Facility Location Theory Research Articles

Optimal scale and capacity integration in a port cluster under demand uncertainty

We address the problem of capacity integration in a port cluster under demand uncertainty, which involves determining the optimal capacity investment and exit decisions for the ports in a port cluster over multiple stages. Based on real option theory, we first investigate the optimal investment and exit decisions for a single incapacitated port without integration under uncertainty. Second, we present the optimal scale of a port cluster based on the continuous approximation-based approach in facility location theory, which offers an optimization objective for capacity integration in an existing port cluster. Third, we build a multistage capacity investment and exit (MCIEI) model to minimize the gap between the social welfare under an existing port cluster and the social welfare at the optimal scale of a port cluster. In addition, we present a dynamic programming-based pattern search algorithm (DP-GPS) to solve the proposed model. Finally, the optimal investment and exit decisions for a single port are derived from the case of Chinese seaports. The results indicate that when the potential maritime demand of the catchment area is above a threshold, the optimal investment capacity increases linearly in the potential maritime demand while the optimal exit capacity decreases linearly in the potential maritime demand. Furthermore, the MCIEI model and the corresponding DP-GPS algorithm are verified with respect to the Liaoning port cluster in mainland China. The numerical results illustrate that the Jinzhou and Dalian Ports should adopt exit decisions in the optimal capacity integration scheme, while the Yingkou and Dandong Ports should opt to invest. Our research outcomes can help guide port integration in port clusters and further establish resource-saving ports in coastal regions.

Rank-two update algorithm versus Frank–Wolfe algorithm with away steps for the weighted Euclidean one-center problem

The weighted Euclidean one-center (WEOC) problem is one of the classic problems in facility location theory, which is also a generalization of the minimum enclosing ball (MEB) problem. Given m points in $${\mathbb {R}}^{n}$$, the WEOC problem computes a center point $$c\in {\mathbb {R}}^{n}$$ that minimizes the maximum weighted Euclidean distance to m given points. The rank-two update algorithm is an effective method for solving the minimum volume enclosing ellipsoid (MVEE) problem. It updates only two components of the solution at each iteration, which was previously proposed in Cong et al. (Comput Optim Appl 51(1):241–257, 2012). In this paper, we further develop and analyze the rank-two update algorithm for solving the WEOC problem. At each iteration, the calculation of the optimal step-size for the WEOC problem needs to distinguish four different cases, which is a challenge in comparison with the MVEE problem. We establish the theoretical results of the complexity and the core set size of the rank-two update algorithm for the WEOC problem, which are the generalizations of the currently best-known results for the MEB problem. In addition, by constructing an important inequality for the WEOC problem, we establish the linear convergence of this rank-two update algorithm. Numerical experiments show that the rank-two update algorithm is comparable to the Frank–Wolfe algorithm with away steps for the WEOC problem. In particular, the rank-two update algorithm is more efficient than the Frank–Wolfe algorithm with away steps for problem instances with $$m\gg n$$ under high precision.

Uneven Distribution of Primary and Middle Schools: A Case Study of Changchun, China

Providing further knowledge to and refinement of public facility location theory, this paper focuses on the distribution of basic educational facilities in China. The aim towards an equilibrium in the distribution of education resources has captured widespread attention in recent years. The basis of an education equilibrium is the balanced distribution of teaching facilities. Using the spatial analysis function of ArcGIS, this article discusses the evolution characteristics of education equilibrium and explores its dynamics with reference to primary and middle schools in Changchun City, Jilin Province from 2007 to 2013. The study found the spatial distribution of primary and middle schools in Changchun was uneven and the characteristic of close internal but sparse external has not changed. Low-level equilibrium of primary and middle schools in Changchun has been basically realized, but high-level equilibrium is far from being realized. Although there has been a trend towards suburbanization of these schools in recent years, the high entrance threshold has determined that high-quality school opportunity (schools with high-level resource allocation) has not increased for people. The spatial distribution of primary and middle schools is related to the factors of population, real estate, transportation and the education system itself. Education space, living space, and traffic space all interact and together affect urban spatial structure.

Analysis of the Location of Rescue Ambulance Dispatch Bases: A Case Study in Rio de Janeiro, Brazil

Emergency Medical Services are considered critical elements of modern health services, to assure the appropriate level of service to the population. We applied the facility location theory to indicate strategic points to establish ambulance dispatch centers to attend emergency calls. Therefore, the main objective of this paper is to promote an analysis of the locations of rescue ambulance bases in the city of Rio de Janeiro, focusing on reducing the response time of calls. We propose a mathematical model which aims at maximizing the number of people served by the ambulance dispatch bases and the different types of calls answered (general or calls related to traffic accidents), and minimizing the number of ambulance dispatch centers and the distances from demand points to centers. We used a real dataset from 2014 (approximately 105,000 emergency calls) to perform our evaluations. We concluded that two planning areas exist with potential to improve the service, and with the inclusion of 10 new dispatch bases in the areas with low coverage and only five new vehicles in the system, the number of attended people would increase by 6.4% in relation to the current situation (approximately 409,000 inhabitants served).

Event‐driven probabilistic topology management in sparse wireless sensor network

In a sparse wireless sensor network (WSN), event parameters such as event location and affected area cannot be directly estimated from the sensor observations, as the average distortion of sensor observations, because of the sparsity of network, is greater than in the dense ones. Moreover, observations of all the nodes which detect an event do not have the same significance in the estimation of event parameters. The authors propose a sensor collaboration scheme, named probabilistic event monitoring in sparse network (PEMS), which assists, in a distributed manner, the sensor nodes with significant observations to participate in the event monitoring process. The proposed collaboration scheme, PEMS, is based on the principle of Monte Carlo methods. Further, the event monitoring nodes restructure the network topology with the help of facility location theory for efficient energy management. Extensive simulations show that the event parameters with nominal distortion can be estimated from the observations transmitted by the PEMS-assisted event-monitoring nodes and those nodes can enhance their energy efficiency at the time of event monitoring.

Robust optimization approach to capacitated single and multiple allocation hub location problems

Hub location problem is one of the new emerging and prosperous areas in the classical facility location theory. As a part of the decision-making process, supply chain managers of organizations and companies must pay special attention to these issues. In strategic planning, decisions have long-term effects and program implementation will take a long time. Hence, in the decisions taken, uncertainty should be considered. Uncertainty can be regarded as a property of the system that describes the flaws of human knowledge about a system and its progress included. This paper considers single allocation and multiple allocation hub location problems (SAHLP and MAHLP). First, general models of capacitated single and multiple allocation hub location problems (CSAHLP and CMAHLP) are introduced, then a robust optimization approach is used for dealing with uncertain parameters. Finally, the uncertainty of parameters such as fixed setup cost and capacity of each hub on Iranian Aviation Dataset Karimi and Bashiri (Scientia Iranica 18:1571–1578, 2011) are studied and the results are presented. The results suggest that ignoring uncertainty in the supply chain network design sometimes causes large losses and expenses. In turn, these inflicted losses cause delay in the implementation phase in long-term expected plans and suspicion in all organizational activities.

Basic Approaches to a Location Theory of One Public Firm

Public firms are public economic units that take location decisions or are involved in such decisions. There is a lack of location theories that consider this feature. The literature on public facility location theory mainly concerns location of real capital serving economic units. Attempts to formulate a public firm decision-making oriented location theory are offered. Typical location factors of public firms relate to the goals of public firms, their environment and the number of decision-makers involved in the location decisions. A theory of the public firm is presented, that enables to develop a theory of location for public firms. It is introduced to industrial location theory and to location criteria based on investment rules. Its application in relation to public firms achieving welfare or public objectives is also covered. Interventions by the owner lead to more than one decision-maker and to principal agent models. Public firms compete horizontally due to competition among the public owners or public firms competing against each other. The authors mention some results on location choices within the framework of our basic approach.

LP-Based Approximation Algorithms for Reliable Resource Allocation

We initiate the study of the reliable resource allocation (RRA) problem. In this problem, we are given a set of sites ℱ each with an unconstrained number of facilities as resources. Every facility at site i ∈ ℱ has an opening cost and a service reliability pi. There is also a set of clients 𝒞 to be allocated to facilities. Every client j ∈ 𝒞 accesses a facility at i with a connection cost and reliability lij. In addition, every client j has a minimum reliability requirement (MRR) rj for accessing facilities. The objective of the problem is to decide the number of facilities to open at each site and connect these facilities to clients such that all clients’ MRRs are satisfied at a minimum total cost. The unconstrained fault-tolerant resource allocation problem studied in Liao and Shen [(2011) Unconstrained and Constrained Fault-Tolerant Resource Allocation. Proceedings of the 17th Annual International Conference on Computing and Combinatorics (COCOON), Dallas, Texas, USA, August 14–16, pp. 555–566. Springer, Berlin] is a special case of RRA. Both of these resource allocation problems are derived from the classical facility location theory. In this paper, for solving the general RRA problem, we develop two equivalent primal-dual algorithms where the second one is an acceleration of the first and runs in quasi-quadratic time. In the algorithm's ratio analysis, we first obtain a constant approximation factor of 2+2√2 and then a reduced ratio of 3.722 using a factor revealing program, when lij's are uniform on i (partially uniform) and rj's are uniform above the threshold reliability that a single access to a facility is able to provide. The analysis further elaborates and generalizes the inverse dual-fitting technique introduced in Xu and Shen [(2009) The Fault-Tolerant Facility Allocation Problem. Proceedings of the 20th International Symposium on Algorithms and Computation (ISAAC), Honolulu, HI, USA, December 16–18, pp. 689–698. Springer, Berlin]. Moreover, we formalize this technique for analyzing the minimum set cover problem. For a special case of RRA, where all rj's and lij's are uniform, we derive its approximation ratio through a novel reduction to the uncapacitated facility location problem. The reduction demonstrates some useful and generic linear programming techniques.

Improved Model for Strategic-Loading-Station Location Problem under Incomplete Information

In order to realize scientific planning the layout of strategic loading station, the strategic-loading –station location problem was proposed, which is related to determine the location of each stay with station and the transportation plan on the precise of satisfying the general location constraints and problem related special constraints. Based on theory of capacitated facility location with multiple souring in two stage supply chain, one mixed integer linear programming model was established which took whole logistic cost embedding transportation and location costs as objective. When confronted with small and medium size problem, this model could be exactly solved by optimization software using branch and bound algorithm, and when the problem size was big, this model could be heuristically solved by genetic algorithm which used 0-1 and priority-based combined encoding method to represent solution, cost-based and random-generated combined method to generate initial solution, solution repaired strategy and penalty method and special fitness function to deal illegal individual, and greedy based method to heuristically solve transshipment problem. At last, according to computational tests on randomly generated data demonstrated the practical feasibility of this method.

A credibility-based fuzzy location model with Hurwicz criteria for the design of distribution systems in B2C e-commerce

Facility location problem is one of the most critical elements in the design of distribution systems, and numerous studies have focused on this issue. However, facility location theory and guidelines for B2C firms are sparse. In this paper, with regard to the customer characteristics peculiar to B2C e-commerce and the turbulence of the competitive market, a new fuzzy location model is proposed to optimize the distribution system design in B2C e-commerce. The model adopts a hierarchical agglomerative clustering method to classify customers and estimate the fuzzy delivery cost. At the same time, due to the turbulence of competitive market, both market supply and customer demand are treated as fuzzy variables in the model. Afterward, the credibility measure and Hurwicz criterion are introduced to convert the model into a crisp one which has NP-hard complexity. In order to solve the crisp model, an improved genetic algorithm with particle swarm optimization is developed. Finally, the computational results of some numerical examples are used to illustrate the application and performance of the proposed model and algorithm.

Median Problems in Networks

The P-median problem is a classical location model “par excellence”. In this paper we, first examine the early origins of the problem, formulated independently by Louis Hakimi and Charles ReVelle, two of the fathers of the burgeoning multidisciplinary field of research known today as Facility Location Theory and Modelling. We then examine some of the traditional heuristic and exact methods developed to solve the problem. In the third section we analyze the impact of the model in the field. We end the paper by proposing new lines of research related to such a classical problem.

A NEW CLUSTERING MODEL OF WIRELESS SENSOR NETWORKS USING FACILITY LOCATION THEORY

In this paper, we study mathematical formulations for clustering problems which arise in wireless sensor networks as examined from the standpoint of facility location theory. Following facility location theory, LEACH-C, one of the principal studies on cluster-based network organizations, formulates the clustering problem as a p-median problem. In this paper, we examine some drawbacks to the formulation put forward in LEACH-C. We then formulate the problem as an uncapacitated facility location problem to overcome these drawbacks. Computational experiments show that compared to LEACH-C, the proposed algorithm based on our formulation can extend the total lifetime of sensor networks.

A LOCATION MODEL FOR THE ALLOCATION OF THE OFF-STREET PARKING FACILITIES

In this study, an application of the location theory on the allocation of the off-street parking facilities is explored. A multi-objective linear Integer Programming model is developed for this problem. Due to its linearity, the proposed compromise programming method for the model can be solved by the LINDO compute software. Based on the results of the numerical experiment, the proposed model can provide reasonable solution to the problem addressed. The following information can be provided by the proposed solution procedure for the decision makers to determine the locations of the off-street parking facilities: the optimal locations of facilities, the demands served by each facility, and the optimal type for each of the selected parking facilities. With the rapid increase in the car ownership per household and the urban population, in the newly developed industrial country, the mass use of the private car in the metropolitan area results in a serious parking problem with limited land resource. The more the city is urbanized, the more serious the parking situation is for the city. To develop an effective procedure to allocate appropriate space for the parking facility is a crucial task for the urban planner and the associated traffic agencies. With the scarce land resource in the urban area, the use the non-parking public facilities as the potential candidates of the parking facilities is a promising alternative for the metropolitan decision maker. With the relative high land cost in the urban area, it will be a waste for the public investment, if the public facilities do not used for multiple purposes. The use of the existing public facility as a parking facility, it will not only reduce the public resistance for buying their land, but also decrease the additional investment for the land cost. Therefore, the purpose of this study is to develop an efficient procedure to allocate the off-street parking facilities in the existing public facilities as the reference basis for the decision making process. In the current parking practice, the allocation of the off-street parking facilities is often based on the ratio between forecast parking demand and supply. The facility location theory has seldom been applied to this type of problem. In this study, we explore the application of the facility location theory on the off-street parking facility locations. A suitable location model is developed to deal with the allocation of the public off-street parking facilities. In the previous studies dealt with the parking problem, Kanafani (1972) treated the behavior of the parking system as a distribution process. He developed a gravity-type model to forecast the potential parking demand for each parking facility. The allocation of the parking facility is

Statistical location detection with sensor networks

The paper develops a systematic framework for designing a stochastic location detection system with associated performance guarantees using a wireless sensor network. To detect the location of a mobile sensor, the system relies on RF-characteristics of the signal transmitted by the mobile sensor, as it is received by stationary sensors (clusterheads). Location detection is posed as a hypothesis testing problem over a discretized space. Large deviations results enable the characterization of the probability of error leading to a placement problem that maximizes an information-theoretic distance (Chernoff distance) among all pairs of probability distributions of observations conditional on the sensor locations. The placement problem is shown to be NP-hard and is formulated as a linear integer programming problem; yet, large instances can be solved efficiently by leveraging special-purpose algorithms from the theory of discrete facility location. The resultant optimal placement is shown to provide asymptotic guarantees on the probability of error in location detection under quite general conditions by minimizing an upper bound of the error-exponent. Numerical results show that the proposed framework is computationally feasible and the resultant clusterhead placement performs near-optimal even with a small number of observation samples in a simulation environment.

The 2-Center Problem with Obstacles

Given a set S of n points in the plane and a set O of pairwise disjoint simple polygons with a total of m edges, we wish to find two congruent disks of smallest radius whose union covers S and whose centers lie outside the polygons in O (referred to as locational constraints in facility location theory). We present an algorithm to solve this problem in randomized expected time O(m log2(mn)+mn log2n log(mn)). We also present an efficient approximation scheme that constructs, for a given ε>0, two disks as above of radius at most (1+ε)r*, where r* is the optimal radius, in time O(1/ε log(1/ε)(m log2m+n log2n)) or in randomized expected time O(1/ε log(1/ε)((m+n log n) log(mn))).

Optimization of the Norm of a Vector-Valued DC Function and Applications

In this paper, we show that a DC representation can be obtained explicitly for the composition of a gauge with a DC mapping, so that the optimization of certain functions involving terms of this kind can be made by using standard DC optimization techniques. Applications to facility location theory and multiple-criteria decision making are presented.

Reconsidering the legacy of urban public facility location theory in human geography

In 1968, Michael Teitz initiated a new locational theory, focusing on how best to locate urban public facilities given the need to balance efficiency and equity. This locational problematic would evolve into a coherent set of geographical concepts steeped in normative, neoclassical and quantitative assumptions. Building on Teitz's original formulations, quantitative geographers and regional scientists focused on operationalizing efficiency and equity concerns according to distance, pattern, accessibility, impacts and externalities. The legacy of these concepts in human geography, however, has not been systematically traced. While both reflecting and bolstering wider stances in welfare, urban and behavioral geography during the quantitative era, the legacy of urban public facility theory in the postquantitative era is decidedly uneven. On the one hand, the legacy was effectively refuted by situating location theory within a much broader political, economic and social matrix. Adopting a more conflictual framework, geographers shifted the focus of locational theory to larger questions of how costs and benefits are spatially distributed in urban society. On the other hand, the legacy was sustained by retaining the normative interest in balancing equity with efficiency within a model-building paradigm, while jettisoning the reliance on neoclassical economics and universalistic assumptions for more nuanced, socially embedded accounts. In this sense, the legacy of urban public facility location theory emerges as a nested sequence of normative models that grew increasingly sophisticated, inclusive and contextualized over time. The rise of the nonprofit and privatized sectors, however, threatens to erode the existence of a distinctly public facility location theory.

Application of facility location theory to groundwater remediation

A facility location method developed in this paper derives efficient pumping-well configurations for removing plumes of contaminated groundwater. The method incorporates a modified version of the Location Set Covering Model (LSCM), with a direction-dependent distance threshold, and the theoretical time-dependent capture zone of an extraction well. The objective of the model formulation is to find the locations of the minimum number of wells that capture a plume of known geometry within a specified period of time. A numerical particle tracking scheme is used to verify capture for LSCM-derived pumping-well configurations. The development of stagnation points or local zones of low velocity generally precludes complete contaminant plume removal (that is, a 100 per cent capture efficiency) within a specified time horizon. However, capture efficiency can be improved by an iterative procedure in which the LSCM is constrained to include wells within uncaptured areas identified through particle tracking for a previous solution. A removal efficiency of 90 per cent was attained in an application of the approach. The approach is not difficult to implement, and the formulated integer programming model can be solved with the branch-and-bound method.

A unifying location model on tree graphs based on submodularity properties

Let F be the collection of nonempty subtrees of a given tree T . Each subtree is viewed as a potential facility. Let ƒ be a real objective function defined on F . The facility location model we consider is to select a subtree minimizing f . This model unifies and generalizes several facility location problems discussed in the literature. We prove that the most common objective functions used in facility location theory possess the submodularity property. In particular, the ellipsoid approach provides a unified framework for polynomial solvability.

A location modeling approach for groundwater monitoring network augmentation

A heuristic approach based on facility location theory effectively augments groundwater quality monitoring configurations through the strategic siting of additional wells. The approach is an alternative to variance‐based schemes previously established for the augmentation problem. The method developed herein is practical in that it (1) is relatively easily understood, (2) is not difficult to implement and solve, and (3) does not require a large number of preexisting observation points. The approach has been applied to a case study involving a landfill‐contaminated buried valley aquifer in southwest Ohio. Configurations derived by the heuristic approach exhibit two key characteristics: (1) location of wells near areas of high estimated contaminant concentration and (2) interwell separation distances that facilitate areal plume coverage.