Facility Location Problem Research Articles

Altruism in Facility Location Problems

We study the facility location problems (FLPs) with altruistic agents who act to benefit others in their affiliated groups. Our aim is to design mechanisms that elicit true locations from the agents in different overlapping groups and place a facility to serve agents to approximately optimize a given objective based on agents' costs to the facility. Existing studies of FLPs consider myopic agents who aim to minimize their own costs to the facility. We mainly consider altruistic agents with well-motivated group costs that are defined over costs incurred by all agents in their groups. Accordingly, we define Pareto strategyproofness to account for altruistic agents and their multiple group memberships with incomparable group costs. We consider mechanisms satisfying this strategyproofness under various combinations of the planner's objectives and agents' group costs. For each of these settings, we provide upper and lower bounds of approximation ratios of the mechanisms satisfying Pareto strategyproofness.

Low-Distortion Clustering with Ordinal and Limited Cardinal Information

Motivated by recent work in computational social choice, we extend the metric distortion framework to clustering problems. Given a set of n agents located in an underlying metric space, our goal is to partition them into k clusters, optimizing some social cost objective. The metric space is defined by a distance function d between the agent locations. Information about d is available only implicitly via n rankings, through which each agent ranks all other agents in terms of their distance from her. Still, even though no cardinal information (i.e., the exact distance values) is available, we would like to evaluate clustering algorithms in terms of social cost objectives that are defined using d. This is done using the notion of distortion, which measures how far from optimality a clustering can be, taking into account all underlying metrics that are consistent with the ordinal information available. Unfortunately, the most important clustering objectives (e.g., those used in the well-known k-median and k-center problems) do not admit algorithms with finite distortion. To sidestep this disappointing fact, we follow two alternative approaches: We first explore whether resource augmentation can be beneficial. We consider algorithms that use more than k clusters but compare their social cost to that of the optimal k-clusterings. We show that using exponentially (in terms of k) many clusters, we can get low (constant or logarithmic) distortion for the k-center and k-median objectives. Interestingly, such an exponential blowup is shown to be necessary. More importantly, we explore whether limited cardinal information can be used to obtain better results. Somewhat surprisingly, for k-median and k-center, we show that a number of queries that is polynomial in k and only logarithmic in n (i.e., only sublinear in the number of agents for the most relevant scenarios in practice) is enough to get constant distortion.

Strategyproof Mechanisms for Group-Fair Obnoxious Facility Location Problems

We study the group-fair obnoxious facility location problems from the mechanism design perspective where agents belong to different groups and have private location preferences on the undesirable locations of the facility. Our main goal is to design strategyproof mechanisms that elicit the true location preferences from the agents and determine a facility location that approximately optimizes several group-fair objectives. We first consider the maximum total and average group cost (group-fair) objectives. For these objectives, we propose deterministic mechanisms that achieve 3-approximation ratios and provide matching lower bounds. We then provide the characterization of 2-candidate strategyproof randomized mechanisms. Leveraging the characterization, we design randomized mechanisms with improved approximation ratios of 2 for both objectives. We also provide randomized lower bounds of 5/4 for both objectives. Moreover, we investigate intergroup and intragroup fairness (IIF) objectives, addressing fairness between groups and within each group. We present a mechanism that achieves a 4-approximation for the IIF objectives and provide tight lower bounds.

Orbital Facility Location Problem for Satellite Constellation Servicing Depots

This work proposes an adaptation of the facility location problem for the optimal placement of on-orbit servicing depots for satellite constellations in high-altitude orbit. The high-altitude regime, such as medium Earth orbit, is a unique dynamic environment where low-thrust propulsion systems can provide the necessary thrust to conduct plane-change maneuvers between the various orbital planes of the constellation. As such, on-orbit servicing architectures involving servicer spacecraft that conduct roundtrips between servicing depots and the client satellites of the constellation may be conceived. To this end, a new orbital facility location problem formulation is proposed based on binary linear programming, in which the costs of operating and allocating the facility(ies) to satellites are optimized in terms of the sum of the effective mass to low Earth orbit (EMLEO). The low-thrust transfers between the facilities and the clients are computed using a parallel implementation of a Lyapunov feedback controller. The total launch cost of the depot, along with its servicers, propellant, and payload, is taken into account as the cost to establish a given depot. The proposed approach is applied to designing an on-orbit servicing depot architecture for the Galileo and the GPS constellations.

A fuzzy interval optimization approach for p-hub median problem under uncertain information.

Stochastic and robust optimization approaches often result in sub-optimal solutions for the uncertain p-hub median problem when continuous design parameters are discretized to form different environmental scenarios. To solve this problem, this paper proposes a triangular fuzzy number model for the Non-Strict Uncapacitated Multi-Allocation p-hub Median Problem. To enhance the quality and the speed of optimization, a novel optimization approach, combining the triangular fuzzy number evaluation index with the Genetic-Tabu Search algorithm, is proposed. During the iterations of the Genetic-Tabu Search algorithm for finding the optimal solution, the fitness of fuzzy hub schemes is calculated by considering the relative positional relationships of triangular fuzzy number membership functions. This approach directly addresses the triangular fuzzy number model and ensures the integrity of information in the p-hub problem as much as possible. It is verified by the classic Civil Aeronautics Board and several self-constructed data sets. The results indicate that, compared to the traditional Genetic Algorithm and Tabu Search algorithm, the Genetic-Tabu Search algorithm reduces average computation time by 49.05% and 40.93%, respectively. Compared to traditional random, robust, and real-number-based optimization approaches, the proposed optimization approach reduces the total cost in uncertain environments by 1.47%, 2.80%, and 8.85%, respectively.

A Lagrangian bounding and heuristic principle for bi-objective discrete optimization

Lagrangian relaxation is a common and often successful way to approach computationally challenging single-objective discrete optimization problems with complicating side constraints. Its aim is often twofold; first, it provides bounds for the optimal value, and, second, it can be used to heuristically find near-optimal feasible solutions, the quality of which can be assessed by the bounds. We consider bi-objective discrete optimization problems with complicating side constraints and extend this Lagrangian bounding and heuristic principle to such problems. The Lagrangian heuristic here produces non-dominated candidates for points on the Pareto frontier, while the bounding forms a polyhedral outer approximation of the Pareto frontier, which can be used to assess the quality of the candidate points. As an illustration example we consider a facility location problem in which both CO2 emission and cost should be minimized. The computational results are very encouraging, both with respect to bounding and the heuristically found non-dominated solutions. In particular, the Lagrangian bounding is much stronger than the outer approximation given by the Pareto frontier of the problem’s linear programming relaxation.

The dynamic facility location problem with mobile production units: A waste recycling application

This paper presents a multi-period location–production problem involving small recycling units that are embedded in standard containers and can, therefore, be relocated from site to site at short notice. The waste generated over time at different locations can be stored up to a specific limit, at which point recycling must occur. A mixed-integer program is implemented to plan the relocation of the mobile recycling units in such a way that the total cost resulting from waste transport and facility relocation is minimized. To solve large instances, three heuristics are developed that form the basis for a detailed computational study. The results reveal that mobile recycling units can significantly reduce the total costs compared to centralized recycling because (a) a larger number of mobile recycling units, (b) larger storage capacities, and (c) more short-term relocation possibilities increase the optimization scope and thus the possibility to reduce the total transport distances, and thereby, the costs. However, achieving this requires intelligent planning that considers the complex interdependencies between the influencing parameters and balances the existing trade-offs.

A new approach to the multiple obnoxious facility location problem based on combinatorial and continuous tools

In this paper we address the multiple obnoxious facility location problem. In this problem p facilities need to be spread within the unit square in such a way that they are far enough from each other and that their minimal distance from n communities, with known positions within the unit square, is maximized. The problem has a combinatorial component, related to the key observation made in Drezner (Omega 87:105–116, 2019) about the role played by Voronoi points. We propose a new approach, which exploits both the combinatorial component of the problem and, through continuous local optimizations, also its continuous component. We also propose techniques to limit the impact on computation times of the number n of communities. The approach turns out to be quite competitive and is able to return 24 new best known solutions with respect to the best results reported in Kalczynski (Optim Lett 16:1153–1166, 2022).

A self-supervised learning model for graph clustering optimization problems

The graph clustering optimization problems are ubiquitous in both scientific and engineering fields, for example the graph partitioning problem and facility location problem. Since most of these problems are NP-hard, it is challenging to design effective algorithms for them. Recently, deep learning has achieved promising performances in solving combinatorial optimization problems. However, existing supervised learning-based methods are limited by the absence of labeled instances, while reinforcement learning-based methods tend to be hard to train and converge slowly for large instances. In this paper, we propose a self-supervised model named GCOM to address NP-hard graph clustering optimization problems. It adopts a pre-training and fine-tuning framework. In the pre-training process, we utilize graph contrastive learning to mine the latent clustering relations and useful optimization strategies, which can be generalized to the downstream tasks. Additionally, two effective graph encodings are introduced to enhance the expressive power of our model. We evaluate our model on facility location problem (FLP) and balanced graph partitioning (BGP). Extensive experiments conducted on both synthetic and real-world datasets validate superior performance, strong generalization ability and high sample-efficiency of our model.

Unified Framework for Choice-Based Facility Location Problem

The choice-based facility location (CBFL) problem arises in various industrial and business contexts. The problem stands on a decentralized perspective: Companies set up chains of facilities, and customers determine from which chain or facility to seek service according to their own preferences. Essentially, customer preferences or choices play a key role in characterizing various CBFL problems, which differ mainly in the models or rules used to characterize the choice. Consequently, a large number of formulations appear and are often solved by dedicatedly designed approaches in the literature. Such a situation significantly complicates practitioners’ decision-making process when they are facing practical problems but are unsure which ad hoc model is suitable for their cases. In this article, we address this dilemma by providing a unified modeling framework based on the concept of preference dominance. Specifically, we conceptualize the choice behavior as a sequential two-step procedure: Given a set of open facilities, each customer first forms a nondominated consideration set and then splits the buying power within the set. Such an interpretation renders practitioners high modeling flexibility as they can tailor how preference dominance is constructed according to their specific contexts. In particular, we show that our model can represent several streams of CBFL problems. To support our model’s applicability, we design an efficient exact decomposition algorithm. Extensive computational studies reveal that although the algorithm is designed for a general purpose, it outperforms most approaches that are tailored for ad hoc problems by a large margin, which justifies both the effectiveness and the efficiency of the unified framework. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0366 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0366 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Code and Data Repository for Unified Framework for Choice-Based Facility Location Problem

The choice-based facility location (CBFL) problem arises in various industrial and business contexts. The problem is based on a decentralized perspective: Companies set up chains of facilities, and customers determine from which chain or facility to seek service according to their own preferences. Essentially, customer preferences or choices play a key role in characterizing various CBFL problems, which differ mainly in the models or rules employed to characterize the choice. Consequently, a large number of formulations appear and are often solved by dedicatedly designed approaches in the literature. Such a situation significantly complicates practitioners' decision-making process when they are facing practical problems but are unsure which ad hoc model is suitable for their cases. In this article, we address this dilemma by providing a unified modeling framework based on the concept of preference dominance. Specifically, we conceptualize the choice behavior as a sequential two-step procedure: Given a set of open facilities, each customer first forms a nondominated consideration set and then splits the buying power within the set. Such an interpretation renders practitioners high modeling flexibility, as they can tailor how preference dominance is constructed according to their specific contexts. In particular, we show that our model can represent several streams of CBFL problems. To support the applicability of our model, we design an efficient exact decomposition algorithm. Extensive computational studies reveal that although the algorithm is designed for a general purpose, it outperforms most approaches that are tailored for ad hoc problems by a large margin, which justifies both the effectiveness and the efficiency of the unified framework. This repository provides data for the problem and code for the algorthm. The main folders are 'data', 'src', and 'results'. 'data': four datasets generator (and instances) used in the paper. 'src': the source code for the decomposition algorithm. 'results': high-resoultion figures in our paper All experimental results can be found in the paper (manuscript and electronic companion).

Solving a real world non-convex Quadratic Assignment Problem

The India-Japan Lighting company operates three plants in India. These three plants manufacture headlamps and taillights for the automotive industry. This study examines the facility location problem in one of these plants where 12 facilities must be placed in a two-column multi-row cellular layout. The machining sequences for the 20 parts conveyed among the 12 facilities were specified. The Quadratic Assignment Problem (QAP) is classified as an NP-hard problem in large instances. We modelled the specific instance as a QAP and reported the solution obtained by an easily available generalised reduced gradient (GRG) nonlinear solver and the solution obtained from the Gurobi optimiser. The Gurobi optimiser provides an excellent incumbent solution in quick time, but takes exponential time to reduce the duality gap.

방재비축창고 위치 실증연구

Purpose – Gyeongsangbuk-do is a region prone to frequent natural disasters, and there are high expectations for the establishment of an Integrated National Management System of Disaster Resources. For this purpose, it is necessary to expand disaster prevention stockpiles in the province. However, currently, the logistics perspective has not adequately been considered, leading to network inefficiency. Therefore, this study proposes an optimal location-allocation plan for disaster stockpile warehouses in Gyeongsangbuk-do. Design/Methodology/Approach – This research applied a discrete-linear facility location problem based on maximal covering location algorithm. The optimal location is determined by prioritizing nearby areas and setting the service distance limit lower than the current maximum service distance. Findings – As a result, Gyeongju-si was identified as a more suitable facility location instead of Pohangsi, one of the current disaster stockpile center locations. Furthermore, the proposed optimal locationallocation plan is more efficient than the current network and reduces regional deviations due to the objective function of the applied algorithm. Research Implications – Based on the Integrated National Management System of Disaster Resources plan, this study holds potential for practical use by using the current operating warehouse locations in Gyeongsangbuk-do as parameters. Additionally, since logistics is often overlooked in disaster management, the optimal location and distribution plan proposed in this study can serve as an indicator of logistics efficiency.

Multiple obnoxious facility location: the case of protected areas

Multiple obnoxious facility location: the case of protected areas

A parallel variable neighborhood search for [formula omitted]-neighbor facility location problems

In this paper, we employ the less is more approach to develop a Parallel Variable Neighborhood Search (VNS) algorithm for the α-neighbor p-center problem (αNpCP) and the α-neighbor p-median problem (αNpMP). The αNpCP and the αNpMP are generalizations of the p-center (pCP) and p-median (pMP) problems, respectively. In the α-neighbor problems, one seeks to open p facilities and assign each of the n customers to their closest α ones. The objective is to minimize the maximum distance of a customer to its αth facility, in the case of the αNpCP, and the sum of the distances from each customer to their α nearest facilities, in the case of the αNpMP. Our VNS adapts simple but efficient algorithms and data structures from the pCP and pMP literature to the αNpCP and αNpMP context. We also introduce an updated objective function for the αNpCP, which adds more information to the solution cost and helps the VNS to escape from local optima. Several experimental tests show that our VNS outperforms more complex state-of-the-art algorithms. Regarding the αNpCP, on 120 instances derived from the OR-library set, our algorithm improved best-known solutions for 22, with an average improvement of 34.26%; the overall gap on the 120 instances is 6.18% in favor of our algorithm. Moreover, on 231 instances derived from the TSPLIB set, we improved the solutions for 115, with an average improvement of 5.30%, and an overall improvement gap of 2.47% for all 231 instances. Considering the αNpMP results, our heuristic obtained better results than a heuristic from literature in all 80 instances tested, finding optimal solutions in all these instances.

Optimization in Territorial Partitioning to Improve the Performance of a Common Building Maintenance Service Contract: A Case Study of a Public Agency in Paraná State, Brazil

All public administration contracts must be evaluated in order to improve their performance while respecting the limits established by laws and regulations. The purpose of this article is to apply an approach to improve the performance of a common building maintenance service contract for the Paraná State Court of Justice (PRCJ), which has a total built area of ​​544 283,79 m² in 224 buildings distributed over 161 counties, by optimizing the territorial partitioning of Paraná State. To partition the state into 14 regions, a binary integer linear programming (BILP) mathematical model is applied to the facilities location problem (FLP) in three scenarios. The results show that Scenario 3 (in which the location of the 14 maintenance offices and the configuration of their areas of activity were optimized) is the best in terms of minimizing the distances traveled by maintenance teams. In this scenario, the total distance traveled would be 9 775 km per day (instead of the current 11 150 km), achieving savings of around 12,3% when compared to the current solution. With this solution, in addition to the distance, the direct and indirect costs associated with the displacement of work teams and the time spent on their corresponding trips would be minimized. Furthermore, the users of maintenance services could be served more quickly, resulting in a higher number of services and greater satisfaction for the target audience of the contract.

Robust optimization of a closed-loop supply chain network based on an improved genetic algorithm in an uncertain environment

Aiming at the network structure design problems of facility location, path planning, and flow distribution in an e-commerce closed-loop supply chain network under an uncertain environment, the uncertainties of both the forward and reverse logistics demands and the impact of facility disruptions are analyzed. A robust optimization model is established using the robust peer-to-peer optimization method. An algorithm is designed that combines the minimum spanning tree algorithm with a two-layer adaptive genetic algorithm (Prim-DMGA) to solve the model. The results show that the Prim-DMGA not only requires less computation time, but also generates solutions of higher quality. In addition, the application of the robust optimization model reduces the adverse effects of uncertain factors on the e-commerce closed-loop supply chain network, thereby improving its robustness.

Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions

Typically, within facility location problems, fairness is defined in terms of accessibility of users. However, for facilities perceived as undesirable by communities hosting them, fairness between the usage of facilities becomes especially important. Limited research exists on this notion of fairness. To close this gap, we develop a series of optimization models for the allocation of populations of users to facilities such that access for users is balanced with a fair utilization of facilities. The optimality conditions of the underlying nonconvex quadratic models state the precise balance between accessibility and fairness. We define new classes of fairness and a metric to quantify the extent to which fairness is achieved in both optimal and suboptimal allocations. We show that a continuous relaxation of our central model is sufficient to achieve a perfect extent of fairness, while a special case reduces to the classical notion of proportional fairness. Our work is motivated by pervasive ecological challenges faced by the waste management community as policymakers seek to reduce the number of recycling centers in the last few years. As a computational case study, applying our models on data for the state of Bavaria in Germany, we find that even after the closure of a moderate number of recycling centers, large degrees of access can be ensured, provided that the closures are conducted optimally. Fairness, however, is impacted more, with facilities in rural regions shouldering larger loads of visiting populations than those in urban regions. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: Computer resources and support provided by the Erlangen Regional Computing Center are gratefully acknowledged. B. Singh was partially financially supported by the Bavarian State Ministry for Science and Art (Bayerisches Staatsministerium für Wissenschaft und Kunst) under the Competence Network for Scientific High Performance Computing in Bavaria. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0308 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0308 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Code and Data Repository for Quadratic Optimization Models for Balancing Preferential Access and Fairness: Formulations and Optimality Conditions

This directory provides code used for the computations associated with the quadratic optimization models in the context of undesirable facility location problems for the abovementioned article. src contains scripts for the optimization of the MIQP model and visualization of the results: model.py contains functions for building and optimizing the MIQP model, while greedy_heuristic.py applies a greedy heuristic to achieve a feasible solution. plotting.py and results.py contain functions tasked with visualizing results through various different plots as well as excel tables. They also contain superordinate functions that create the corresponding results first by running functions from model.py and/or greedy_heuristic.py before creating the corresponding visualization. These functions are called by functions in tables_and_figures.py to create the exact same figures and tables that are included in the paper from scratch. Lastly, utils.py contains helper and utility functions. catchment_population presents an efficient algorithm to compute the "catchment population" of each recycling center that was used to estimate the capacities. An implementation of this algorithm is contained in catchment_population.py. Further, this directory contains two corresponding input data files in csv format: bavaria_grid_population.csv is a file containing the latitude and longitude of the centroid of each 100m x 100m grid in Bavaria as well as the residing population. rc_locations.csv contains the latitude and longitude of each recycling center in Bavaria. data contains the two input data files that are used in the MIQP model: users_and_facilities.xlsx contains all ZIP codes and recycling centers related data like the population, centroid and regional spatial type (rural/urban) of each ZIP code as well as the capacity, centroid and regional spatial type of each recycling center. travel_dict.json.pbz2 is a compressed json file that contains the travel probabilities from each ZIP code to each recycling center. results contains the excel tables and figures visualizing the results that are included in the paper.

Multi-product maximal covering second-level facility location problem

This paper introduces a new hierarchical facility location model with three levels: first-level facilities which manufacture different products, second-level facilities which act as warehouses and a third-level consisting of the clients who demand the products that have been manufactured in the first level and stored in the second level. In this model, called multi-product maximal covering second-level facility location problem (SL-MCFLP), the aim is to decide the location of the second-level facilities and the products to be stored in each of them maximizing the overall clients’ satisfaction with respect their coverage. To deal with this model, we introduce a Mixed Integer Linear Program (MILP) which is reinforced by some families of valid inequalities. Since some of these families have an exponential number of constraints, separation algorithms are proposed. In addition, three variants of a matheuristic procedure are developed. Computational studies are included, showing the potentials and limits of the formulation and the effectiveness of the heuristic.