Optimal facility location problem on polyhedral terrains using descending paths

We describe algorithms for optimal single facility location problems with forbidden regions and barriers to travel. The former are those where location is not permitted, but one can travel through them, e.g., a lake. The latter are the regions where neither location nor travel is permitted, e.g., large parks in a city. Using the convexity properties of the objective function, in the first case, we develop an algorithm for finding the optimal solution. The objective function in the barrier case is shown to be non-convex. We use the concept of visibility to create a network with the location point as the source and use Dijkstra's algorithm to compute the shortest distance to all the other demand points. Using simulated annealing we find an approximate optimal solution. Numerical examples illustrate the implementation of the algorithms.

Cloud computing has emerged as a buzzword of IT-enabled business services. It makes business sense to choose an optimal location for setting up the cloud service facilities such as data centres. The distribution of services between data centre facilities and clients of a cloud can be devised mathematically as the well-known facility location problem (FLP). The decisions of location of data centres are a vital element in strategic planning for a wide range of cloud service providers. In this paper, we have applied facility location techniques in operations management for evaluating the available potential locations and zero down to the best optimal facility location, which can be used to minimise the cost associated with setting up of data centre facilities. A case study is also presented applying FLP in Indian cloud computing scenario. By using these techniques, one can ensure desired QoS and optimum use of data centre facilities.

Set Covering model determines the location of facilities that can be used that minimize the cost of assigning facilities to the point of request with the limitation that each facility was used for a number points of request. If there is an imbalance between the volume of demand points and the capacity of the facilities, it is necessary to open/closed facilities. In fact, facility location problem can extended for the decision not only open/closed but rezising area the existing facilities that can be adjusted considering the avaibility area of facilities location and demand points. This case has not been accommodated on the basic model of set covering. Not all the existing facilities can be resized. Rezising the area of facility location was assumed discrete. The aims of this study was optimized the alghorithm of set covering model. The solution this study was devided into two stages. The first stage was screening facilities that can be resized with survey location. The second stage was set covering model which the facilities will be close/opened and resize the existing facilities.

A globally convergent algorithm for facility location on a sphere

A quadtree-based allocation method for a class of large discrete Euclidean location problems

Facility location selection is a vital decision for companies that affects both cost and delivery time over the years. However, determination of the facility location is a NP-hard problem. A hybrid algorithm that combines revised weighted fuzzy c-means with Nelder Mead (RWFCM-NM) performs well when compared with well-known algorithms for the facility location problem (FLP) with deterministic customer demands and positions. The motivation of the study is both analyzing performance of the RWFCM-NM algorithm with probabilistic customer demands and positions and proposing a new approach for this problem. This paper develops two new algorithms for FLP when customer demands and positions are probabilistic. The proposed algorithms are a probabilistic fuzzy c-means algorithm and Nelder-Mead (Probabilistic FCM-NM), a probabilistic revised weighted fuzzy c-means algorithm and Nelder Mead (Probabilistic RWFCM-NM) for the un-capacitated planar multi-facility location problem when customer positions and customer demands are probabilistic with predetermined service level. Proposed algorithms performances were tested with 13 data sets and comparisons were made with four well known algorithms. According to the experimental results, probabilistic RWFCM-NM algorithm demonstrates superiority on compared algorithms in terms of total transportation costs.

The sample average approximation (SAA) approach is a widely used technique, based on Monte‐Carlo simulation, often applied to large‐scale stochastic optimization problems. In this approach, a set of sample average problems with multiple copies of sampled scenarios are generated and solved exactly. In other words, there is an implicit assumption that the sample average problems are solvable to optimality. In some instances, however, the sample average problems might be NP‐hard problems, often difficult or impractical to solve to optimality. In this article, we broaden the scope of the SAA approach and show that even without solving the sample problems to optimality, by combining a heuristic and a lower bounding approach, high‐quality solutions with tight confidence bounds on the optimal solution value can be obtained. We demonstrate this “inexact SAA approach” on two problems. First, we apply it to the Stochastic Connected Facility Location (SConFL) problem, the motivating application for this article, that arises in the design of telecommunications networks. As an additional application, we also use it for the Stochastic Uncapacitated Facility Location (SUFL) problem. Our computational results demonstrate the effectiveness of the inexact SAA approach. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 70(1), 19–33 2017

Dispersed starting solutions in facility location: The case of the planar [formula omitted]-median problem

The authors present in this work a proposal that allows establishing the relationships between the facilities location problem and the client allocation within a dense demand environment in territorial design. This proposal can be seen as a basic methodology to give support to the decision making. The use of this application lets one know the production facilities location, warehouses or distribution centers in a geographical space division. On the other hand, solving the client's dense demand for goods or services, means finding the location of facilities in a populated geographic territory, where the population has a demand for services in a constant basis. Finding the location is obtaining the decimal geographical coordinates in longitude, latitude where the facility is located, such that the product or service transport costs the least. The implications and practical benefits of the results from this work allow an organization to be able to design an efficient logistics plan in benefit of its supply chain. The problem the authors present is a territorial design and optimization one due to the fact that the required territorial partition demands the creation of compact zones where the minimum distance between the geographical objects is implicitly optimized. This problem belongs to the NP-hard class, where the use of a metaheuristic to attain approximated solutions becomes a necessity, Variable Neighborhood Search was chosen because it achieves good solutions for this kind of problems. Once the territory has been partitioned into k zones where the centroid of each zone is the distribution center, as a first step the authors proceed to apply the dense demand with continuous functions and this is the main original contribution of this paper: Finding the location of facilities inside a territory where the population has a dense demand for services. The location obtained means having available the decimal geographic coordinates in longitude and latitude from the location point in such a way that the products or services transfer has a minimum cost. Finally the Weber function is minimized, which weights are a function that represents the population's demand in every territory, multiplied by the Euclidean distance between the potential location points and demand points.

We consider a network facility location problem with unbounded production levels. This problem is NP-hard in the general case and is known to have an optimal solution with quadratic complexity on a tree network. We study the case of a network representable by an outerplanar graph, i.e., by a graph whose vertices belong to one (outer) face. This problem is known to have an optimal algorithm with time complexity O(nm3), where n is the number of vertices and m is the number of possible facility locations. Using some properties of outerplanar graphs (binary 2-trees) and the existence of an optimal solution with a family of centrally connected service areas, we obtain recurrence relations for the construction of an optimal algorithm with time complexity that is smaller by a factor of \(\sqrt m \) than the time complexity of the earlier algorithm.

This paper considers the problem of locating a path-shaped facility of a specific size on a weighted tree network. The criterion for optimality used in this paper is the minimax criterion in which the weighted distance to the farthest vertex from the facility is minimised. The minimax criterion gives acceptable results from the point of view of the fast response for the clients who are located far away from the facility. This location problem usually has applications in computer science, information science, and operations research. An O(n) time algorithm is proposed for finding the optimal location of a path-shaped facility of a bounded length on a weighted tree network, where n is the number of vertices in the tree.

The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. Often, both in the case of public facilities (such as libraries, municipal swimming pools, fire stations,....) and private facilities (such as distribution centers, switching stations, ....), we may want to find a 'fair' allocation of the total cost to the customers-this is known as the cost allocation problem. A central question in cooperative game theory is whether the total cost can be allocated to the customers such that no coalition of customers has any incentive to build their own facility or to ask a competitor to service them. We establish strong connections between fair cost allocations and linear programming relaxations for several variants of the facility location problem. In particular, we show that a fair cost allocation exists if and only if there is no integrality gap for a corresponding linear programming relaxation; this was only known for the simplest unconstrained variant of the facility location problem. Moreover, we introduce a subtle variant of randomized rounding and derive new proofs for the existence of fair cost allocations for several classes of instances. We also show that it is in general NP-complete to decide whether a fair cost allocation exists and whether a given allocation is fair.

Recently, the magnitude and frequency of the natural disaster have been increased, the damage has become severer. The importance of disaster response system to relieve the damage has arised continuously. This study has tried to develop the algorithm to solve the facility location and size problem in emergency logistics. A facility in the emergency logistics has various roles in victim care, casualty treatment, relief resource management and relief vehicle assistance. Moreover, the location of facility in emergency logistics has to consider the safety and reliability. To gather these information, information management system with IoT sensors are suggested. The location problem in this study also covers various features to response various demands in disaster. To solve this problem, this study suggested MIP based algorithm. Scenario based simulation experiments are conducted to verify the performance suggested algorithm.

A systematic technique to bound factor-revealing linear programs is presented. We show how to derive a family of upper bound factor-revealing programs (UPFRP), and show that each such program can be solved by a computer to bound the approximation factor of an associated algorithm. Obtaining an UPFRP is straightforward, and can be used as an alternative to analytical proofs, that are usually very long and tedious. We apply this technique to the metric facility location problem (MFLP) and to a generalization where the distance function is a squared metric. We call this generalization the squared metric facility location problem (SMFLP), and prove that there is no approximation factor better than $$2.04$$2.04, assuming $$\mathrm{P} \ne \mathrm{NP} $$P?NP. Then, we analyze the best known algorithms for the MFLP based on primal-dual and LP-rounding techniques when they are applied to the SMFLP. We prove very tight bounds for these algorithms, and show that the LP-rounding algorithm achieves a ratio of $$2.04$$2.04, and therefore has the best possible factor for the SMFLP. We use UPFRPs in the dual-fitting analysis of the primal-dual algorithms for both the SMFLP and the MFLP, improving some of the previous analysis for the MFLP.

This paper is divided into two parts. In the first part of this paper, we present a 2-approximation algorithm for the soft-capacitated facility location problem. This achieves the integrality gap of the natural LP relaxation of the problem. The algorithm is based on an improved analysis of an algorithm for the linear facility location problem, and a bifactor approximate-reduction from this problem to the soft-capacitated facility location problem. We will define and use the concept of bifactor approximate reductions to improve the approximation factor of several other variants of the facility location problem. In the second part of the paper, we present an alternative analysis of the authors’ 1.52-approximation algorithm for the uncapacitated facility location problem, using a single factor-revealing LP. This answers an open question of [16]Furthermore, this analysis, combined with a recent result of Thorup [21] shows that our algorithm can be implemented in quasi-linear time, achieving the best known approximation factor in the best possible running time.KeywordsApproximation AlgorithmFacility LocationFacility Location ProblemApproximation FactorFacility CostThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.