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Let G=(V,E)$$ G=\left(V,E\right) $$ be a graph with unit‐length edges and nonnegative costs assigned to its vertices. Given a list of pairwise different vertices S=(s1,s2,...,sp)$$ S=\left({s}_1,{s}_2,\dots, {s}_p\right) $$, the prioritized Voronoi diagram of G$$ G $$ with respect to S$$ S $$ is the partition of G$$ G $$ in p$$ p $$ subsets V1,V2,...,Vp$$ {V}_1,{V}_2,\dots, {V}_p $$ so that, for every i$$ i $$ with 1≤i≤p$$ 1\le i\le p $$, a vertex v$$ v $$ is in Vi$$ {V}_i $$ if and only if si$$ {s}_i $$ is a closest vertex to v$$ v $$ in S$$ S $$ and there is no closest vertex to v$$ v $$ in S$$ S $$ within the subset {s1,s2,...,si−1}$$ \left\{{s}_1,{s}_2,\dots, {s}_{i-1}\right\} $$. For every i$$ i $$ with 1≤i≤p$$ 1\le i\le p $$, the load of vertex si$$ {s}_i $$ equals the sum of the costs of all vertices in Vi$$ {V}_i $$. The load of S$$ S $$ equals the maximum load of a vertex in S$$ S $$. We study the problem of adding one more vertex v$$ v $$ at the end of S$$ S $$ in order to minimize the load. This problem occurs in the context of optimally locating a new service facility (e.g., a school or a hospital) while taking into account already existing facilities, and with the goal of minimizing the maximum congestion at a site. There is a brute‐force algorithm for solving this problem in 풪(nm) time on n$$ n $$‐vertex m$$ m $$‐edge graphs. We prove a matching time lower bound–up to sub‐polynomial factors–for the special case where m=n1+o(1)$$ m={n}^{1+o(1)} $$ and p=1$$ p=1 $$, assuming the so called Hitting Set Conjecture of Abboud et al. On the positive side, we present simple linear‐time algorithms for this problem on cliques, paths and cycles, and almost linear‐time algorithms for trees, proper interval graphs and (assuming p$$ p $$ to be a constant) bounded‐treewidth graphs. [ABSTRACT FROM AUTHOR]

The objective of the median problem is to optimize the location of a facility so that the sum of demand-weighted distances from a set of demand points is minimized. In this article, an algorithm for solving the median problem on real road networks is proposed. The proposed algorithm, referred to as multi-threaded Dijkstra's (MTD), works with very large road networks, does not require computationally intensive pre-processing of the network data and offers reasonable runtime. The MTD algorithm is used to evaluate several facility location scenarios on various road networks with 2000–50,000 nodes. Solutions are compared against an exhaustive search. The results show that the MTD algorithm is capable of solving median problems on very large networks and its runtime is influenced by factors such as the number of demand points, network size and size of the area in which the demand points are distributed. [ABSTRACT FROM AUTHOR]

The Resource Allocation Problem with Time Dependent Penalties (RAPTP) is a variant of uncapacitated resource allocation problems generally referred as uncapacitated facility allocation problems or uncapacitated facility location problem (UFLP). Work done in this paper is motivated by the work of Du, Lu and Xu [7] in which authors considered facility location problems with submodular penalties and presented a 3-approximation primal dual algorithm. This paper considers that each unallocated demand point adds to penalty that increases as time passes and is thus represented by function x (t i , p i) where t i and p i are elapse time and priority of demand point d i . As this problem has been considered for emergency service allocation, all demand points should be allocated to some facility or resource within some stipulated time limit beyond which it may lose its purpose. Thus penalty incurred by a demand point is considered till that threshold value only. Thus it is assumed that penalty contribution by a demand point remains constant after a specified threshold value. By exploiting the properties of time dependent penalties, a 4-approximation primal-dual algorithm is proposed which is based on LP framework, and is the first constant-factor approximation algorithm for RAPTP. [ABSTRACT FROM AUTHOR]

To cope with the facility location problem, a method based on simulated annealing and “ZKW” algorithm is proposed in this article. The method is applied to some real cases, which aims to deploy video content server at appropriate nodes in an undirected graph to satisfy the requirements of the consumption nodes with the least cost. Simulated annealing can easily find the optimum with less reliance on the initial solution. “ZKW” algorithm can find the shortest path and calculate the least cost from the server node to consumption node quickly. The results of three kinds of cases illustrate the efficiency of our method, which can obtain the optimum within 90 s. A comparison with Dijkstra and Floyd algorithms shows that, by using “ZKW” algorithm, the method can have large iteration with limited time. Therefore, the proposed method is able to solve this video content server location problem. [ABSTRACT FROM AUTHOR]

An important problem confronting port cities is where and how to accommodate port growth. Larger ships combined with increased container throughput require more yard space and generate more traffic, straining the urban fabric in the vicinity of the port. A promising solution to this problem is the development of urban intermodal container terminals (IMTs) that interface with both road and rail (or possibly inland waterway) networks. This raises two linked choices; where to locate the intermodal terminals and what will be their likely usage by multiple shippers, each having a choice of whether or not to use the IMT as part of an intermodal transport chain . The use of an IMT by a shipper indicates the shipper's choice of intermodal transport, which comprises a combined use of a high capacity mode (rail or barge between the port and the IMT) and trucks (between the IMT and the cargo origin or destination). The overall problem therefore comprises a mode choice problem embedded within a facility location problem. This paper employs the method of entropy maximisation to combine a logit mode choice model with a facility location model, leading to a non-linear mixed integer programming model. The principal features of the entropy maximising facility location model are illustrated by small and large numerical examples. [ABSTRACT FROM AUTHOR]

Recently, a novel method for aggregating crisp values into intuitionistic fuzzy number is introduced by Yue. The aim of this short communication is to show how Yue's method can be improved to increase accuracy. A revised method is proposed to overcome the existing shortages. Some desirable properties of the revised method are studied. A problem of facility location selection is developed to illustrate the validity of proposed method. [ABSTRACT FROM AUTHOR]

In China, the occurrence of a series of disasters and the tremendous loss in human lives expose the vulnerability the emergency system and the incomplete of the methodology. Faced with the needs of the practice, this paper conducted a comprehensive review both from the system and the methodology prospective. From the system prospective, this paper aims at analyzing the existing problems and the solution finding. From the methodology prospective, emergency facility location problem, emergency resource allocation problem, and emergency management technical support problem are examined. [ABSTRACT FROM AUTHOR]

This article considers facility location in a Weber problem with weights including both uncertainty and vagueness. By representing its weights as fuzzy random variables, it can be extended to a fuzzy random weighted Weber problem, and then formulated as a fuzzy random programming problem. By introducing possibility and necessity measures and chance constraints, the extended problem is reformulated to new two types of Weber problems. Based upon characteristics of facility location, theorem for solving the reformulated problems are shown. [ABSTRACT FROM AUTHOR]

Many traditional facility location models have sought optimal solutions in two-dimensional space. However, certain locations in reality need to be modeled in three-dimensional space. This paper addresses a location problem in three-dimensional space from the application perspective. Specifically, we introduce a 3D coverage location model of Wi-Fi access points (APs) in an indoor environment. To do this, we first incorporate a generic radio propagation assuming typical obstructions of a building into the standard coverage model, using 3D Euclidean distance characterizing radio signal penetration. The suggested model is then applied for an efficient AP placement plan in a multi-story building at a university campus. The empirical results present 3D representations of the solutions for multi-floor deployment of Wi-Fi APs. This research is expected to provide a useful modeling framework for combining facility location model with wireless network design in a 3D environment. [ABSTRACT FROM AUTHOR]

Facility location-allocation (FLA) decisions play a significant role in the performance of supply network in many practical applications, such as emergency service system, supply chain system, public service system, etc. In this paper, a multi-criteria model (including multi-attribute and multi-objective) for optimal and efficient facility location-allocation patterns was proposed. We first utilize multi attribute decision making (MADM) method-DEA to evaluate the relative efficiency of each potential location, and then combine the efficiency identified from DEA as a goal in a multi objective decision making (MODM) framework by using goal programming. A hypothetical example is presented to illustrate the effectiveness and the efficiency of the proposed model. Results demonstrate that the proposed multi-criteria model is an effective tool for generating a set of more realistic and flexible optimal solution in solving facility location-allocation problems by adjusting the goal priorities with respect to the importance of each objective and the aspiration level with respect to desired target values. The proposed model is also flexible and general enough to consider other specific location decisions such as emergency facilities, undesirable facilities and supply chain design by combing specific location modeling goal with the DEA model. [ABSTRACT FROM AUTHOR]

Most previous studies on reliable facility location design assume that disruptions at different locations are independent. In this paper, we present a model that allows disruptions to be correlated with an uncertain joint distribution, and we apply distributionally robust optimization to minimize the expected cost under the worst-case distribution with given marginal disruption probabilities. The worst-case distribution has a practical interpretation with disruption propagation, and its sparse structure allows solving the problem efficiently. Our numerical results show that ignoring disruption correlation could lead to significant loss that increases dramatically in key factors such as source disaster probability, disruption propagation effect, and service interruption penalty. On the other hand, the robust model results in very low regret, even when disruptions are independent, and starts to outperform the model assuming independence when disruptions are mildly correlated. Most of the benefit of the robust model can be captured with a very low additional cost, which makes it easy to implement. Given these advantages, we believe that the robust model can serve as a promising alternative approach for solving reliable facility location problems. [ABSTRACT FROM AUTHOR]

This paper deals with a special class of competitive facility location problems, in which two non-cooperative firms compete to capture the most of a given market, in order to maximize their profit. This paper intends to present a simple and effective nested strategy based on the quantum binary particle swarm optimization (QBPSO) method for solving the bi-level mathematical model of the problem. In solution approach, an improvement procedure is embedded into QBPSO to increase the convergence speed and generate more accurate solutions. Taguchi's method is employed to systematically determine the optimal values of QBPSO parameters. Finally, computational results on large-scale instances with up to 300 locations and 350 clients (more than 100,000 variables and 300,000 constraints at each level) confirmed the method efficiency in terms of solution quality and time. [ABSTRACT FROM AUTHOR]

This paper discusses the Single Source Capacitated Facility Location Problem (SSCFLP) where the problem consists in determining a subset of capacitated facilities to be opened in order to satisfy the customers’ demands such that total costs are minimized. The paper presents an iterated tabu search heuristic to solve the SSCFLP. The iterated tabu search heuristic combines tabu search with perturbation operators to avoid getting stuck in local optima. Experimental results show that this simple heuristic is capable of generating high quality solutions using small computing times. Moreover, it is also competitive with other metaheuristic approaches for solving the SSCFLP. [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]

Highlights: [•] We propose an integrated facility location and product distribution–collection model for bidirectional flows. [•] We develop an efficient Lagrangian relaxation-based heuristic to address the proposed model. [•] We apply the heuristic in an industrial case study. [•] Several interesting managerial insights are reported from numerous computational experiments. [Copyright &y& Elsevier]

Highlights: [•] We presented the methods for solving large-scale location problems. [•] We studied relationship between setup and transportation costs of location problem. [•] The results obtained by proposed methods are compared with CPLEX. [•] Waste management system of Chiang Mai city is used to compare performance of methods. [•] The proposed methods are used to solve waste management system of Northern Thailand. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the multi level uncapacitated facility location problem (MLUFLP). A new mixed integer linear programming (MILP) formulation is presented and validity of this formulation is given. Experimental results are performed on instances known from literature. The results achieved by CPLEX and Gurobi solvers, based on the proposed MILP formulation, are compared to the results obtained by the same solvers on the already known formulations. The results show that CPLEX and Gurobi can optimally solve all small and medium sized instances and even some large-scale instances using the new formulation. [Copyright &y& Elsevier]

Abstract: This work presents a method to solve a class of discrete optimization problems, including linear, quadratic, convex, and discrete geometric programming problems. The methodology consists of inserting, in the original problem, additional geometric constraints where any viable solution is also discrete. Moreover, a strategy to solve signomial geometric programming problems is developed. Computational results are shown through some examples of facility location, machining economics and economic order quantity problems. [Copyright &y& Elsevier]

We review the problem for the design of supply chains called Capacitated Fixed Cost Facility Location Problem with Transportation Choices (CFCLP-TC). The problem is based on a production network of two echelons with multiple plants, a set of potential distribution centers, and customers. The problem is formulated as an optimization model with two objective functions based on time and cost. This paper proposes three changes to the original model to compare the sets of efficient solutions and the computational time required to obtain them. The main contribution of this paper is to extend the existing literature by incorporating approaches for the supply of product to customers through multiple sources, the direct flow between plants and customers, without this necessarily implying removing the distribution centers, and the product flow between distribution centers. From these approaches, we generate mathematical programming models and propose to solve through the epsilon-constraint approach for generating Pareto fronts and thus compare each of these approaches with the original model. The models are implemented in GAMS and solved with CPLEX. [ABSTRACT FROM AUTHOR]

This research highlights the use of game theory to solve the classical problem of the uncapacitated facility location optimization model with customer order preferences through a bilevel approach. The bilevel model provided herein consists of the classical facility location problem and an optimization of the customer preferences, which are the upper and lower level problems, respectively. Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem. An evolutionary algorithm based on the equilibrium in a Stackelberg's game is proposed to solve the bilevel model. Numerical experimentation is performed in this study and the results are compared to benchmarks from the existing literature on the subject in order to emphasize the benefits of the proposed approach in terms of solution quality and estimation time. [ABSTRACT FROM AUTHOR]

In this article, we propose a practical algorithm for capacitated facility location problems (CFLP). There are some approaches which can obtain primal solutions while simultaneously exploiting the primal structure and the dual structure. One of these approaches is the mean value cross decomposition (MVCD) method that ensures convergence without solving master problems. However, MVCD has been previously applied only to uncapacitated facility location problems (UFLP), due to the fact that the performance is highly dependent on the structure of the problem. The proposed algorithm, named the dynamic mean value cross decomposition algorithm (DMVCD), is effectively integrated with MVCD and cutting plane methods in order to tighten the bounds by reducing the duality gap. Computational results of various instances are also reported to verify the effectiveness and efficiency of DMVCD. [ABSTRACT FROM AUTHOR]

In order to character a two-level emergency repair facility location problem, this paper proposed a 0-1 integer linear programming model which could guarantee the service quality of whole emergency repair system. And it designed two kernel search algorithms to solve the model. Based on linear programming relaxation and Lagrangian relaxation of the original model respectively, these two algorithms identified kernel problem and sub-problem, which significantly reduced the scale of the original problem. Appling these two algorithms to the solution of 56 numerical instances, the results show that the kernel search algorithm based on Lagrangian relaxation of the original problem can find better solution in reasonable computational time than MOSEK solver. It confirms the optimized solution of Lagrangian relaxation dual problem can be very helpful to solving original problem. [ABSTRACT FROM AUTHOR]

In this research, facility location problem-network design under uncertainty robust mode has been discussed. In this regard a model will be developed, so that the uncertainty in parameters such as demand and problem's various costs considered. Facility location-network design, unlike classical facility location models, which are assumed that network structure is pre-defined and pre-specified, will also decide on the structure of the network. This has been in many actual applications such as road network, communication systems and, etc. and finding facility location and main network designing simultaneously has deemed important and the need for simultaneous design and optimization models to meet the mentioned items is felt. Different approaches have been developed in the uncertainty optimization literature. Amongst them, robust and stochastic optimizations are well known. To deal with uncertainty and problem modeling, in this research robust optimization approach have been used. In addition, by using generated random samples, the proposed model has been tested and computational analysis is presented for various parameters. [ABSTRACT FROM AUTHOR]

This article addresses a stochastic facility location and vehicle assignment problem in which customers are served by full return trips. The problem consists of simultaneously locating a set of facilities, determining the vehicle fleet size at each facility, and allocating customers to facilities and vehicles in the presence of random travel times. Such travel times can arise, for example, due to daily traffic patterns or weather-related disturbances. These various travel time conditions are considered as different scenarios with known probabilities. A stochastic programming with bounded penalties model is presented for the problem. In order to solve the problem, integer programming and two-level and three-level logic-based Benders’ decomposition models are proposed. Computational experiments demonstrate that the Benders’ models were able to substantially outperform the integer programming model in terms of both finding and verifying the optimal solution. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a column generation approach for a storage replenishment transportation-scheduling problem. The problem is concerned with determining an optimal combination of multiple-vessel schedules to transport a product from multiple sources to different destinations based on demand and storage information at the destinations, along with cost-effective optimal strategic locations for temporary transshipment storage facilities. Such problems are faced by oil/trucking companies that own a fleet of vessels (oil tankers or trucks) and have the option of chartering additional vessels to transport a product (crude oil or gasoline) to customers (storage facilities or gas stations) based on agreed upon contracts. An integer-programing model that determines a minimum-cost operation of vessels based on implicitly representing feasible shipping schedules is developed in this paper. Due to the moderate number of constraints but an overwhelming number of columns in the model, a column generation approach is devised to solve the continuous relaxation of the model, which is then coordinated with a sequential fixing heuristic in order to solve the discrete problem. Computational results are presented for a range of test problems to demonstrate the efficacy of the proposed approach. [Copyright &y& Elsevier]

Abstract: In this study, we consider a variant of the Bilevel Uncapacitated Facility Location Problem (BLUFLP) in which the clients choose suppliers based on their own preferences. We propose three metaheuristic methods for solving this problem: Particle Swarm Optimization (PSO), Simulated Annealing (SA) and a combination of Reduced and Basic Variable Neighborhood Search Method (RVNS-VNS). The solution encoding and constructive elements of all three proposed algorithms are adapted to the problem under consideration. The results of computational tests on problem instances with up to 2000 clients and 2000 potential facility locations show good performance of all three proposed methods, even on large problem dimensions. Finally, the obtained results indicate that the proposed RVNS-VNS method outperforms the PSO and SA methods in the sense of solutionsʼ quality and running times. [Copyright &y& Elsevier]

Abstract: Given , a simple connected, possibly non-convex, polyhedral surface composed of positively weighted triangular faces, we consider paths from generalized sources (points, segments, polygonal chains or polygonal regions) to points on that stay on and avoid obstacles (segments, polygonal chains or polygonal regions). The distance function defined by a generalized source is a function that assigns to each point of the cost of the shortest path from the source to the point. In this paper we present an algorithm for computing approximate generalized distance functions. We also provide an algorithm that computes a discrete representation of the approximate distance function and, as applications, algorithms for computing discrete order- Voronoi diagrams and for approximately solving facility location problems. Finally, we present experimental results obtained with our implementation of the provided algorithms. [Copyright &y& Elsevier]

Abstract: In the present paper, the quasiconcavity of membership functions is generalized based on conjunctive aggregation functions, and the properties of the generalized quasiconcavity are investigated. Fuzzy multicriteria and scalar programming problems are then considered, and the properties of Pareto optimal solutions and compromise solutions as well as their relationships are derived. Finally, we discuss the application of the obtained results to facility location problems. [Copyright &y& Elsevier]

Abstract: In this work we develop a method to solve a class of discrete optimization problems. This class covers linear, quadratic, convex, and discrete geometric programming problems. The methodology consists in inserting additional geometric constraints where any viable solution is also discrete. Moreover, we also adopt a methodology for solution of signomial geometric programming problems and solve the problem. We present some examples of facility location problems and the results obtained. [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]

In this study, we apply a robust optimization approach to a p-center facility location problem under uncertainty. Based on a symmetric interval and a multiple allocation strategy, we use three types of uncertainty sets to formulate the robust problem: box uncertainty, ellipsoidal uncertainty, and cardinality-constrained uncertainty. The equivalent robust counterpart models can be solved to optimality using Gurobi. Comprehensive numerical experiments have been conducted by comparing the performance of the different robust models, which illustrate the pattern of robust solutions, and allocating a demand node to multiple facilities can reduce the price of robustness, and reveal that alternative models of uncertainty can provide robust solutions with different conservativeness. [ABSTRACT FROM AUTHOR]