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The facility location problem (FLP) is a complex optimization problem that has been widely researched and applied in industry. In this research, we proposed two innovative approaches to complement the limitations of traditional methods, such as heuristics, metaheuristics, and genetic algorithms. The first approach involves utilizing crowdsourcing through video game players to obtain improved solutions, filling the gap in existing research on crowdsourcing for FLP. The second approach leverages machine learning techniques, specifically prediction methods, to provide an efficient exploration of the solution space. Our findings indicate that machine learning techniques can complement existing solutions by providing a more comprehensive approach to solving FLP and filling gaps in the solution space. Furthermore, machine learning predictive models are efficient for decision making and provide quick insights into the system’s behavior. In conclusion, this research contributes to the advancement of problem-solving techniques and has potential implications for solving a wide range of complex, NP-hard problems in various domains.

Science & Technology Asia, 27, 3, 204-215

The location of a logistics center is very important in a logistics system, as the success of the location determines the whole logistics system’s structure, shape, and mode, and not only affects the logistics center’s own operating costs, performance, and future development, but also affects the operation of the entire logistics system. Therefore, the selection of the location for a logistics center has great significance for improving the efficiency of regional logistics and optimizing the structure of a logistics system. This study constructed a multi-factor constrained P-median site-selection model to optimize the locations of logistics centers to improve the efficiency of logistics and optimize the structure of the logistics system in a region. The results show that the optimal distribution of logistics center sites and the coverage of freight capacity demand derived from the particle swarm algorithm are more balanced than those derived by the other algorithm. Following the comparison of the results for the utility of the optimized layout points solved by the particle swarm algorithm and the immune genetic algorithm, it is concluded that the optimal fitness value obtained by the particle swarm algorithm is lower than the other. It is proven that the particle swarm algorithm of the P-median site-selection model under this multi-factor constraint has some reference value for the selection of the sites of multi-logistics centers.

Given an n-vertex m-edge graph G of clique-width at most k, and a corresponding k-expression, we present algorithms for computing some well-known centrality indices (eccentricity and closeness) that run in O(2^{O(k)}(n+m)^{1+��}) time for any �� > 0. Doing so, we can solve various distance problems within the same amount of time, including: the diameter, the center, the Wiener index and the median set. Our run-times match conditional lower bounds of Coudert et al. (SODA'18) under the Strong Exponential-Time Hypothesis. On our way, we get a distance-labeling scheme for n-vertex m-edge graphs of clique-width at most k, using O(klog��{n}) bits per vertex and constructible in O��(k(n+m)) time from a given k-expression. Doing so, we match the label size obtained by Courcelle and Vanicat (DAM 2016), while we considerably improve the dependency on k in their scheme. As a corollary, we get an O��(kn��)-time algorithm for computing All-Pairs Shortest-Paths on n-vertex graphs of clique-width at most k, being given a k-expression. This partially answers an open question of Kratsch and Nelles (STACS'20). Our algorithms work for graphs with non-negative vertex-weights, under two different types of distances studied in the literature. For that, we introduce a new type of orthogonal range query as a side contribution of this work, that might be of independent interest., LIPIcs, Vol. 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021), pages 16:1-16:16

We compare two models of two-level facility location problems for network design in autonomous ground vehicle (AGV) operations. The two-level model consists of locations for charging stations (main facilities), as well as for storage locations (substations). Demand points will represent processing locations. In both formulations, demands are assigned to substations and substations are assigned to main facilities. The formulations differ in whether each connection between a facility and a substation is counted once in absolute terms, or once per demand. These represent two different views, in which transfer between a main facility and substation is carried out either in bulk, e.g. using a shuttle, or by each AGV independently. Selected experimental results are presented for geometric networks and networks consisting of uniformly distributed points on a regular mesh. These results indicate that the two formulations lead to vastly different network designs in terms of the number of facilities and connectivity.

Facility location is a prominent optimization problem that has inspired a large quantity of both theoretical and practical studies in combinatorial optimization. Although the problem has been investigated under various settings reflecting typical structures within the optimization problems of practical interest, little is known on how the problem behaves in conjunction with parity constraints. This shortfall of understanding was rather discouraging when we consider the central role of parity in the field of combinatorics. In this paper, we present the first constant-factor approximation algorithm for the facility location problem with parity constraints. We are given as the input a metric on a set of facilities and clients, the opening cost of each facility, and the parity requirement - odd, even, or unconstrained - of every facility in this problem. The objective is to open a subset of facilities and assign every client to an open facility so as to minimize the sum of the total opening costs and the assignment distances, but subject to the condition that the number of clients assigned to each open facility must have the same parity as its requirement. Although the unconstrained facility location problem as a relaxation for this parity-constrained generalization has unbounded gap, we demonstrate that it yields a structured solution whose parity violation can be corrected at small cost. This correction is prescribed by a T-join on an auxiliary graph constructed by the algorithm. This auxiliary graph does not satisfy the triangle inequality, but we show that a carefully chosen set of shortcutting operations leads to a cheap and sparse T-join. Finally, we bound the correction cost by exhibiting a combinatorial multi-step construction of an upper bound., LIPIcs, Vol. 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020), pages 21:1-21:17

The introduction of automated parcel locker (APL) systems is one possible approach to improve urban logistics (UL) activities. Based on the city of Dortmund as case study, we propose a simulation-optimization approach integrating a system dynamics simulation model (SDSM) with a multi-period capacitated facility location problem (CFLP). We propose this integrated model as a decision support tool for future APL implementations as a last-mile distribution scheme. First, we built a causal-loop and stock-flow diagram to show main components and interdependencies of the APL systems. Then, we formulated a multi-period CFLP model to determine the optimal number of APLs for each period. Finally, we used a Monte Carlo simulation to estimate the costs and reliability level with random demands. We evaluate three e-shopper rate scenarios with the SDSM, and then analyze ten detailed demand configurations based on the results for the middle-size scenario with our CFLP model. After 36 months, the number of APLs increases from 99 to 165 with the growing demand, and stabilizes in all configurations from month 24. A middle-demand configuration, which has total costs of about 750,000&euro, already locates a suitable number of APLs. If the budget is lower, our approach offers alternatives for decision-makers.

This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for effective and efficient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP.

Paper aims This work aims at proposing a mathematical model for allocation of oncological treatment units of SUS. Originality A model of the same architecture was not found in the literature for the delimited problem. Research method The mathematical models of location in the literature were reviewed and based the choice by the two-level hierarchical pq-median model with additional constraints of maximum distance and vertices eligibility, which was implemented in the CPLEX optimization software. Main findings Satisfactory results with homogeneous networks, centralized facilities in their service area and shorter distance traveled by users indicate the efficiency of the model in determining the optimum location given the number of facilities to be allocated. Implications for theory and practice The model proved to be an efficient tool to assist health managers in their decision-making about the network of facilities, not just oncological, but of any nature and many others public sectors.

Predmet ovog rada je analiza i re²avanje dva diskretna lokacijska problema: problema odre ivanja lokacija autobuskih terminala (engl. Bus Terminal Location Problem - BTLP) i problema uspostavljanja centara za produºenu negu pacijenata (engl. Long-term Care Facility Location Problem - LTCFLP). U radu je prikazana metoda promenljivih okolina (engl. Variable Neighborhood Search - VNS) za re²avanje BTLP i LTCFLP problema. VNS je metaheuristika vo ena jednim re- ²enjem i zasnovana je na sistemati£noj pretrazi okolina re²enja prostora pretrage. Sastoji se iz dve faze, faze razmrdavanja i faze lokalne pretrage. BTLP predstavlja diskretan lokacijski problem koji podrazumeva uspostavljanje velikih autobuskih terminala kako bi se omogu¢ila ²to kvalitetnija usluga klijentima. Klijenti predstavljaju lokacije autobuskih i metro stanica javnog prevoza. Za re²avanje BTLP problema VNS metodom predstavljena je unapre ena lokalna pretraga zasnovana na brzoj zameni okolina. Metoda je paralelizovana (PVNS) i postignuto je zna£ajno vremensko ubrzanje metode u zavisnosti od broja jezgara procesora na kome se izvr²ava. Predloºena PVNS metoda daje re²enja boljeg kvaliteta u odnosu na poznata re²enja BTLP problema iz literature. Algoritam je testiran i na ve¢im instancama problema dobijenih modikacijom biblioteke instanci za problem trgova£kog putnika i predstavljeni su rezultati metode na ovim instancama. LTCFLP je nastao kao deo planiranja sistema zdravstvene za²tite u Juºnoj Koreji. Klijenti predstavljaju lokacije na kojima se nalaze grupe pacijenata kojima je potrebna produºena nega, dok uspostavljeni centri predstavljaju lokacije na kojima ¢e se izgraditi zdravstveni centri koji ¢e pruºati negu pacijentima. Unapred je zadato n lokacija na kojima mogu biti uspostavljeni centri. Potrebno je odabrati najvi²e K lokacija za uspostavljanje zdravstvenih centara tako da oni budu ²to ravnomernije optere¢eni zahtevima klijenata. Za re²avanje LTCFLP problema VNS metodom predstavljena je struktura podataka zasnovana na brzoj zameni okolina uz pomo¢ koje je vremenska sloºenost jedne iteracije lokalne pretrage smanjena na O(nmax(n;K2)) u odnosu na vremensku sloºenosti poznatu u literaturi O(K2 n2). Smanjena vremenska sloºenost predstavljene lokalne pretrage dovela je do boljih rezultata zbog ve¢eg broja iteracija VNS algoritma koje koje se mogu izvr²iti u kra¢em vremenskom periodu. Prikazani su rezultati predstavljenog algoritma koji nadma- ²aju poznate rezultate iz literature. This paper considers two discrete location problems: Bus Terminal Location Problem (BTLP) and Long-term Care Facility Location Problem (LTCFLP). Variable Neighborhood Search (VNS) method for solving BTLP and LTCFLP is presented in this paper. VNS is a single-solution based metaheuristic based on systematic change of neighborhoods while searching for optimal solution of the problem. It consists two main phases: shake phase and local search phase. BTLP is a discrete location problem which considers locating bus terminals in order to provide the highest possible quality of public service to the clients. Clients are presented as public transportation stations, such as bus or metro stations. VNS algorithm is used for solving BTLP. This algorithm uses improved local search based on ecient neighborhood interchange. VNS is parallelized (PVNS) which leads to signicant time improvement in function of the processor core count. Computational results show that proposed PVNS method improves existing results from the literature in terms of quality. Larger instances, based on instances from the Traveling Salesman Problem library, are presented and computational results for those instances are reported. LTCFLP is created as a part of health care infrastructure planning in South Korea. Clients are considered as groups of patients with a need of long-term health care, while established facilities present locations where the centers that provide health care services should be built. Predened are n locations where centers are to be established. This problem seeks at most K locations to establish health centers so they are to be equally loaded with clients demand. For solving LTCFLP, by using VNS algorithm, data structure based on fast interchange is presented. It reduces the time complexity of one iteration of local search algorithm to O(n max(n;K2)) comparing to the known time complexity from the literature O(K2 n2). Reduced time complexity of the presented VNS leads to better quality solutions, due to larger number of VNS iterations that can be performed in less computational time. This paper presents computational results that outperform the best known results from the literature.

There has been a number of discrete facility location models that deal with the use of some equality measures of the distances between the facility and the users. They have been used in order to guarantee a similar level of equity among the users that may be affected in a positive or in a good way from a facility. These models have been formulated trying to adapt equality measures taken from context different from the location one. This way, every measure is very specific to the particular application and it is not highlighted why a measure should be selected and what is the contribution to the equity distribution among the users that can provide. In this paper, we propose a Facility Location Problem (FLP) in which we have to locate a given number of facilities among a set of potential facilities, optimizing an equality measure. We propose a computational study in order to test the similarity and the differences of a good number of measures with more than a single facility to locate and we point out which measures produce similar results and how they depend on each other.

Facility Location (FL) problems are among the most fundamental problems in combinatorial optimization. FL problems are also closely related to Clustering problems. Generally, we are given a set of facilities, a set of clients, and a symmetric distance metric on these facilities and clients. The goal is to ``open'' the ``best'' subset of facilities, subject to certain budget constraints, and connect all clients to the opened facilities so that some objective function of the connection costs is minimized. In this dissertation, we consider generalizations of classical FL problems. Since these problems are NP-hard, we aim to find good approximate solutions in polynomial time. We study the classic $k$-median problem which asks to find a subset of at most $k$ facilities such that the sum of connection costs of all clients to the closest facility is as small as possible. Our main result is a $2.675$-approximation algorithm for this problem. We also consider the Knapsack Median (KM) problem which is a generalization of the $k$-median problem. In the KM problem, each facility is assigned an opening cost. A feasible set of opened facilities should have the total opening cost at most a given budget. The main technical challenge here is that the natural LP relaxation has unbounded integrality gap. We propose a $17.46$-approximation algorithm for the KM problem. We also show that, after a preprocessing step, the integrality gap of the residual instance is bounded by a constant. The next problem is a generalization of the $k$-center problem, which is called the Knapsack Center (KC) problem and has a similar budget constraint as in the KM problem. Here we want to minimize the maximum distance from any client to its closest opened facility. The KC problem is well-known to be $3$-approximable. However, the current approximation algorithms for KC are deterministic and it is not hard to construct instances in which almost all clients have the worst-possible connection cost. Unfairness also arises in this context: certain clients may consistently get connected to distant centers. We design a randomized algorithm which guarantees that the expected connection cost of ``most'' clients will be at most $(1+2/e) \approx 1.74$ times the optimal radius and the worst-case distance remains the same. We also show a similar result for the $k$-center problem: all clients have expected approximation ratio about $1.592$ with a deterministic upper-bound of $3$ in the worst case. It is well-known that a few \emph{outliers} (very distant clients) may result in a very large optimal radius in the center-type problems. One way to deal with this issue is to cover only some $t$ out of $n$ clients in the so-called robust model. In this thesis, we give tight approximation algorithms for both robust $k$-center and robust matroid center problems. We also introduce a lottery model in which each client $j$ wants to be covered with probability at least $p_j \in [0,1]$. We then give randomized approximation algorithms for center-type problems in this model which match the worst-case bounds of the robust model and slightly violate the coverage and fairness constraints. Several of our results for FL problems in this thesis rely on novel dependent rounding schemes. We develop these rounding techniques in the general setting and show that they guarantee new correlation properties. Given the wide applicability of the standard dependent rounding, we believe that our new techniques are of independent interests.

Facility location problems have been investigated in the Operations Research literature from a variety of algorithmic perspectives, including those of approximation algorithms, heuristics, and linear programming. We introduce the study of these problems from the point of view of parameterized algorithms and complexity. Some applications of algorithms for these problems in the processing of semistructured documents and in computational biology are also described.

Bu çalışmada, olası bir İstanbul depreminden zarar görmüş bölge sakinlerinin erişebileceği yaralı toplama noktalarının en uygun konuş yerlerinin bulunması amaçlanmıştır. Çalışmada, İstanbul deprem afet planında yer alan dört senaryo deprem içerisinde meydana gelme olasılığı en yüksek olan senaryo deprem modeli ve ilçelere göre tahmini ağır yaralı sayıları kullanılmıştır. Problem, uygun kapsama uzaklıkları kullanılarak (1, 2, 3 km) bir maksimum kapsama problemi olarak modellenmiş ve SITATION yazılımı ile çözülmüştür. Yaralı toplama noktalarının her biri, bu noktalara ulaşan/ulaştırılan yaralılara sağlık hizmeti sunacağı için birer tesis olarak düşünülürken; sağlık hizmeti alacak yaralıların bulundukları ilçe merkezleri de talep noktaları olarak kabul edilmiştir. Uygun kapsama uzaklıklarının her biri için yapılan çözümleme sonuçları, ağır yaralı talebi karşılanan ve karşılanmayan ilçelerden oluşan tablolar halinde verilmiştir. Bu sonuçlar karşılaştırıldığında, kapsama uzaklığı arttığında talebin karşılanma oranı da beklendiği gibi artış göstermektedir. Ayrıca, çalışmada talep noktaları olarak ağır yaralı tahminlerine ilçeler bazında ulaşılabildiği için, her bir ilçenin ağır yaralı sayısı o ilçe merkezinin talebi olarak alınmıştır. Sağlık Bakanlığı’nın İstanbul için önerdiği yaralı toplama noktalarının ilgilenilen deprem senaryosu karşındaki yeterlilik durumu değerlendirilerek önerilerde bulunulmuştur.

Geometric branch-and-bound solution methods, in particular the big square small square technique and its many generalizations, are popular solution approaches for non-convex global optimization problems. Most of these approaches differ in the lower bounds they use which have been compared empirically in a few studies. The aim of this paper is to introduce a general convergence theory which allows theoretical results about the different bounds used. To this end we introduce the concept of a bounding operation and propose a new definition of the rate of convergence for geometric branch-and-bound methods. We discuss the rate of convergence for some well-known bounding operations as well as for a new general bounding operation with an arbitrary rate of convergence. This comparison is done from a theoretical point of view. The results we present are justified by some numerical experiments using the Weber problem on the plane with some negative weights. peerReviewed

International audience; There exist many variants of facility location problems. This chapter discusses some most recent advances and issues in this field including a capacitated plant location problem with multi commodity flow (CPLPMF), a multi-type transshipment point location problem with multi commodity flow (MTTLMF), a large scale new variant of capacitated clustering problem (VCCP), a location problem with selective matching and vehicles assignment (LCSMVA), and competitive. CPLPMF is a combination of capacitated plant location problem (CPLP) and multi commodity min-cost flow (MMCF) problem. MTTLMF is an extension of two-stage capacitated facility location problem (TSCFLP) considering both MMCF and several transshipment point (TP) types for the goal to locate TPs with appropriate types to ship different commodities from plants to customers while minimizing the total cost for opening TPs and shipment. VCCP is a new variant of the capacitated clustering problem, which describes a location-replenishment problem in upstream supply network design. © 2015 The Institute of Electrical and Electronics Engineers, Inc. All rights reserved.

Yaralı toplanma merkezleri, deprem, kasırga, sel veya savaş gibi büyük afetlerde çok sayıda yaralıya bir anda acil sağlık hizmeti verebilen ilk müdahale merkezleridir. Bu merkezlerin yerleri en uygun şekilde önceden saptanmalı ve olası bir afette halk, hangi merkezlerden hizmet alacağını bilmelidir. Bu çalışmada, Düzce ili için oluşturulacak yaralı toplanma merkezlerinin (YTM) optimum belirlenmesi amaçlanmıştır. Bu amaca yönelik, tesis yerleştirme problemlerinin çözümü için yaygın olarak kullanılan P- Medyan Tesis Yerleştirme Modeli seçilmiştir.Çalışmanın uygulandığı bölgede toplanma merkezi olabilecek yerler ve sayısı, bölge sınır koordinatları, yerleşim birimleri koordinatları ve güncel nüfus verileri Düzce il valiliği ilgili birimlerinden alınmıştır. Bu veriler kullanılarak yerleşim birimleri ve aday toplanma merkezleri arası uzaklıklar Google Maps programı vasıtasıyla hesaplanmıştır. Çalışmanın matematiksel modelini analiz etmek için Sitation tesis yerleştirme yazılımı kullanılmıştır. Sitation yazılımının ara yüzleri kullanılarak çalışmanın modeli hem Lagrange Çarpanları yöntemi hem de Genetik Algoritma yöntemi ile ayrı ayrı analiz edilerek karşılaştırılmıştır.Çalışmanın modeli, ilk olarak Düzce il merkezindeki 56 yerleşim biriminde kurulacak üç adet Yaralı Toplanma Merkezi ile maksimum talebin karşılanması için Lagrange Çarpanları yöntemi kullanılarak kapsama mesafesi 2 km için analiz edildiğinde Düzce merkez nüfusunun % 99.44'ü yani 142217 kişinin talebi Kültür, Sallar ve Çamköy merkezleri ile karşılanmıştır. Bir yerleşim biriminin (Kemal Işıldak) yani 800 kişinin talebi karşılanamamıştır. Daha sonra model Genetik Algoritma yöntemi kullanılarak kapsama mesafesi 2 km için analiz edildiğinde Düzce merkez nüfusunun % 99.46'sı yani 142245 kişinin talebi Bayram Gökmen, Bahçelievler ve Kültür yaralı toplanma merkezleri ile karşılanmıştır. Bir yerleşim biriminin (Soğukpınar) yani 773 kişinin talebi karşılanamamıştır. İki farklı optimizasyon yöntemi ile yapılan analizler karşılaştırıldığında Genetik Algoritma ile yapılan analiz sonuçlarının optimum ve daha fazla toplumsal fayda oluşturduğu izlenmiştir. Elde edilen sonuçlar afet koordinasyon yetkilileri ile paylaşılmış ve ilgili afet planlarına dâhil edilmesi önerilmiştir.Anahtar Kelimeler: Tesis Yerleştirme Problemleri, P-medyan Tesis Yerleştirme Modeli, Yaralı Toplanma Merkezleri Casuality collection centers are the first-aid centers where a large number of casualities are provided with urgent medical service at a time in big disasters such as earthquakes, tornadoes, floods and wars. Location of these casuality collection centers must be determined appropriately beforehand and people must be informed of what center they are to be provided with service at.In this study it is aimed that optimum location is determined for casuality collection centers (CCC) to be founded for the province of Duzce. For this aim, P-Median Location Model frequently used in the solution of facility location problems has been chosen.The places and the number of them that could be casuality collection centers in the area where the study has been applied, the coordinates of residence centers and the current data of population have been obtained from the related units of Düzce Governer Office. Using this data, the distance between residence centers and probable casuality collection centers have been calculated through Google Maps program. Sitation facility location software has been used to analize the model established. By using the interface of the Sitation software, the model of the study has been compared with both Langrange multupliers and Genetic Algorithm through analyzing separately.When the model of the study has been analized for 2 kilometres of covering distance using Langrange Multupliers method in order to meet the maximum demand with 3 casuality collection centers to be located for the first time in 56 residence centers of Düzce province centrum ,the demand of 99,44 percent of centrum population that meant 142217 people was met through Kültür,Sallar and Çamköy residences. The demand of only one residence (Kemal Işıldak) that meant 800 people could not be met. Later when the covering distance for 2 kilometres was analized using model Genetic Algorithm method, the demand of 99,46 percent of centrum population of Düzce that meant 142245 people was met through the casuality collection centers of Bayram Gökmen, Bahçelievler and Kültür. The demand of only one residence (Soğukpınar) that meant 773 people could not be met.When the analyses conducted through these 2 different methods of optimization have been compared it is seen that the results of the analyse through Genetic Algorithm method are optimum and more of socially benefical. The results obtained have been shared with the authorities of disaster coordination and recommended to be included in related disaster plans.Key words: : Facility Location Problems, P-median Facility Location Model, Casuality Collection Centers 156

Bu çalışmada, olası bir İstanbul depreminden zarar görmüş bölge sakinlerinin erişebileceği yaralı toplama noktalarının en uygun konuş yerlerinin bulunması amaçlanmıştır. Çalışmada, İstanbul deprem afet planında yer alan dört senaryo deprem içerisinde meydana gelme olasılığı en yüksek olan senaryo deprem modeli ve ilçelere göre tahmini ağır yaralı sayıları kullanılmıştır. Problem, uygun kapsama uzaklıkları kullanılarak (1, 2, 3 km) bir maksimum kapsama problemi olarak modellenmiş ve SITATION yazılımı ile çözülmüştür. Yaralı toplama noktalarının her biri, bu noktalara ulaşan/ulaştırılan yaralılara sağlık hizmeti sunacağı için birer tesis olarak düşünülürken; sağlık hizmeti alacak yaralıların bulundukları ilçe merkezleri de talep noktaları olarak kabul edilmiştir. Uygun kapsama uzaklıklarının her biri için yapılan çözümleme sonuçları, ağır yaralı talebi karşılanan ve karşılanmayan ilçelerden oluşan tablolar halinde verilmiştir. Bu sonuçlar karşılaştırıldığında, kapsama uzaklığı arttığında talebin karşılanma oranı da beklendiği gibi artış göstermektedir. Ayrıca, çalışmada talep noktaları olarak ağır yaralı tahminlerine ilçeler bazında ulaşılabildiği için, her bir ilçenin ağır yaralı sayısı o ilçe merkezinin talebi olarak alınmıştır. Sağlık Bakanlığı’nın İstanbul için önerdiği yaralı toplama noktalarının ilgilenilen deprem senaryosu karşındaki yeterlilik durumu değerlendirilerek önerilerde bulunulmuştur., In this study, the selection of the casualty collection points that can be accessible for the wounded residents who have been damaged from the possible Istanbul earthquake is aimed to find the most appropriate location. In the four scenarios of earthquakes which take place in the İstanbul earthquake disaster plan, the most possible scenario earthquake plan and the number of estimated wounded people are used in the study. The problem is modelled as a maximum coverage problem using the appropriate coverage distances (1, 2, 3 km) and solved with SITATION software. The each of casualty collection points are considered to be a facility to supply a health care for wounded people reached/transported this point, while the center of districts are accepted as demand points where wounded people demanding health care. The results of the analysis for each of the appropriate coverage distances are shown in tables composed of being covered and uncovered demand for seriously injured. According to these compared results, when the coverage distance increases, the percentage of covering demands increase which is expected. In addition to this, the center of districts are determined as demand points since the number of estimated wounded people are attainable only for districts in the study. In addition to the efficieny of the wounded collection points which ministry of health has offered for İstanbul has been assessed and advised.

In this study, the selection of the casualty collection points that can be accessible for the wounded residents who have been damaged from the possible İstanbul earthquake is aimed to find the most appropriate location. In the four scenarios of earthquakes which take place in the İstanbul earthquake disaster plan, the most possible scenario earthquake plan and the number of estimated wounded people are used in the study. The problem is modelled as a maximum coverage problem using the appropriate coverage distances (1, 2, 3 km) and solved with SITATION software. The each of casualty collection points are considered to be a facility to supply a health care for wounded people reached/transported this point, while the center of districts are accepted as demand points where wounded people demanding health care. The results of the analysis for each of the appropriate coverage distances are shown in tables composed of being covered and uncovered demand for seriously injured. According to these compared results, when the coverage distance increases, the percentage of covering demands increase which is expected. In addition to this, the center of districts are determined as demand points since the number of estimated wounded people are attainable only for districts in the study. In addition to the efficieny of the wounded collection points which ministry of health has offered for İstanbul has been assessed and advised., Bu çalışmada, olası bir İstanbul depreminden zarar görmüş bölge sakinlerinin erişebileceği yaralı toplama noktalarının en uygun konuş yerlerinin bulunması amaçlanmıştır. Çalışmada, İstanbul deprem afet planında yer alan dört senaryo deprem içerisinde meydana gelme olasılığı en yüksek olan senaryo deprem modeli ve ilçelere göre tahmini ağır yaralı sayıları kullanılmıştır. Problem, uygun kapsama uzaklıkları kullanılarak (1, 2, 3 km) bir maksimum kapsama problemi olarak modellenmiş ve SITATION yazılımı ile çözülmüştür. Yaralı toplama noktalarının her biri, bu noktalara ulaşan/ulaştırılan yaralılara sağlık hizmeti sunacağı için birer tesis olarak düşünülürken; sağlık hizmeti alacak yaralıların bulundukları ilçe merkezleri de talep noktaları olarak kabul edilmiştir. Uygun kapsama uzaklıklarının her biri için yapılan çözümleme sonuçları, ağır yaralı talebi karşılanan ve karşılanmayan ilçelerden oluşan tablolar halinde verilmiştir. Bu sonuçlar karşılaştırıldığında, kapsama uzaklığı arttığında talebin karşılanma oranı da beklendiği gibi artış göstermektedir. Ayrıca, çalışmada talep noktaları olarak ağır yaralı tahminlerine ilçeler bazında ulaşılabildiği için, her bir ilçenin ağır yaralı sayısı o ilçe merkezinin talebi olarak alınmıştır. Sağlık Bakanlığı’nın İstanbul için önerdiği yaralı toplama noktalarının ilgilenilen deprem senaryosu karşındaki yeterlilik durumu değerlendirilerek önerilerde bulunulmuştur.

In this work, we study the Simple Plant Location Problem (SPLP). Using its classical mathematical programming formulation and another recently proposed formulation, we develop several algorithms to …nd lower and upper bounds for the problem as well as branch-and-bound algorithms. With the classical formulation, such bounds are obtained via the data correction method and dominance criteria between …xed and transportation costs. We propose a projection of this formulation that has shown to be computationally atractive. Using the new formulation, we propose and prove the correctness of several iterative procedures that attempt to …nd an optimal solution to the problem by solving a sequence of parametric sub-problems, each one obtained by removing some variables and constraints of the original formulation. At each iteration of this process, we can obtain lower and upper bounds. We also apply Lagrangean relaxation to this new formulation in order to get other bounds. We consider several possibilities of relaxing the constraints. In addition, we develop branch-and-bound algorithms based on both formulations and the obtained bounds. We evaluate the computational e¢ ciency of all proposed algorithms with hard test instances from the literature. Computational results are reported and comparisons with other algorithms from the literature are carried out. Neste trabalho, estudamos o problema de localização simples (SPLP - Simple Plant Location Problem). Usando a formulação matemática clássica e uma outra formulação proposta recentemente, desenvolvemos vários algoritmos para encontrar limites inferiores e superiores, bem como algoritmos tipo branch-and-bound. Com a formulação clássica, tais limites são obtidos utilizando o método de correção de dados e critérios de dominância entre os custos …xos e de transporte. Propomos uma projeção dessa formulação, que se mostrou computacionalmente atrativa. Usando a nova formulação propomos e mostramos a corretude de vários procedimentos iterativos que procuram encontrar uma solução para o problema, resolvendo uma seqüência de subproblemas paramétricos obtidos com a remoção de variáveis e restrições da formulação original. Em cada iteração desse processo, podemos gerar limites inferiores e superiores. Aplicamos ainda relaxação lagrangeana a essa nova formulação para obter outros limites. Analisamos várias possibilidades de relaxação das restrições. Desenvolmento também algoritmos branch-and-bound baseados em ambas as formulações e nos limites obtidos. Avaliamos a e…ciência computacional de todos os algoritmos com instâncias de teste difíceis, disponíveis na literatura. Resultados computacionais e comparações com outros algoritmos da literatura são reportados.

Given P, a simple connected, possibly non-convex, polyhedral surface composed of positively weighted triangular faces, we consider paths from generalized sources (points, segments, polygonal chains or polygonal regions) to points on P that stay on P and avoid obstacles (segments, polygonal chains or polygonal regions). The distance function defined by a generalized source is a function that assigns to each point of P the cost of the shortest path from the source to the point. In this paper we present an algorithm for computing approximate generalized distance functions. We also provide an algorithm that computes a discrete representation of the approximate distance function and, as applications, algorithms for computing discrete order-k Voronoi diagrams and for approximately solving facility location problems. Finally, we present experimental results obtained with our implementation of the provided algorithms This work was partially supported by the Spanish Ministerio de Ciencia e Innovacion under grant TIN2010-20590-C02-02

Geometric branch-and-bound methods are commonly used solution algorithms for non-convex global optimization problems in small dimensions, say for problems with up to six or ten variables, and the efficiency of these methods depends on some required lower bounds. For example, in interval branch-and-bound methods various well-known lower bounds are derived from interval inclusion functions. The aim of this work is to analyze the quality of interval inclusion functions from the theoretical point of view making use of a recently introduced and general definition of the rate of convergence in geometric branch-and-bound methods. In particular, we compare the natural interval extension, the centered form, and Baumann’s inclusion function. Furthermore, our theoretical findings are justified by detailed numerical studies using the Weber problem on the plane with some negative weights as well as some standard global optimization benchmark problems. peerReviewed

The dynamic facility location problem is a generalization of the classic facility location problem proposed by Eisenstat, Mathieu, and Schabanel to model the dynamics of evolving social/infrastructure networks. The generalization lies in that the distance metric between clients and facilities changes over time. This leads to a trade-off between optimizing the classic objective function and the “stability” of the solution: There is a switching cost charged every time a client changes the facility to which it is connected. While the standard linear program (LP) relaxation for the classic problem naturally extends to this problem, traditional LP-rounding techniques do not, as they are often sensitive to small changes in the metric resulting in frequent switches. We present a new LP-rounding algorithm for facility location problems, which yields the first constant approximation algorithm for the dynamic facility location problem. Our algorithm installs competing exponential clocks on the clients and facilities and connects every client by the path that repeatedly follows the smallest clock in the neighborhood. The use of exponential clocks gives rise to several properties that distinguish our approach from previous LP roundings for facility location problems. In particular, we use no clustering and we allow clients to connect through paths of arbitrary lengths . In fact, the clustering-free nature of our algorithm is crucial for applying our LP-rounding approach to the dynamic problem.