Single Facility Location Problem Research Articles

Reviewing extensions and solution methods of the planar Weber single facility location problem

One of the classic foundational constructs of Location Science was proposed by Alfred Weber in 1909. His construct involved finding the location for a single production facility which minimized the sum of weighted distances of transporting the needed raw materials from localized sources along with the sum of weighted distances in delivering the final product to one or more markets.The first objective of this paper is to review the major advancements in this simple classic single facility location problem and its variations. One can find in the literature a very large number of algorithms to solve the standard Weber problem. Some are iterative and others are finite even for geometric Euclidean and rectilinear spaces. Moreover, some schemes are efficient (theoretically) and others are practically quite fast.The second goal of this paper is to show that many extensions of the standard Weber problem can be solved by solving a polynomial number of standard Weber problems. This unifying result implies, in particular, that all these extensions are polynomially solvable since the standard Weber problem can be solved in polynomial time. In addition, with this unifying approach we solve some important planar non-convex Euclidean location problems in polynomial time.

A hybrid iterated local search matheuristic for large-scale single source capacitated facility location problems

A hybrid iterated local search matheuristic for large-scale single source capacitated facility location problems

Solving a minisum single facility location problem in three regions with different norms

Solving a minisum single facility location problem in three regions with different norms

A row generation method for the inverse continuous facility location problems

In the most single facility location problems, a set of points is given and the goal is to find the optimal location of a new facility with respect to given criteria such as minimizing time, cost, and distances between the clients and facilities. On the other side, the inverse single facility location problems try to modify the parameters of the problem with the minimum cost such that a given point becomes optimal. In this paper, we introduce a novel algorithm for the general case of the inverse single facility location problem with variable weights in the plane. The optimality conditions of the algorithm are presented. Then in the special cases the inverse minisum and minimax single facility location problems are considered and the algorithm is tested on some instances. The results indicate the efficiency of the algorithm on these instances.

Globally Optimal Facility Locations for Continuous-Space Facility Location Problems

The continuous-space single- and multi-facility location problem has attracted much attention in previous studies. This study focuses on determining the globally optimal facility locations for two- and higher-dimensional continuous-space facility location problems when the Manhattan distance is considered. Before we propose the exact method, we start with the continuous-space single-facility location problem and obtain the global minimizer for the problem using a statistical approach. Then, an exact method is developed to determine the globally optimal solution for the two- and higher-dimensional continuous-space facility location problem, which is different from the previous clustering algorithms. Based on the newly investigated properties of the minimizer, we extend it to multi-facility problems and transfer the continuous-space facility location problem to the discrete-space location problem. To illustrate the effectiveness and efficiency of the proposed method, several instances from a benchmark are provided to compare the performances of different methods, which illustrates the superiority of the proposed exact method in the decision-making of the continuous-space facility location problems.

A dual RAMP algorithm for single source capacitated facility location problems

A dual RAMP algorithm for single source capacitated facility location problems

Optimal planar facility location with dense demands along a curve

This paper studies a multi-facility location problem with demand distributed continuously along a curve (MFLCD) in a planar space. We first model a single facility location problem in this setting. When the curve is approximated by a collection of line segments, an exact algorithm is proposed to solve the problem. Then we extend the model to the multi-facility case and propose an “alternate location and allocation” (ALA) based algorithm. Extensive computational experiments are conducted to justify the proposed models and algorithms. We show that using the proposed model to deal with continuous demand directly is much more effective than using other models with discrete demand generated by demand aggregation. As a by-product, some sufficient conditions that ensure an error-free demand aggregation from continuous demand to discrete demand are provided. Computational results are in support of the solution quality and computational efficiency of the proposed ALA-based algorithm for solving MFLCD problems. Our sensitivity analysis also offers some insights and suggestions.

Facilities Layout and Location Analysis based on Police Department Position in Dekalb, IL

The officers of Dekalb Police Department were aware of the high crime rate and they’re considering whether set up a new office or relocate the existing department to shorten the distance, also, ensure to reach the crime scene in super speedy. To select a more reasonable location, an essential assumption is that the current office will no longer associated with. Besides the existed office, geo-policing is not a necessary factor neither. Therefore, the police officers will work from the new location that we inferred and answer the incoming calls there. First thing first is to model it as a single facility location problem, and then, calculate by the Minisum model with rectangular distances as well as the Minimax model with tchebychev distances.

Lower and upper bounds for the continuous single facility location problem in the presence of a forbidden region and travel barrier

In this paper, we investigate FRB, which is the single facility Euclidean location problem in the presence of a (non-)convex polygonal forbidden region where travel and location are not permitted. We search for a new facility’s location that minimizes the weighted Euclidean distances to existing ones. To overcome the non-convexity and non-differentiability of the problem’s objective function, we propose an equivalent reformulation (RFRB) whose objective is linear. Using RFRB, we limit the search space to regions of a set of non-overlapping candidate domains that may contain the optimum; thus we reduce RFRB to a finite series of tight mixed integer convex programming sub-problems. Each sub-problem has a linear objective function and both linear and quadratic constraints that are defined on a candidate domain. Based on these sub-problems, we propose an efficient bounding-based algorithm (BA) that converges to a (near-)optimum. Within BA, we use two lower and four upper bounds for the solution value of FRB. The two lower and two upper bounds are solution values of relaxations of the restricted problem. The third upper bound is the near-optimum of a nested partitioning heuristic. The fourth upper bound is the outcome of a divide and conquer technique that solves a smooth sub-problem for each sub-region. We reveal via our computational investigation that BA matches an existing upper bound and improves two more.

Inverse single facility location problem on a tree with balancing on the distance of server to clients

<p style='text-indent:20px;'>We introduce a case of inverse single facility location problem on a tree where by minimum modifying in the length of edges, the difference of distances between the farthest and nearest clients to a given facility is minimized. Two cases are considered: bounded and unbounded nonnegative edge lengths. In the unbounded case, we show the problem can be reduced to solve the problem on a star graph. Then an <inline-formula><tex-math id="M1">\begin{document}$ O(nlogn) $\end{document}</tex-math></inline-formula> algorithm is developed to find the optimal solution. For the bounded edge lengths case an algorithm with time complexity <inline-formula><tex-math id="M2">\begin{document}$ O(n^2) $\end{document}</tex-math></inline-formula> is presented.</p>

Solving Multiple Distribution Center Location Allocation Problem Using K-Means Algorithm and Center of Gravity Method Take Jinjiang District of Chengdu as an example

In the logistics system, logistics nodes play an important role. The centre-of-gravity method is one of the most basic methods in solving the problem of single facility location. The thesis first uses the K-means clustering algorithm to divide the demand points into k clusters, and the k value is selected by the elbow method. Then, the k clusters are regarded as a single facility location problem and analyzed by the center of gravity method. In practical applications, the discrete model analysis can be cited to further obtain the optimal solution.

Computational aspects of the inverse single facility location problem on trees under lk-norm

We consider in this paper the inverse versions of the two popular problems in location theory, say the 1-median and the 1-center problems on trees. The cost for modifying vertex weights is measured under lk-norm for a positive integer k and hence the cost function is nonlinear. For the inverse 1-median problem, we develop a linear time algorithm based on the optimal solution of the induced unconstrained problem. For the inverse 1-center problem, we prove that the problem can be decomposed into linearly many subproblems and the objective function in each subproblem is piecewise-convex. Furthermore, we also discuss an O(nlog⁡n) time algorithm for the inverse 1-center problem under l2-norm based on the convexity of the cost function of each subproblem.

Optimal algorithms for weighted 1-center problem in deterministic and stochastic tree networks

This paper deals with two single facility location problems. The first problem is about the deterministic weighted (DW) 1-center of a deterministic tree network (DTN). The optimality criterion for the DW 1-center is minimizing the weighted distance to the furthest node from the facility. This problem has many applications in the emergency field since it gives satisfactory results for the customers sited at the furthest node of the DTN. The second problem is about the stochastic weighted (SW) 1-center of the stochastic tree network (STN). The criterion for optimality used in the SW 1-center is maximizing the minimum weighted reliability from the nodes of the STN to the facility. The applications of the SW 1-center problem appear in computer and communication fields. Two linear-time algorithms are presented for both problems.

FUZZY LOCATION PROBLEMS WITH TRIANGULAR NORM : EXISTENCE AND STABILITY

A fuzzy max-T location problem is considered. The fuzzy max-T location problem is a generalization of a fuzzy maximin location problem by allowing in the objective function arbitrary triangular norms instead of the triangular norm defined by the minimum operation. Then we give conditions for the existence of its optimal solutions, and derive a relationship between its optimal solutions and efficient solutions of a fuzzy multicriteria location problem. Furthermore, we give some properties of triangular norms, and for triangular norms, we investigate the stability of optimal solutions of the fuzzy max-T location problem. 1 Introduction and preliminaries In a general continuous location model, finitely many points called demand points in R n , modeling existing facilities or customers, are given. Let di ∈ R n , i =1 , 2, ··· , � (≥ 2) be demand points. We put I ≡{ 1, 2, ··· , � }. Then a problem to locate a new facility in R n is called a single facility location problem. If one prefers the location of the facility near demand points, then the problem is formulated as follows: (1) min x∈Rn f (γ1(x − d1) ,γ 2(x − d2), ··· ,γ � (x − d� ))

Single facility siting involving allocation decisions

Single facility siting is often viewed as the most basic of location planning problems. It has been approached by many researchers, across a range of disciplines, and has a rich and distinguished history. Much of this interest reflects the general utility of single facility siting, but also the mathematical and computational advancements that have been made over past decades to support better decision making. This paper discusses a recently rediscovered form of Weber's classic single facility location problem that is both important and relevant in contemporary planning and decision making. This form of the Weber problem involves locating a production plant where there are multiple sources of each needed raw material (input) distributed throughout a region. This means that the selection of a given raw material source may vary depending on the plant location. In essence, this makes the problem non-convex, even when locating only one production plant. We review elements of the Weber problem that have been addressed in the literature along with proposed solution techniques. In doing so, we highlight elements of the problem originally noted by Weber, but to date have not been operationalized in practice––allocation selection among multiple sources of given raw material inputs. A problem formulation involving allocation decisions for this generalization is derived and an optimal solution approach is developed. Application results demonstrate the significance of addressing important planning characteristics and the associated nuances that result.

A novel facility location problem for taxi hailing platforms

PurposeMotivated by a problem in the context of DiDi Travel, the biggest taxi hailing platform in China, the purpose of this paper is to propose a novel facility location problem, specifically, the single source capacitated facility location problem with regional demand and time constraints, to help improve overall transportation efficiency and cost.Design/methodology/approachThis study develops a mathematical programming model, considering regional demand and time constraints. A novel two-stage neighborhood search heuristic algorithm is proposed and applied to solve instances based on data sets published by DiDi Travel.FindingsThe results of this study show that the model is adequate since new characteristics of demand can be deduced from large vehicle trajectory data sets. The proposed algorithm is effective and efficient on small and medium as well as large instances. The research also solves and presents a real instance in the urban area of Chengdu, China, with up to 30 facilities and demand deduced from 16m taxi trajectory data records covering around 16,000 drivers.Research limitations/implicationsThis study examines an offline and single-period case of the problem. It does not consider multi-period or online cases with uncertainties, where decision makers need to dynamically remove out-of-service stations and add other stations to the selected group.Originality/valuePrior studies have been quite limited. They have not yet considered demand in the form of vehicle trajectory data in facility location problems. This study takes into account new characteristics of demand, regional and time constrained, and proposes a new variant and its solution approach.

A cover based competitive facility location model with continuous demand

AbstractIn this paper we propose and solve a competitive facility location model when demand is continuously distributed in an area and each facility attracts customers within a given distance. This distance is a measure of the facility's attractiveness level which may be different for different facilities. The market share captured by each facility is calculated by two numerical integration methods. These approaches can be used for evaluating functional values in other operations research models as well. The single facility location problem is optimally solved by the big triangle small triangle global optimization algorithm and the multiple facility problem is heuristically solved by the Nelder‐Mead algorithm. Extensive computational experiments demonstrate the effectiveness of the solution approaches.

The incorporation of fixed cost and multilevel capacities into the discrete and continuous single source capacitated facility location problem

In this study we investigate the single source location problem with the presence of several possible capacities and the opening (fixed) cost of a facility that is depended on the capacity used and the area where the facility is located. Mathematical models of the problem for both the discrete and the continuous cases using the Rectilinear and Euclidean distances are produced. Our aim is to find the optimal number of open facilities, their corresponding locations, and their respective capacities alongside the assignment of the customers to the open facilities in order to minimise the total fixed and transportation costs. For relatively large problems, two solution methods are proposed namely an iterative matheuristic approach and VNS-based matheuristic technique. Dataset from the literature is adapted to assess our proposed methods. To assess the performance of the proposed solution methods, the exact method is first applied to small size instances where optimal solutions can be identified or lower and upper bounds can be recorded. Results obtained by the proposed solution methods are also reported for the larger instances.

Single-facility location problems in two regions with ℓ1- and ℓq-norms separated by a straight line

In this paper, Fermat–Weber location problems with demand points located in two regions Ω1 and Ωq separated by a straight line, are addressed. Ω1 and Ωq are, respectively, endowed by different norms ℓ1 and ℓq, with q > 1. In order to compute distances between points in different regions, the concept of Gate point is applied.With the aim of solving the problem, a new algorithm, called Gate(1, q), is designed. This algorithm uses the characterization of the solutions in the regions Ω1 and Ωq, and the straight line.A comparative study with other well-known algorithms is carried out in order to test the performance of the proposed algorithm. The results are promising since they show that the Gate(1, q) algorithm leads to a more accurate solution than those of the other algorithms in a relatively short computing time.

Improved complexity results for the robust mean absolute deviation problem on networks with linear vertex weights

In a recent paper Lopez-de-los-Mozos et al. (2013), an algorithmic approach was presented for the robust (minmax regret) absolute deviation single-facility location problem on networks with node weights which are linear functions of an uncertain or dynamically changing parameter. The problem combines the mean absolute deviation criterion, which is the weighted average of the absolute deviations of individual customer–facility distances from the mean customer–facility distance and is one of the standard measures of “inequality” between the customers, with the minmax regret approach to optimization under uncertainty. The uncertain data are node weights (demands) which are assumed to change in a correlated manner being linear functions of a single uncertain parameter. The analysis in Lopez-de-los-Mozos et al. (2013) presented complexity bounds that are polynomial but too high to be of practical value. In this note, we present improvements of the analysis that significantly reduce the computational complexity bounds for the algorithm.