristics such as the frequency of collection and handling of materials, allowing to reorganize and increase the storage capacity of the different SKUs, passing from a classification by families to a cluster classification. Furthermore, the results support decision-making on storage capacity, allowing the space required by the materials that make up the different clusters to be identified. Conclusions: This article provides an approach to improving decision-making for inventory management, showing a proposal for a warehouse distribution design with data mining techniques, which use indicators and key attributes for operational performance for a case study in a company. The use of data mining techniques such as PAM clustering makes it possible to group the inventory into different clusters considering both qualitative and quantitative factors. The clustering proposal with PAM offers a more realistic approach to the problem of inventory management, where factors as diverse as time and capacities must be considered, to the types and handling that must be had with the materials inside the warehouse.

PL

Wstęp: W obecnych warunkach ekonomicznych, charakteryzujących się wysoką konkurencyjnością i nieprzewidywalnością działalności w obrębie łańcucha dostaw, istotne jest dążenia do optymalizacji kosztów i poprawy poziomu obsługi klientów, poprzez prawidłowe zarządzanie zapasem, jako czynnikiem kluczowym. Właściwe zarządzanie zapasami prowadzi do pozytywnych wpływów na wyniki logistyczne. W ujęciu ekonomicznym, około 15% kosztów logistycznych jest związane z operacjami magazynowymi. Poprzez zastosowanie studium przypadku z branży spożywczej, w pracy proponowana jest metoda klasyfikacji zapasów z zmiennymi jakościowymi i ilościowymi, przy zastosowaniu technik eksploracji danych, kategoryzując materiały przy użyciu zmiennych takich jak częstotliwość pobrań, poziom konsumpcji, jak i charakterystyki jakościowe związane z operacjami magazynowymi. Proponowany model łączy klasyfikację materiałową z technikami lokalizacyjnymi w celu ułatwienia procesu decyzyjnego w obszarze zarządzania zapasem oraz operacji magazynowych. Metody: Zastosowana metoda opiera się na algorytmie Partitioning Around Medoids, który w innowacyjny sposób, stosuje strategię lokalizacji optymalnego punktu poboru w oparciu o klasyfikację klastrową, uwzględniając jakościowe jak i ilościowe czynniki, mające duży wpływ na określanie priorytetów w zarządzaniu zapasem w przedsiębiorstwie. Wyniki: Uzyskane wyniki poprawiają marszruty dystrybuowanych materiałów w oparciu o identyfikację ich charakterystyk takich jak częstotliwość pobrań i handlingu, pozwalając na reorganizację i wzrost pojemności magazynowej różnych indeksów materiałowych, przechodząc z klasyfikacji na podstawie rodzin do klasyfikacji opartej na klusterze. Dodatkowo, wyniki wspomagają proces decyzyjny związany ze zdolnościami magazynowymi, umożliwiając identyfikację na najniższym poziomie miejsca magazynowego. Wnioski: Praca prezentuje podejście do poprawy procesu decyzyjnego w zarządzaniu zapasem poprzez propozycję projektu magazynu w oparciu o techniki eksploracji danych, które stosują mierniki i wskaźniki działań operacyjnych. Zastosowanie technik eksploracji danych takich jak klustrowanie PAM umożliwia grupowanie zapasów przy uwzględnieniu różnych czynników jakościowych i ilościowych. Proponowana metod PAM umożliwia bardziej realistyczne podejście do problemów zarządzania zapasem, gdzie muszą być uwzględnione tak różne czynniki jak czas czy zdolności oraz typu operacji magazynowych.

5

Pythagorean Fuzzy Analytical Network Process (ANP) and Its Application to Warehouse Location Selection Problem

Yaman Tutku Tuncalı

Annals of Computer Science and Information Systems

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2020

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Vol. 21

137--140

EN

Although new techniques are added to multi-criteria decision-making (MCDM) techniques every day, fuzzy applications of current and proven methods also take a large place in the literature. The main subject of this study is to propose an extension of Pythagorean fuzzy sets (PFS), which are useful to overcome the uncertainty in multi-criteria decision processes, to the well-known Analytical Network Process (ANP) technique. For this purpose, an empirical application of the proposed method was carried out in defining criteria weights of the warehouse location selection problem in the medical sector.

6

Telematic Support in Improving Safety of Maritime Transport

Neumann T.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2018

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Vol. 12, no. 2

231--235

EN

Security mechanisms of a telematics system are exceedingly intersecting as they could pretend the ordinary influence of the vehicle and perhaps terminate in accidents. This paper includes a new look at automotive and telematics transportation systems, also refers to methods in modelling, facility location, data processing and assessment of risk in telematics networks.

7

Warunki założenia budowli sakralnych w systemie miasta

Koznarska H.

Zeszyty Naukowe Politechniki Częstochowskiej. Budownictwo

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2014

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Z. 20 (170)

98--104

PL

Autorka zwraca uwagę na złożony mechanizm wyznaczania lokalizacji obiektów sakralnych, który podlegał bardzo restrykcyjnym parametrom w zależności od kręgu cywilizacyjnego. Dokonano analizy kompozycyjno-estetycznych, funkcjonalnych i kanonicznych warunków zakładania budowli sakralnych w strukturze miasta. Przedstawiono sposoby rozlokowania, akcentując duchową rolę świątyń i ich znaczenie dla kształtowania ogólnego obrazu miasta.

EN

In the article there were researched compositional, aesthetic, functional and canonical terms of laying down of sacred buildings in the city system. Emphasis was put on finding the techniques of locating that underline spiritual importance of temples and their significance for the formation of the general image of a city.

8

The bi-partial version of the p-median / p-center facility location problem and some algorithmic considerations

Owsinski J. W.

Journal of Automation Mobile Robotics and Intelligent Systems

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2014

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Vol. 8, No. 3

59--63

EN

The paper introduces the bi-partial version of the well known p-median or p-center facility location problem. The bi-partial approach, developed by the author, primarily to deal with the clustering problems, is shown here to work for a problem that does not possess some of the essential properties, inherent to the bi-partial formulations. It is demonstrated that the classical objective function of the problem can be correctly interpreted in terms of the bi-partial approach, that it possesses the essential properties that are at the core of the bi-partial approach, and, finally, that the general algorithmic precepts of the bi-partial approach can also be applied to this problem. It is proposed that the use of bi-partial approach for similar problems can be beneficial from the point of view of flexibility and interpretation.

9

A new planning model to support logistics service providers in selecting mode, route, and terminal location

Huynh N., Fotuhi F.

Polish Maritime Research

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2013

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S 1

67--73

EN

In this paper, we address thefreight network design problem. A mixed integer linear program is formulated to help logistics service providers jointlyselect the best terminal locations among a set of candidate locations, shipping modes, and route for shipping different types of commodities. The developed model isapplied to two different networksto show its applicability. Results obtained from CPLEX for the case studiesare presented, and the benefit of the proposed model is discussed.

10

A Simulation Environment for Modelling and Analysis of the Distribution of Shore Observatory Stations - Preliminary Results

Neumann T.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2011

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Vol. 5, no. 4

555--560

EN

The paper has presented the usage of mathematical theory of evidence in evaluating of the pos-sibility of object detection by monitoring radar stations. The level of object detection allows for effortless conversion to optimisation problem of monitored area coverage. Development of such task enables such dis-tribution of observatory stations that maintains the detection rate higher than the assumed value. An appropri-ate rate level is achieved by covering the analysed set of points with sufficient number of radar stations. Combining evidence allows for calculating corresponding parameters for each set of observing equipment.

11

Algorithms for joint location-routing problem in a class of network systems

Drwal M., Józefczyk J.

Management and Production Engineering Review

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2011

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Vol. 2, No. 1

10-18

EN

In many decision making problems, the facility location and route design subproblems are commonly approached separately. This standard practice results in conceptually simpler models, but it often turns out to be too constraining and inaccurate. We propose a mathematical modeling framework of a wide applicability that enriches the locational analysis with the routing aspect, and leads to joint location-routing binary optimization problem. The usefulness of this general framework is presented through an application example in a merchandise delivery of online shopping companies (business-to-consumer e-commerce). Other applications for logistic systems as well as for computer systems are also described and justified. The main advantage of the proposed approach comes out from the precise contrasting suppliers' and consumers' needs. Moreover, if a repeated relocation of facilities is under consideration then taking the long-term planning horizon into account is necessary to obtain realistic and competitive results. Static and dynamic versions of the optimization problem are introduced for which the heuristic solution algorithm based on the Lagrange relaxation and the dynamic programming approach are respectively presented.

12

On the Fermat-Weber Point of a Polygonal Chain and its Generalizations

Bhattacharya Bhargab.B.

Fundamenta Informaticae

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2011

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Vol. 107, nr 4

331-343

EN

In this paper, we study the properties of the Fermat-Weber point for a set of fixed points, whose arrangement coincides with the vertices of a regular polygonal chain. A k-chain of a regular n-gon is the segment of the boundary of the regular n-gon formed by a set of k (≤n) consecutive vertices of the regular n-gon. We show that for every odd positive integer k, there exists an integer N(k), such that the Fermat-Weber point of a set of k fixed points lying on the vertices a k-chain of a n-gon coincides with a vertex of the chain whenever n≥ N(k). We also show that πm(m + 1) - .π^2/4. . N(k)≤πm(m + 1) + 1., where k (= 2m + 1) is any odd positive integer. We then extend this result to a more general family of point set, and give an O(hk log k) time algorithm for determining whether a given set of k points, having h points on the convex hull, belongs to such a family.

13

Wybrane modele i metody optymalizacji alokacji zasobów

Pieńkosz K.

Prace Naukowe Politechniki Warszawskiej. Elektronika

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2010

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z. 174

3-132

PL

Monografia dotyczy zagadnień związanych z efektywnym rozdziałem szeroko rozumianych zasobów. Prezentowane są metody optymalizacji dla problemów alokacji pojedynczego zasobu, zasobu dostępnego w porcjach o określonej wielkości oraz zestawu różnych rodzajów zasobów. Szczegółowo analizowane są właściwości modeli i algorytmów rozwiązywania dla problemów alokacji formułowanych jako zadania plecakowe, zadania pakowania i rozkroju oraz zagadnienia transportowe i dystrybucyjne. Klasyczne modele alokacji mają głównie charakter dyskretny, wykluczający możliwość częściowej realizacji zapotrzebowań, bądź ciągły z pełną swobodą przydziału zasobu. W pracy szczególną uwagę poświęcono analizie semi-ciągłych problemów rozdziału zasobów i algorytmom ich rozwiązywania. W modelach semi-ciągłych zakłada się, że wielkość przydzielanego zasobu nie może być mniejsza od wartości zadanego parametru β. Tego typu modele były dotychczas badane w literaturze w ograniczonym stopniu, pomimo ich istotnego znaczenia praktycznego i teoretycznego. Stanowią one uogólnienie klasycznych modeli alokacji. Poprzez możliwość wyboru wartości parametru β dostosowanej do rzeczywistych uwarunkowań, pozwalają wyznaczać bardziej elastyczne sposoby gospodarowania zasobami.

EN

The book investigates resource allocation problems. We present models and methods fbr effective allocation of resources among competing activities. Classical discrete optimization models assume that if a resource is allocated to an activity then its demand must be fully satisfied. In continuous models, it is allowed to allocate a very small amount of resource. The main subject of the monograph are semi-continuous models which can be seen as a generalization of the classical discrete and continuous approaches. In semi-continuous models, the amount of resource allocated to an activity cannot be smaller than a given parameter β. In the case when only a single resource is available, the Semi-Continuous Knapsack Problem is formulated and its structural properties are analyzed. As a result, a procedure is developed which enables to fix the optimal values of some variables and transforms the resulting problem of reduced size into the Cardinality Constrained Knapsack Problem. Next, two classes of approximation algorithms are proposed and their performance in the worst case is analyzed. For multi resource allocation problems with uniform resources, the One-Dimensional Semi-Continuous Bin Packing model is formulated. We describe several approximation algorithms for solving such problem and analyze their properties. The results of computational experiments and conclusions relating to the effectiveness of the algorithms are also presented. The Two-Dimensional Bin Packing Problem is discussed only for the discrete case concerning cutting stock process. The application of an approximation algorithm exploiting bottom-up approach and the best-first strategy is described. General multi resource allocation problems are considered in the context of the General Assignment Problem, Transportation Problem and Capacitated Facility Location Problem. The semi-continuous model is discussed mainly for the Transportation Problem. The conditions for existing feasible solutions of semi-continuous model arę formulated. Moreover, an exact algorithm is developed for a special case concerning two resources and sufficiently small β. For the Capacitated Facility Location Problem a Lagrangian heuristic is described and the possibility of its application to the semi-continuous model is discussed.

14

A multi-product and multi-period facility location model for reverse logistics

Benaissa M., Benabdelhafid A.

Polish Journal of Management Studies

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2010

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Vol. 2

7-19

EN

Reverse logistics has become an important entity in the world economy. Businesses increasingly have to cope with product returns, mandated environmental regulations and increasing costs associated with product disposal. This study presents a cost-minimization model for a multi-time-step, multi-type product waste reverse logistics system. The facility location is a central issue of the logistics networks. In this article we are interested in optimizing of the sites facility location for a reverse logistics network for product end of life. Specifically, we present a Mixed Linear Program model for the strategic problem of collection sites facility location, cannibalization and recycling. This model allows determining to open or to close the sites previously in the reverse logistics network. All of these decisions are to minimize the costs of end of life product returns at various time periods considered in the planning. To solve the mathematical program, we have used the evaluation process and separation implemented in CPLEX commercial solver.

PL

Logistyka odwrotna stała się bardzo ważnym elementem świata ekonomii. Przedsiębiorstwa coraz częściej muszą radzić sobie ze zwrotami produktów, obowiązującymi przepisami dotyczącymi środowiska oraz rosnącymi kosztami usuwania wyrobu. W artykule zaprezentowano model minimalizacji kosztów dla systemu wielu kroków czasowych usuwania wielu typów produktów w logistce odwrotnej. Problem lokalizacji jest główną kwestią sieci logistycznych. W niniejszej pracy skupiono się przede wszystkim na optymalizacji miejsc lokalizacji w sieciach logistyki odwrotnej w przypadku końcowego życia produktu. Zaprezentowano model Liniowego Programowania Mieszanego w strategicznym problemie lokalizacji w miejscu zbierania odpadów, kanibalizacji i recyclingu. Ten model umożliwia określenie wcześniejszego otwarcia lub zamknięcia miejsc zbierania odpadów w sieci logistyki odwrotnej. Celem tych decyzji jest minimalizacja kosztów końcowego życia zwrotu wyrobu w różnych okresach czasu na etapie planowania. Aby rozwiązać ten problem matematyczny zastosowano proces oceny i separacji zaimplementowany w komercyjnym solverze CPLEX.