Facility Location Problem Research Articles

A multi-objective optimization model for a multi-period mobile facility location problem with environmental and disruption considerations.

The present work addresses a multi-period facility location decision during crisis—Pandemic—situation with highly uncertain demand. Our paper identifies failing distribution centres (DCs) over several periods of time and decides about relocation. Several scenarios arise: DCs can be opened, displaced from one location to another, closed or even reopened during a certain time, using mobile facility. We recommend a multi-objective non-linear mixed-integer mathematical model that identifies, for each period, the best possible location for DCs and their allocation to customers. Our model analyses the trade-off between economic costs and CO_2 emissions generated by facilities operations. We suggest a multi-objective approach based on a Non-dominated Sorting Genetic Algorithm II (NSGA-II). Our simulations demonstrate how mobile facility should be managed to ensure a good balance between economic and environmental criteria.

An improved genetic algorithm with local refinement for solving hierarchical single-allocation hub median facility location problem

An improved genetic algorithm with local refinement for solving hierarchical single-allocation hub median facility location problem

A congested capacitated location problem with continuous network demand

This paper presents a multi-objective mixed-integer non-linear programming model for a congested multiple-server discrete facility location problem with uniformly distributed demands along the network edges. Regarding the capacity of each facility and the maximum waiting time threshold, the developed model aims to determine the number and locations of established facilities along with their corresponding number of assigned servers such that the traveling distance, the waiting time, the total cost, and the number of lost sales (uncovered customers) are minimized simultaneously. Also, this paper proposes modified versions of some of the existing heuristics and metaheuristic algorithms currently used to solve NP-hard location problems. Here, the memetic algorithm along with its modified version called the stochastic memetic algorithm, as well as the modified add and modified drop heuristics are used as the solution methods. Computational results and comparisons demonstrate that although the results obtained from the developed stochastic memetic algorithm are slightly better, the applied memetic algorithm could be considered as the most efficient approach in finding reasonable solutions with less required CPU times.

Obnoxious facility location in multiple dimensional space

Obnoxious facility location in multiple dimensional space

A note on LP-based approximation algorithms for capacitated facility location problem

In the capacitated facility location problem, we are given a set F of potential facilities and a set D of clients, where each facility has a capacity and an open cost, and each client has a demand to be served by the facilities with service costs. The goal is to open some facilities in F and assign all clients in D to these open facilities such that the total cost is minimum. Based on the natural integer programming formulation, Levi et al. [8] presented an LP-based 5-approximation algorithm for this problem under the assumption that the facility costs are uniform. Based on the same integer programming formulation, we remove the uniformity assumption and present an (R+R2+8R2+3)-approximation algorithm for the capacitated facility location problem, where R is the upper bound of the ratio between facility costs. Our result is a slight extension of the corresponding result in [8], as when R=1 the worst-case ratio of our algorithm is R+R2+8R2+3=5.

Employing an Effective Robust Optimization Approach for Cooperative Covering Facility Location Problem under Demand Uncertainty

The traditional covering problem has two assumptions: “all or nothing coverage” and “individual coverage”. There are settings where the two assumptions may be unrealistic. In this research, we relax the two assumptions and study the cooperative covering facility location problem with demand uncertainty. Previous research on the covering problem has not considered cooperative covering under uncertain demand, particularly our approach to effectiveness maximization and offering full control of the conservatism of the model. We propose a cooperative covering model to maximize effectiveness, including the quality per dollar as a criterion. Then, the demand at each node is assumed to be uncertain, and the robust counterparts of the deterministic model are presented by considering the different degrees of conservatism of the robust solution. More importantly, the non-linear programming is transformed into equivalent linear programming by introducing auxiliary variables and using duality theory. The numerical examples show that the optimal location of the facility is affected by the protection level and the decision maker can make a trade-off between conservatism and effectiveness in an uncertain environment. Moreover, when the protection level is large, the objective function value makes a smaller sacrifice to get high robustness. In addition, two ways to measure the price of robustness are defined. The facility location decision can be made by evaluating the relative decrease in effectiveness compared to the nominal demand model or by evaluating the relative increase in effectiveness compared to the complete protection model.

Service interruption and customer withdrawal in the congested facility location problem

This research addresses the location problem of congested facilities, assuming service interruptions and customer withdrawals. Service interruptions can occur as a result of events such as machine failures, power outages, and communication system disconnections. As long as no interruption occurs, each facility functions as a M/M/1 queuing system. Upon an interruption, the server stops working, and customers receiving service or waiting in line leave the queue before being served. Moreover, customers who visit the facility during the repair avoid entering the facility. The problem is first formulated as a mixed-integer nonlinear programming (MINLP) model, for which two piecewise mixed-integer linear programming (MILP) relaxations, an exact solution algorithm (the branch and bound algorithm), and a metaheuristic algorithm (the antlion algorithm), are then presented for solution. Numerical experiments indicate the efficiency of the branch and bound algorithm. The antlion algorithm also exhibits the proper convergence speed to obtain near-optimal solutions.

Robust competitive facility location model with uncertain demand types.

In competitive settings, firms locate their facilities according to customers’ behavior to maximize their market share. A common behavior is consuming from different motivations: one is for convenient demand, and the other is for quality demand. In this behavioral pattern, consumers patronize facilities within convenience for some demands, and patronize high quality facilities beyond convenience range for other demands. This behavior has never been included in competitive facility location problems. Given several other companies’ facilities in the market offering similar products or services, we study how a new entrant company can locate facilities based on this customer behavior to maximize its market share. A two-level robust model for the new entrant company is proposed to locate its facilities by taking into account the uncertainty of the types of customers’ demands. For medium size problems, we propose an equivalent mixed binary linear programming to obtain exact solutions. For large size problems, an exact algorithm (GCKP-A) for solving the inner-level model is given first by exploring the optimal solution. Then a heuristic algorithm is proposed by imbedding (GCKP-A) and 2-opt strategy into the framework of the improved ranking-based algorithm. The performance of the proposed heuristic algorithm is checked for different size problems. The sensitivity analysis of a quasi-real example shows that: (1) in most cases, the uncertainty between two types of demands does not affect the location scheme; (2) the convenience range, the quality range and the quality threshold play an important role in the market share of the new entrant company.

Approximating activation edge-cover and facility location problems

What approximation ratio can we achieve for the Facility Location problem if whenever a client u connects to a facility v, the opening cost of v is at most θ times the service cost of u? We show that this and many other problems are a particular case of the Activation Edge-Cover problem. Here we are given a multigraph G=(V,E), a set R⊆V of terminals, and thresholds {tue,tve} for each uv-edge e∈E. The goal is to find an assignment a={av:v∈V} to the nodes minimizing ∑v∈Vav, such that the edge set Ea={e=uv:au≥tue,av≥tve} activated by a covers R. We obtain ratio 1+maxx≥1⁡ln⁡x1+x/θ≈ln⁡θ−ln⁡ln⁡θ for the problem, where θ≤maxe∈E⁡max⁡{tue,tve}min⁡{tue,tve} is a problem parameter. This result is based on a simple generic algorithm for the problem of minimizing a sum of a decreasing and a sub-additive set functions, which is of independent interest. As an application, we get the same ratio for the above variant of Facility Location. If for each facility all service costs are identical then we show a better ratio 1+maxk∈N⁡Hk−11+k/θ, where Hk=∑i=1k1/i. For the Min-Power Edge-Cover problem we improve the ratio 1.406 of [4] (achieved by iterative randomized rounding) to 1.2785. For unit thresholds we improve the ratio 73/60≈1.217 of [4] to 15551347≈1.155.

Sequential Competitive Facility Location: Exact and Approximate Algorithms

In “Sequential Competitive Facility Location: Exact and Approximate Algorithms,” Qi et al. consider a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets and maximize their market shares of demand following a probabilistic choice model. They derive an equivalent, single-level mixed-integer nonlinear program (MINLP) reformulation of the bilevel MINLP and exploit the problem structures to derive valid inequalities based on submodularity and concave overestimation. They also develop an approximation algorithm with a constant approximation guarantee. They further study several extensions of CFLP that have general facility-opening costs, outside competitors, and diverse facility-planning decisions. Their approaches significantly accelerate the computation of CFLP on large-sized instances that have not been solved optimally or even heuristically by existing methods.

A human learning optimization algorithm with competitive and cooperative learning

Human learning optimization (HLO) is a simple yet powerful metaheuristic developed based on a simplified human learning model. Competition and cooperation, as two basic modes of social cognition, can motivate individuals to learn more efficiently and improve their efficiency in solving problems by stimulating their competitive instincts and increasing interaction with each other. Inspired by this fact, this paper presents a novel human learning optimization algorithm with competitive and cooperative learning (HLOCC), in which a competitive and cooperative learning operator (CCLO) is developed to mimic competition and cooperation in social interaction for enhancing learning efficiency. The HLOCC can efficiently maintain the diversity of the algorithm as well as achieve the optimal values, demonstrating that the proposed CCLO can effectively improve algorithm performance. HLOCC has been compared with other heuristic algorithms on CEC2017 functions. In the second study, the uncapacitated facility location problems (UFLPs) which are one of the pure binary optimization problems are solved with HLOCC. The experimental results show that the developed HLOCC is superior to previous HLO variants and other metaheuristics with its improved exploitation and exploration abilities.

Eccentricity queries and beyond using hub labels

Hub labeling schemes are popular methods for computing distances on road networks and other large complex networks, often answering to a query within a few microseconds for graphs with millions of edges. In this work, we study their algorithmic applications beyond distance queries. Indeed, several implementations of hub labels were reported to have good practical performances, both in terms of pre-processing time and maximum label size. There are also a few relevant graph classes for applications for which we know how to compute hub labelings with sublinear labels in quasi linear time. These positive results raise the question of what can be computed efficiently given a graph and a hub labeling of small maximum label size as input. We focus on eccentricity queries and distance-sum queries, for several versions of these problems on directed weighted graphs, that is in part motivated by their importance in facility location problems. On the negative side, we show conditional lower bounds for these above problems on unweighted undirected sparse graphs, via standard constructions from “Fine-grained” complexity. Specifically, under the Strong Exponential-Time Hypothesis (SETH), answering to these above queries requires Ω(|V|2−o(1)) pre-processing time or Ω(|V|1−o(1)) query time, even if we are given as input a hub labeling of maximum label size in ω(log⁡|V|). However, things take a different turn when the hub labels have a sublogarithmic size. Indeed, for every ε>0 there exists a δε>0 such that the following hold, being given a hub labeling of maximum label size ≤k: after pre-processing the labels in total O(2δε⋅k⋅|V|1+ε) time, we can compute both the eccentricity and the distance-sum of any vertex in O(2δε⋅k⋅|V|ε) time. Our data structure is a novel application of the orthogonal range query framework of Cabello and Knauer (2009) [17]. It can also be applied to the fast global computation of some topological indices. Finally, as a by-product of our approach, on any fixed class of unweighted graphs with bounded expansion, we can decide whether the diameter of an n-vertex graph in the class is at most k in fε(k)⋅n1+ε time for any ε>0, for some “explicit” function fε that depends on ε and the graph class considered. This result is further motivated by the empirical evidence that many classes of complex networks have bounded expansion (Demaine et al., 2019 [24]), and that some of these networks, such as the online social networks, have a relatively small diameter.

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.

The min-p robust optimization approach for facility location problem under uncertainty

The min-p robust optimization approach for facility location problem under uncertainty

A branch-and-price approach for the continuous multifacility monotone ordered median problem

In this paper, we address the Continuous Multifacility Monotone Ordered Median Problem. The goal of this problem is to locate p facilities in Rd minimizing a monotone ordered weighted median function of the distances between given demand points and its closest facility. We propose a new branch-and-price procedure for this problem, and three families of matheuristics based on: solving heuristically the pricer problem, aggregating the demand points, and discretizing the decision space. We give detailed discussions of the validity of the exact formulations and also specify the implementation details of all the solution procedures. Besides, we assess their performances in an extensive computational experience that shows the superiority of the branch-and-price approach over the compact formulation in medium-sized instances. To handle larger instances it is advisable to resort to the matheuristics that also report rather good results.

Comparative Study for Facilities Location Problem in Supply Chain Design

The interest in supply chains has increased in the last few years. The supply chain optimization aims to reduce the delays and costs generated between suppliers and customers. The researchers focus primarily on the supply chain design to transport products to clients. This paper attempts to find an optimal warehouse location using a metaheuristic method. The goal is to select the optimum warehouse location. FLP-GA (Facility Location Problem - Genetic Algorithms) is the proposed approach based on genetic algorithms that reduce the number of warehouses to be opened, the overall costs, and the distances between them from a set of customers and candidate warehouses. The authors compared the approach with three other methods. This approach can select a reduced number of warehouses with minimal cost.

ANALISIS PENENTUAN LOKASI ATM MENGGUNAKAN DIAGRAM VORONOI PADA BANK SYARIAH

Determining the right location for distribution of ATM Bank Syariah in Jember Regency considers several parameters including public facilities, ease of access and population. The problem in determining of location is called Facility Location Problem (FLP). The problem solving of location determination can use Voronoi diagram, which is to divide each desired region into several parts. Each part of the region represents a single point of location. Each point of location will be mapped with each point of the nearest location. Determining the nearest location point using Euclid distance. Determination of location based on parameters by giving a score on each data and giving a weight value on each parameter. From the score value and weight values owned will be obtained the total weight value of each region. The region with the highest weight value is designated as the district center. Each subdistrict center will have several service areas based on the nearest Google Maps distance. Determinating location of ATM Bank Syariah will be carried out based on parameters potential analysis in each service area.

Locating facilities under competition and market expansion: Formulation, optimization, and implications

As the ongoing battle between brick‐and‐mortar stores and e‐commerce shops escalates, managers of the former are becoming more cautious regarding their strategic store site selection and decoration decisions, particularly if foreseeable competition from rival companies exists. This paper investigates a bilevel competitive facility location (BCFL) problem, where two companies, a leader and a follower, plan to enter a market sequentially. Each company has a budget to open and design facilities. The goal is to maximize expected revenue that is forecasted through a discrete choice model. To reflect a practical environment, we further consider a situation with elastic demand, explaining the market expansion effect when customers are offered better service due to the opening of new facilities. We formulate the problem as a nonlinear 0‐1 bilevel program. Because of the bilevel structure and the market expansion effect, this problem is so challenging that we are unaware of any exact algorithms in the literature. Motivated by this gap, we develop an exact framework that leverages the state‐of‐the‐art value‐function–based approach. However, this framework requires solving a mixed‐integer nonconvex optimization problem (MINOP) at each iteration, which is computationally prohibitive even for medium‐scale instances. To mitigate the intractability, we propose a new framework that avoids MINOP and tackles instances with hundreds of location variables. Finally, we conduct extensive computational studies to show the efficiency and effectiveness of our method as well as provide insightful guidance for managers to have win–win/dominate outcomes and choose an appropriate market size function when dealing with expansion decisions in chained business operations.

Flow-Capture Location Model with Link Capacity Constraint Over a Mixed Traffic Network

Abstract This paper constructs and settles a charging facility location problem with the link capacity constraint over a mixed traffic network. The reason for studying this problem is that link capacity constraint is mostly insufficient or missing in the studies of traditional user equilibrium models, thereby resulting in the ambiguous of the definition of road traffic network status. Adding capacity constraints to the road network is a compromise to enhance the reality of the traditional equilibrium model. In this paper, we provide a two-layer model for evaluating the efficiency of the charging facilities under the condition of considering the link capacity constraint. The upper level model in the proposed bi-level model is a nonlinear integer programming formulation, which aims to maximize the captured link flows of the battery electric vehicles. Moreover, the lower level model is a typical traffic equilibrium assignment model except that it contains the link capacity constraint and driving distance constraint of the electric vehicles over the mixed road network. Based on the Frank-Wolfe algorithm, a modified algorithm framework is adopted for solving the constructed problem, and finally, a numerical example is presented to verify the proposed model and solution algorithm.

Multi-objective two-level medical facility location problem and tabu search algorithm

The medical facility location problem has attracted increasing attention in recent years because the rational layout of medical facilities plays an important role in implementing the hierarchical diagnosis and treatment system in many countries. To promote the implementation of a hierarchical diagnosis and treatment system, a two-level medical facility location problem with multiple patient flows between demand points and medical facilities is studied in this paper. We use a direct interpretation of the two-level medical facility location problem as a multi-objective problem to effectively balance different conflicting objectives. Based on the multi-objective tabu search algorithm and the fast construction method of the Pareto non-dominated solution, we also propose a solution approach to yield a set of solutions that can represent the trade-offs among conflicting objectives. The applicability and validation of the presented model and performance of the proposed optimization approach are evaluated using a real case. The experimental results not only indicate that the proposed solution approach can effectively solve the two-level medical facility location problem, but also suggest that the presented model can provide significant results in determining locations for medical facilities.