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The delineation of the transportation network is a strategic issue for all over the place. The problem of locating new facilities among several existing facilities and minimizing the total transportation cost are the main topics of the location network system. This paper addresses the transportation-p-facility location problem (T-p-FLP) which makes a connection between the facility location problem and the transportation problem, where p corresponds to the number of facilities. The T-p-FLP is a generalization of the classical transportation problem in which we have to seek where and how we impose the p-number of facilities such that the total transportation cost from existing facility sites to the potential facility sites will be minimized. The exact approach, based on the iterative procedure, and a heuristic approach as applied to the T-p-FLP are discussed and corresponding results are compared. An experimental example is incorporated to explore the efficiency and effectiveness of our proposed study in reality. Finally, a summary is given together with suggestions for future studies. [ABSTRACT FROM AUTHOR]

Determining optimum places for the facilities and optimum transportation from existing sites to the facilities belongs to the main problems in supply chain management. The solid transportation-p-facility location problem (ST-p-FLP) is an integration between the facility location problem and the solid transportation problem (STP). This paper delineates the ST-p-FLP, a generalization of the classical STP in which location of p-potential facility sites are sought so that the total transportation cost by means of conveyances from existing facility sites to potential facility sites will be minimized. This is one of the most important problems in the transportation systems and the location research areas. Two heuristic approaches are developed to solve such type of problem: a locate-allocate heuristic and an approximate heuristic. Thereafter, the performance of the proposed model and the heuristics are evaluated by an application example, and the obtained results are compared. Moreover, a sensitivity analysis is introduced to investigate the resiliency of the proposed model. Finally, conclusions and an outlook to future research works are provided. [ABSTRACT FROM AUTHOR]

There is a growing need for integer solutions in industries, production units, etc. Specifically, there is an increasing demand to develop precise methods for solving integer-programming problems (IPPs). In this paper, we propose a new algorithm for solving IPPs in a general form by combining two decomposition techniques: Benders decomposition (BD) and decomposition-based pricing methods (DBP). Moreover, we generate some conditions for solving problems having either infeasible or unbounded solutions. In addition, we present an application and evaluation of a solution method for solving IPPs, while also giving a brief description of the different classical decomposition methods, namely the Dantzig-Wolfe decomposition (DWD), decomposition-based pricing (DBP), Benders decomposition (BD), and recently proposed improved decomposition (ID) methods for solving IPPs. We also discuss the use of the decomposition methods for solving IPPS to develop a heuristic algorithm, describe the limitations of the classical algorithms, and present extensions enabling its application to a broader range of problems. To illustrate the decomposition procedures, we will provide corresponding models and numerical results for two standard mathematical programs: the Fixed Charge Problem (FCP) and the Facility Location Problem (FLP). Our findings from this study suggest that our algorithm produces the most efficient computational solutions of IPPs. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of mesh router placement in a wireless mesh network (WMN). The latter is an emerging networking technology consisting of three kinds of nodes: mesh clients, mesh routers and gateways. Mesh routers form a backbone to forward data between client nodes and the external network. Therefore, the optimization of mesh routers positions strongly influences the performance of the WMN. Since this issue has already been proved as being computationally NP-hard to solve, the use of non-exact methods (such as heuristics and metaheuristics) is indispensable. In this sense, our current work consists to apply and adapt the electromagnetism-like mechanism (EM) metaheuristic to solve the router node placement issue. The idea is to consider a population of solutions encoded as particles subject to attractions and repulsions as in electromagnetic systems. Finally, we have evaluated our proposed approach by simulating different scenarios under various settings. The obtained results indicate that the proposed EM algorithm outperforms the existing particle swarm intelligence algorithm and genetic algorithm in defining near optimal positions for mesh routers with regard to coverage and connectivity. [ABSTRACT FROM AUTHOR]

In this article, a new Monte Carlo hybrid local search algorithm (Hyb-LS) is proposed for solving the uncapacitated facility location problem. Hyb-LS is based on repeated sampling using two local search strategies based on best improvement and randomized neighbourhood search. A major advantage of Hyb-LS for its practical use is that the number of restarts is its only parameter to tune. The algorithm is also simple to reimplement, scalable and robust to changes in coefficients within a problem instance. The stopping criterion for local search is learned automatically. Experimental results are presented for four representative and contrasting cost and distance models. The results obtained by Hyb-LS are compared to the optimal or near-optimal solutions found by a mixed integer linear programming (MILP) solver with a generous time limit. For three out of the four models, Hyb-LS obtains better solutions than the upper bound found by the MILP solver for at least one instance. [ABSTRACT FROM AUTHOR]

Abstract This work addresses a two-level facility location problem in a military logistic system, named the military logistic depot location problem (MLDLP). Unlike most previous research on facility location problems, the objective of MLDLP is to maximize the average utility of requisitioned buildings, and the utility of a selected building depends on its attributes. This work develops an integer programming model and provides a two-stage method for this problem. In the first stage, the analytic hierarchy process (AHP) is applied to estimate the relative weights of the attributes as the coefficients of the objective function. In the second stage, simplified swarm optimization (SSO) is combined with a novel local search scheme based on AHP, called SSO AHP , which is proposed to deal with the problem. SSO AHP is empirically verified on thirty-six randomly generated problems, and the corresponding results are reported comparing the results with those obtained by up-to-date evolutionary computation methods. Highlights • Addressed a facility location problem in a military logistic system, named MLDLP. • The objective of MLDLP is to maximize the average utility of requisitioned buildings. • Proposed a novel local search scheme based on AHP to guide the proposed algorithm. • Statistical results indicate that the proposed method is better than its competitors. [ABSTRACT FROM AUTHOR]

The facility location problem and its related financial issues have a significant impact on the configuration of a supply chain structure (SCS). Although affording the setup cost of facilities requires a huge financial investment, a meticulous planning to recoup it has been neglected by an overwhelming majority of previous studies. To fill this gap, an economical investment plan of facilities is determined by striking a trade‐off between the contribution of the stockholders' capital and the loan arrangement. In the context of a multiperiod three‐echelon SCS, the model also determines the optimum location of plants and the best supply and distribution patterns. The model maximizes the fill rate and the net present value of the periodic cash flow including the sale revenues minus the mortgage payment, purchase, and transportation costs. To solve the proposed problem, a finely tuned Pareto‐based nondominated sorting genetic algorithm (NSGA‐II) and a multi‐objective biogeography‐based optimization (MOBBO) algorithm are employed. Moreover, the solution methods are equipped with the heuristic DROP approach and data envelopment analysis to expedite the convergence process and derive the most efficient solutions, respectively. The experiments indicate the adequacy of the solution methods due to the close proximity to the results of the exact branch‐and‐bound method via the general algebraic modeling system optimization software. Finally, the results of a case study associated with designing SCS of an emerging biofuel industry demonstrate the significant implication of the research. [ABSTRACT FROM AUTHOR]

To determine the spatial distribution of rental stations and bikeways in a public bike system, this paper proposes a facility location and network design model. The model is developed as a multi-objective programing problem that considers four objectives (minimizing cyclist risk, maximizing cyclist comfort, minimizing adverse impacts on traffic and maximizing service coverage) and multiple constraints (monetary budget, network connectivity, station spacing, bikeway types, station number and value ranges of decision variables). The ε-constraint method solves the programing problem for the public bike system in Daan District, Taipei City, Taiwan. The nine non-dominated alternatives generated are all markedly better than existing locations of rental stations and bikeways. Scenario analysis results indicate that increasing the construction budget for bikeways significantly improves cyclist safety and comfort whilst increasing the adverse impact on traffic. Planners can use this model to develop public bike systems that spatially integrate rental stations and bikeway networks. [ABSTRACT FROM AUTHOR]

The application of wireless charging technology in traditional battery-powered wireless sensor networks (WSNs) grows rapidly recently. Although previous studies indicate that the technology can deliver energy reliably, it still faces regulatory mandate to provide high power density without incurring health risks. In particular, in clustered WSNs there exists a mismatch between the high energy demands from cluster heads and the relatively low energy supplies from wireless chargers. Fortunately, solar energy harvesting can provide high power density without health risks. However, its reliability is subject to weather dynamics. In this paper, we propose a hybrid framework that combines the two technologies - cluster heads are equipped with solar panels to scavenge solar energy and the rest of nodes are powered by wireless charging. We divide the network into three hierarchical levels. On the first level, we study a discrete placement problem of how to deploy solar-powered cluster heads that can minimize overall cost and propose a distributed $1.61(1+\epsilon)^2$ -approximation algorithm for the placement. Then, we extend the discrete problem into continuous space and develop an iterative algorithm based on the Weiszfeld algorithm. On the second level, we establish an energy balance in the network and explore how to maintain such balance for wireless-powered nodes when sunlight is unavailable. We also propose a distributed cluster head re-selection algorithm. On the third level, we first consider the tour planning problem by combining wireless charging with mobile data gathering in a joint tour. We then propose a polynomial-time scheduling algorithm to find appropriate hitting points on sensors’ transmission boundaries for data gathering. For wireless charging, we give the mobile chargers more flexibility by allowing partial recharge when energy demands are high. The problem turns out to be a Linear Program. By exploiting its particular structure, we propose an efficient algorithm that can achieve near-optimal solutions. Our extensive simulation results demonstrate that the hybrid framework can reduce battery depletion by 20 percent and save vehicles’ moving cost by 25 percent compared to previous works. By allowing partial recharge, battery depletion can be further reduced at a slightly increased cost. The results also suggest that we can reduce the number of high-cost mobile chargers by deploying more low-cost solar-powered sensors. [ABSTRACT FROM AUTHOR]

In this work, we consider the robust/soft-capacitated 2-level facility location problems. For the robust version, we propose a primal-dual based $$(3+\epsilon )$$ -approximation algorithm via construction of an adapted instance which explores some open facilities in the optimal solution. For the soft-capacitated version, we propose a $$ (4+ 1/ (e-1) +\epsilon )$$ -approximation algorithm via construction of the associated uncapacitated version whose connection cost is re-defined appropriately. [ABSTRACT FROM AUTHOR]

This paper addresses a multi-objective facility location problem, concerning the location of noise-sensitive and noise-generating facilities in urban environments. To promote sustainable solutions, two main criteria are incorporated within the optimisation model: minimising total noise-threshold violation levels and the total system travel time on the underlying road network. A bi-level formulation is proposed, which is eventually re-formulated into a single-level model. The augmented ε -constraint method is implemented to yield non-dominated solutions. A Benders-Decomposition approach is proposed to handle large instances of the problem. Numerical tests highlight the effectiveness of the proposed solution method in designing the layout of urban regions. [ABSTRACT FROM AUTHOR]

The hierarchical facility location problem (HFLP) is defined as determining the location of facilities in such a way that high-level facilities can serve the facilities in low-level efficiently. In this paper, a mixed integer programming model for the HFLP with the flow capacity constraint is proposed. An approach hybrided PSO and Tabu search (TS) (HPSO-TS) is proposed to solve the HFLP. The objective is to minimize overall demand-weighted distance travel, facility operating costs, and flow assignment costs. This method transforms PSO particles representing various dimensions of the attributes into a Tabu priority list and then constructs the assignment networks. The performance of the proposed algorithm is compared with branch-and-bound algorithm, a genetic algorithm, and classical PSO. Numerical results show that the performance of the proposed algorithm is better than those with exact methods when solving such problems. Finally, the proposed algorithm is applied to solve a case company in Jakarta. [ABSTRACT FROM PUBLISHER]

This article deals with a problem of determining locations for installing long-term care facilities in the given network, in order to minimize the maximum number of patients that are assigned to a single installed facility. The problem is known as the Long-Term Care Facility Location Problem (LTCFLP). We propose an improved mathematical formulation for the LTCFLP and evaluate its efficiency through a set of computational experiments on test instances with up to 80 potential facility locations. To solve instances of larger problem dimensions, we develop a metaheuristic method based on a Variable Neighbourhood Search (VNS). A reduced VNS algorithm is employed to provide a good-quality initial solution, which is then used as a starting point of the basic VNS method. A local search procedure with efficient fast interchange method is implemented in the proposed VNS-based approach. The algorithm is benchmarked on a large-scale dataset involving up to 400 potential facility locations. Presented computational results show that the proposed VNS quickly reaches all optimal solutions from the literature, and in most cases outperforms existing heuristic methods for solving the LTCFLP. [ABSTRACT FROM AUTHOR]

In this paper, a new modeling approach is introduced for a competitive facility location problem in which multiple competitors aim to maximize their market shares. The problem is called the Competitive Maximal Covering Location Problem (CMCLP) based on the classical Maximal Covering Location Problem. Typically, the CMCLP is modeled as a Stackelberg game in which the first player and then the other one locate a fixed number of facilities. On the other hand, the present work considers multiple competitors, and the objective is on discovering a set of the competitors’ decision tuples that are not dominated by any other decision tuples in the solution space. Thereby, the proposed modeling approach aims to help competing firms understand tradeoffs when they engage in negotiations. A mathematical formulation for the CMCLP with two competitors is presented. A multi-objective genetic algorithm is used to solve the problems with multiple competitors. Computational experiments demonstrate that the genetic algorithm is able to approximate the true Pareto front. [ABSTRACT FROM AUTHOR]

The (weighted) -median, -means, and -center problems in the plane are known to be NP-hard. In this paper, we study these problems with an additional constraint that requires the sought facilities to be on a given line. We present efficient algorithms for various distance measures such as . We assume that all weighted points are given sorted by their projections on the given line. For -median, our algorithms for and metrics run in time and time, respectively. For -means, which is defined only on the squared distance, we give an time algorithm. For -center, our algorithms run in time for all three metrics, and in time for the unweighted version under and metrics. While our results for the -center problem are optimal, the results for the -median problem almost match the best algorithms for the corresponding one-dimensional problems. [ABSTRACT FROM AUTHOR]

Purpose The purpose of this paper is to find a sustainable facility location solution for a closed-loop distribution network in the uncertain environment created by of high levels of product returns from online retailing coupled with growing pressure to reduce carbon emissions. Design/methodology/approach A case study approach attempts to optimize the distribution centre (DC) location decision for single and double hub scenarios. A hybrid approach combining centre of gravity and mixed integer programming is established for the un-capacitated multiple allocation facility location problem. Empirical data from a major national UK retail distributor network is used to validate the model. Findings The paper develops a contemporary model that can take into account multiple factors (e.g. operational and transportation costs and supply chain (SC) risks) while improving performance on environmental sustainability. Practical implications Based on varying product return rates, SC managers can decide whether to choose a single or a double hub solution to meet their needs. The study recommends a two hub facility location approach to mitigate emergent SC risks and disruptions. Originality/value A two-stage hybrid approach outlines a unique technique to generate candidate locations under twenty-first century conditions for new DCs. [ABSTRACT FROM AUTHOR]

This paper presents a particular case of the facility location problem. The characteristic of this problem is that it contains a set of clusters or nodes that represent the accumulation of clients who demand a single product. It is desired to locate P distribution centers (DC) where the demand of clusters is only satisfied if we located a distribution center in this cluster. Moreover, the number of capacitated plants and its location must be determined in order to supply the different distributions centers. The objective is to maximize the utility by considering, in one hand, the incomes that are obtained for satisfying the demand of different clusters and in the other hand, the installation costs incurred when locating the Distribution Centers and the plants as well as the costs of material transport from the plants to the distribution center. Other applications of this problem are appreciated in telecommunications networks, electrical networks, etc. The paper also present a new model of integer programming that allows to solve small instances, up to 300 clusters, in an acceptable CPU time, the problems were programmed with AMPL and solved with CPLEX 11.0. For two larger instances the authors present heuristics, which allow obtaining solutions with a GAP least than 1%. [ABSTRACT FROM AUTHOR]

In this paper, we consider the robust facility location problem with penalties, aiming to serve only a specified fraction of the clients. We formulate this problem as an integer linear program to identify which clients must be served. Based on the corresponding LP relaxation and dual program, we propose a primal-dual (combinatorial) 3-approximation algorithm. Combining the greedy augmentation procedure, we further improve the above approximation ratio to 2. [ABSTRACT FROM AUTHOR]

We study the incremental facility location problem, wherein we are given an instance of the uncapacitated facility location problem (UFLP) and seek an incremental sequence of opening facilities and an incremental sequence of serving customers along with their fixed assignments to facilities open in the partial sequence. We say that a sequence has a competitive ratio of k, if the cost of serving the first ℓ customers in the sequence is at most k times the optimal solution for serving any ℓ customers for all possible values of ℓ. We provide an incremental framework that computes a sequence with a competitive ratio of at most eight and a worst-case instance that provides a lower bound of three for any incremental sequence. We also present the results of our computational experiments carried out on a set of benchmark instances for the UFLP. The problem has applications in multistage network planning. © 2015 Wiley Periodicals, Inc. NETWORKS, Vol. 65(4), 306-311 2015 [ABSTRACT FROM AUTHOR]

The main contribution of this work is to propose a primal–dual combinatorial 3 ( 1 + ε ) -approximation algorithm for the two-level facility location problem (2-LFLP) by exploring the approximation oracle concept. This result improves the previous primal–dual 6-approximation algorithm for the multilevel facility location problem, and also matches the previous primal–dual approximation ratio for the single-level facility location problem. One of the major merits of primal–dual type algorithms is their easy adaption to other variants of the facility location problems. As a demonstration, our primal–dual approximation algorithm can be easily adapted to several variants of the 2-LFLP, including models with stochastic scenario, dynamically arrived demands, and linear facility cost. [ABSTRACT FROM AUTHOR]

This article presents an efficient method for simultaneously finding both the Weber cell and optimal connective paths in a grid. As numerous barriers of arbitrary shape and weighted regions are distributed in the cell map of this research, the problem scenario is similar to working out a real-life facility location selection and path-routing problems in a geographical map. In this study, the Weber problem of finding a single-facility location from an accumulation cost table is generated by a grid wave propagation method (higher-geometry maze router). After finding the Weber point (cell), optimal connective paths with minimum total weighted cost are backtracked between the Weber location cell and the demand cells. This new computation algorithm with linear time and space complexity can be integrated as a spatial analytical function within GIS. [ABSTRACT FROM PUBLISHER]

In this article, we present a primal-dual 3-approximation algorithm for the stochastic priority facility location problem. Combined with greedy augmentation procedure, such performance factor is further improved to 1.8526. [ABSTRACT FROM PUBLISHER]

We consider a healthcare facility location problem in which there are two types of patients, low-income patients and middle- and high-income patients. The former can use only public facilities, while the latter can use both public facilities and private facilities. We focus on the problem of determining locations of public healthcare facilities to be established within a given budget and allocating the patients to the facilities for the objective of maximizing the number of served patients while considering preference of the patients for the public and private facilities. We present an integer programming formulation for the problem and develop a heuristic algorithm based on Lagrangian relaxation and subgradient optimization methods. Results of computational experiments on a number of problem instances show that the algorithm gives good solutions in a reasonable computation time and may be effectively used by the healthcare authorities of the government. [ABSTRACT FROM AUTHOR]

Abstract: We offer the currently best approximation ratio 2.375 for the facility location problem with submodular penalties (FLPSP), improving not only the previous best combinatorial ratio 3, but also the previous best non-combinatorial ratio 2.488. We achieve this improved ratio by combining the primal–dual scheme with the greedy augmentation technique. [Copyright &y& Elsevier]

Abstract: We present a 1.488-approximation algorithm for the metric uncapacitated facility location (UFL) problem. Previously, the best algorithm was due to Byrka (2007). Byrka proposed an algorithm parametrized by γ and used it with . By either running his algorithm or the algorithm proposed by Jain, Mahdian and Saberi (STOCʼ02), Byrka obtained an algorithm that gives expected approximation ratio 1.5. We show that if γ is randomly selected, the approximation ratio can be improved to 1.488. Our algorithm cuts the gap with the 1.463 approximability lower bound by almost 1/3. [Copyright &y& Elsevier]

This study is concerned with the long-term strategic decision of simultaneously determining the number and location of new facilities to minimize the total (fixed and variable) cost of interacting with a set of existing facilities. The problem has many practical applications, including locating bus stops for public transportation. A non-linear, mixed integer mathematical formulation, a brute-force algorithm, and four heuristics are developed for the problem. Experimental results show that the proposed Greedy Search Heuristic outperforms all other heuristics considered. The proposed solution methods provide engineering managers with new tools to solve this particular facility location problem. [ABSTRACT FROM AUTHOR]

Currently, industry and academia are undergoing an evolution in developing the next generation of drone applications. Including the development of autonomous drones that can carry out tasks without the assistance of a human operator. In spite of this, there are still problems left unanswered related to the placement of drone take-off, landing and charging areas. Future policies by governments and aviation agencies are inevitably going to restrict the operational area where drones can take-off and land. Hence, there is a need to develop a system to manage landing and take-off areas for drones. Additionally, we proposed this approach due to the lack of justification for the initial location of drones in current research. Therefore, to provide a foundation for future research, we give a justified reason that allows predetermined location of drones with the use of drone ports. Furthermore, we propose an algorithm to optimally place these drone ports to minimize the average distance drones must travel based on a set of potential drone port locations and tasks generated in a given area. Our approach is derived from the Facility Location problem which produces an efficient near optimal solution to place drone ports that reduces the overall drone energy consumption. Secondly, we apply various traveling salesman algorithms to determine the shortest route the drone must travel to visit all the tasks. [ABSTRACT FROM AUTHOR]