Covering Location Problem Research Articles

Multi-period stochastic covering location problems: Modeling framework and solution approach

This paper introduces a very general discrete covering location model that accounts for uncertainty and time-dependent aspects. A MILP formulation is proposed for the problem. Afterwards, it is observed that most of the models existing in the literature related with covering location can be considered as particular cases of this formulation. In order to tackle large instances of this problem a Lagrangian relaxation based heuristic is developed. A computational study is addressed to check the potentials and limits of the formulation and some variants proposed for the problem, as well as to evaluate the heuristic. Finally, different measures to report the relevance of considering a multi-period stochastic setting are studied.

Robust cooperative maximal covering location problem: a case study of the locating Tele-Taxi stations in Tabriz, Iran

Today, maximising the number of steady customers and consistency in meeting their needs are two important factors affecting the profitability of companies. Therefore, researchers are trying to model, study and analyse factors affecting the businesses. To this end and with regard to covering problem applications, this problem is inclusively studied in the operations research (OR) literature. This article proposes a novel maximal covering location problem (MCLP) in which different factors (capacity of facilities, budget, number of available facilities in different types) have been considered. To provide a real case problem, locating Tele-Taxi stations in Tabriz, Iran have been studied. Moreover, to analyse the effects of uncertainty in the rate of demand in each demand point and capacity of facilities as undeniable facts of real-world, the robust counterpart of the proposed model is developed. Furthermore, a sensitivity analysis on the constant perturbation for uncertain parameters has been conducted.

Robust cooperative maximal covering location problem: a case study of the locating Tele-Taxi stations in Tabriz, Iran

Today, maximising the number of steady customers and consistency in meeting their needs are two important factors affecting the profitability of companies. Therefore, researchers are trying to model, study and analyse factors affecting the businesses. To this end and with regard to covering problem applications, this problem is inclusively studied in the operations research (OR) literature. This article proposes a novel maximal covering location problem (MCLP) in which different factors (capacity of facilities, budget, number of available facilities in different types) have been considered. To provide a real case problem, locating Tele-Taxi stations in Tabriz, Iran have been studied. Moreover, to analyse the effects of uncertainty in the rate of demand in each demand point and capacity of facilities as undeniable facts of real-world, the robust counterpart of the proposed model is developed. Furthermore, a sensitivity analysis on the constant perturbation for uncertain parameters has been conducted.

Dynamic capacitated maximal covering location problem by considering dynamic capacity

Dynamic capacitated maximal covering location problem by considering dynamic capacity

Optimizing the spatial location of medical drones

Unmanned aerial vehicles (UAVs) or drones are increasingly proposed for medical uses due to their potential to transport medical supplies quickly and efficiently. A prototype medical drone that is equipped with an on-board automated external defibrillator (AED) was announced recently to significantly reduce the time it takes for an AED to arrive to a patient's side. As drones are battery-operated and have limited service range, a network of medical drones is required to adequately provide service to a large area. This paper developed a new spatial optimization model, the backup coverage location problem with complementary coverage (BCLP-CC), to aid in the deployment of a network of AED enabled medical drones. By explicitly integrating backup coverage and continuously distributed demand, the BCLP-CC can optimally place drones and the corresponding launch sites while significantly improving backup coverage with minimal loss of primary coverage. Our results show that 90.4% of historical out-of-hospital cardiac arrests in Salt Lake County can be responded to within 1 min by using 71 drones and 68 launch sites. In addition, 58.9% of incidents can be served by two or more drones, a significant improvement over existing models. This study shows that drones could significantly reduce life-saving equipment travel times for victims of cardiac arrest by appropriately siting them, which will motivate further research in using UAVs or drones for emergency medical purpose.

An iterative solution approach to a multi-objective facility location problem

This work presents a novel methodology for solving multi-objective facility location problems (mo-FLPs) with the focus on public emergency service stations. Our study is one of a few studies incorporating the objectives of three well-known problems, viz. the p-median problem (pMP), the maximal coverage location problem (MCLP) and the p-center problem (pCP). Aiming to find a set of Pareto optimal solutions and a compromise solution for all three objectives, we have developed an algorithm which solves each individual location problem sequentially. The proposed approach is mainly based on a combination of the branch & bound and iterative goal programming techniques. The performance of the algorithm is demonstrated with numerical examples.

A bi-level maximal covering location problem

In this research a bi-level maximal covering location problem is studied. The problem considers the following situation: a firm wants to enter a market, where other firms already operate, to maximize demand captured by locating p facilities. Customers are allowed to freely choose their allocation to open facilities. The problem is formulated as a bi-level mathematical programming problem where two decision levels are considered. In the upper level, facilities are located to maximize covered demand, and in the lower level, customers are allocated to facilities based on their preferences to maximize a utility function. In addition, two single-level reformulations of the problem are examined. The time required to solve large instances of the problem with the considered reformulations is very large, therefore, a heuristic is proposed to obtain lower bounds of the optimal solution. The proposed heuristic is a genetic algorithm with local search. After adjusting the parameters of the proposed algorithm, it is tested on a set of instances randomly generated based on procedures described in the literature. According to the obtained results, the proposed genetic algorithm with local search provides very good lower bounds requiring low computational time.

Locating helicopter emergency medical service bases to optimise population coverage versus average response time

BackgroundNew South Wales (NSW), Australia has a network of multirole retrieval physician staffed helicopter emergency medical services (HEMS) with seven bases servicing a jurisdiction with population concentrated along the eastern seaboard. The aim of this study was to estimate optimal HEMS base locations within NSW using advanced mathematical modelling techniques.MethodsWe used high resolution census population data for NSW from 2011 which divides the state into areas containing 200–800 people. Optimal HEMS base locations were estimated using the maximal covering location problem facility location optimization model and the average response time model, exploring the number of bases needed to cover various fractions of the population for a 45 min response time threshold or minimizing the overall average response time to all persons, both in green field scenarios and conditioning on the current base structure. We also developed a hybrid mathematical model where average response time was optimised based on minimum population coverage thresholds.ResultsSeven bases could cover 98% of the population within 45mins when optimised for coverage or reach the entire population of the state within an average of 21mins if optimised for response time. Given the existing bases, adding two bases could either increase the 45 min coverage from 91% to 97% or decrease the average response time from 21mins to 19mins. Adding a single specialist prehospital rapid response HEMS to the area of greatest population concentration decreased the average state wide response time by 4mins. The optimum seven base hybrid model that was able to cover 97.75% of the population within 45mins, and all of the population in an average response time of 18 mins included the rapid response HEMS model.ConclusionsHEMS base locations can be optimised based on either percentage of the population covered, or average response time to the entire population. We have also demonstrated a hybrid technique that optimizes response time for a given number of bases and minimum defined threshold of population coverage. Addition of specialized rapid response HEMS services to a system of multirole retrieval HEMS may reduce overall average response times by improving access in large urban areas.

A bi-objective, reliable single allocation p-hub maximal covering location problem: Mathematical formulation and solution approach

In the last few years, the p-hub maximal covering problem (pHMCP) has been applied in a variety of applications, including the design of air transportation networks, distribution systems for perishable products, postal delivery networks, and tourism routing. In hub-based systems, disruptions at hubs or unavailability of routes significantly affect service level and result in excessive costs. To tackle these problems, selecting backup hubs for unavailable hubs and rerouting the related flows are often proposed. This paper develops a bi-objective reliable single allocation p-hub maximal covering problem (BRSApHMCP) considering two objectives: maximizing expected covered flows and minimizing congestion. After formulating an initial non-linear model, a linear model is presented; the NP-Completeness of the developed model is proved and a non-dominated sorting genetic algorithm (NSGA-II) is proposed to solve it. In order to show the superior performance of the proposed NSGA-II, a well-known evolutionary algorithm, the multi-objective particle swarm optimization (MOPSO), and the epsilon constraint methods are utilized and the results are analyzed and compared. The parameters of the proposed algorithms are calibrated using the Taguchi approach. Also, a case study and some parametric analyses are done. The results show that NSGA-II is able to find the better solutions in comparison with MOPSO and by opting this proactive strategy in the investigated case study, NSGA-II could recover up to 73% of lost flow in a well-balanced system.

Integer programming formulations for three sequential discrete competitive location problems with foresight

We deal with three competitive location problems based on the classical Maximal Covering Location Problem. The environment of these problems consists of an open market with two firms (leader and follower), several customers and locations where facilities can be located. In order to capture the demand of the customers, the leader enters the market by locating a set of facilities knowing the potential locations where the follower can locate her facilities after the leader’s decision. We consider here three pairs of objective functions for the leader/follower previously studied in the literature: maximizing/minimizing the demand captured by the leader, minimizing/maximizing the regret of the leader, maximizing the demand captured by each firm (also known as Stackelberg). For each model, we propose an integer linear programming formulation with a polynomial number of variables and an exponential number of constraints. The formulations are solved by branch-and-cut algorithms where the constraints are generated on demand by solving appropriate separation problems. We report extensive computational experiments realized on instances inspired by those from the literature, comparing our algorithms with the exact and heuristic algorithms previously published for these problems.

Analysis of MCLP, Q-MALP, and MQ-MALP with Travel Time Uncertainty Using Monte Carlo Simulation

This paper compares the application of the Monte Carlo simulation in incorporating travel time uncertainties in ambulance location problem using three models: Maximum Covering Location Problem (MCLP), Queuing Maximum Availability Location Problem (Q-MALP), and Multiserver Queuing Maximum Availability Location Problem (MQ-MALP). A heuristic method is developed to site the ambulances. The models are applied to the 33-node problem representing Austin, Texas, and the 55-node problem. For the 33-node problem, the results show that the servers are less spatially distributed in Q-MALP and MQ-MALP when the uncertainty of server availability is considered using either the independent or dependent travel time. On the other hand, for the 55-node problem, the spatial distribution of the servers obtained by locating a server to the highest hit node location is more dispersed in MCLP and Q-MALP. The implications of the new model for the ambulance services system design are discussed as well as the limitations of the modeling approach.

General form of a cooperative gradual maximal covering location problem

Cooperative and gradual covering are two new methods for developing covering location models. In this paper, a cooperative maximal covering location–allocation model is developed (CMCLAP). In addition, both cooperative and gradual covering concepts are applied to the maximal covering location simultaneously (CGMCLP). Then, we develop an integrated form of a cooperative gradual maximal covering location problem, which is called a general CGMCLP. By setting the model parameters, the proposed general model can easily be transformed into other existing models, facilitating general comparisons. The proposed models are developed without allocation for physical signals and with allocation for non-physical signals in discrete location space. Comparison of the previously introduced gradual maximal covering location problem (GMCLP) and cooperative maximal covering location problem (CMCLP) models with our proposed CGMCLP model in similar data sets shows that the proposed model can cover more demands and acts more efficiently. Sensitivity analyses are performed to show the effect of related parameters and the model’s validity. Simulated annealing (SA) and a tabu search (TS) are proposed as solution algorithms for the developed models for large-sized instances. The results show that the proposed algorithms are efficient solution approaches, considering solution quality and running time.

Covering location problem of emergency service facilities in an uncertain environment

• Three models are proposed for uncertain covering location problem. • The crisp equivalences of the models are discussed. • Uncertainty distribution of the covered demand is studied. In practical location problems on networks, the response time between any pair of vertices and the demands of vertices are usually indeterminate. This paper employs uncertainty theory to address the location problem of emergency service facilities under uncertainty. We first model the location set covering problem in an uncertain environment, which is called the uncertain location set covering model. Using the inverse uncertainty distribution, the uncertain location set covering model can be transformed into an equivalent deterministic location model. Based on this equivalence relation, the uncertain location set covering model can be solved. Second, the maximal covering location problem is investigated in an uncertain environment. This paper first studies the uncertainty distribution of the covered demand that is associated with the covering constraint confidence level α . In addition, we model the maximal covering location problem in an uncertain environment using different modelling ideas, namely, the ( α, β )-maximal covering location model and the α -chance maximal covering location model. It is also proved that the ( α, β )-maximal covering location model can be transformed into an equivalent deterministic location model, and then, it can be solved. We also point out that there exists an equivalence relation between the ( α, β )-maximal covering location model and the α -chance maximal covering location model, which leads to a method for solving the α -chance maximal covering location model. Finally, the ideas of uncertain models are illustrated by a case study.

A maritime search and rescue location analysis considering multiple criteria, with simulated demand

ABSTRACTIn this paper, a multi-criteria analysis is performed on the location of Maritime Search and Rescue resources. Two well-known standard location models (the maximal covering location problem and p-median problem) are modified and applied in accordance with our problem characteristics. The study considers several distinct response vessel types with different capabilities. Future incidents are simulated based on the underlying distribution of historical incidents. The models are formulated and solved using data from the Atlantic region of Canada. The optimal solutions of these two models, along with the current resource arrangement, are compared in terms of five decision criteria: (1) mean access time, (2) primary coverage, (3) backup coverage, (4) Gini index and (5) maximum access time. The results indicate a significant increase in efficiency of resource utilization and availability of service based on access time and coverage criteria for the solutions provided by the optimization models compared to the current situation.

A VNS-LP algorithm for the robust dynamic maximal covering location problem

This study introduces a robust variant of the well-known dynamic maximal covering location problem (DMCLP) and proposes an integer linear programming formulation of the robust DMCLP. A hybrid approach for solving both deterministic and robust variant of the DMCLP is developed, which is based on hybridization of a Variable neighborhood search and a linear programming technique. The main idea is to split the problem into subproblems and to combine optimal solutions of the obtained subproblems in order to construct solution of the initial problem. The results of the proposed hybrid approach on instances of the deterministic DMCLP are presented and compared with the results of the state-of-the-art approach from the literature and with the results of commercial CPLEX solver. The presented computational analysis shows that the proposed hybrid algorithm outperforms other approaches for the DMCLP. In addition, the algorithm was tested on the instances of the robust variant of DMCLP, and obtained results are discussed in detail.

Solving maximal covering location problem using genetic algorithm with local refinement

The maximal covering location problem (MCLP) deals with the problem of finding an optimal placement of a given number of facilities within a set of customers. Each customer has a specific demand and the facilities are to be placed in such a way that the total demand of the customers served by the facilities is maximized. In this article an improved genetic algorithm (GA)-based approach, which utilizes a local refinement strategy for faster convergence, is proposed to solve MCLP. The proposed algorithm is applied on several MCLP instances from literature and it is demonstrated that the proposed GA with local refinement gives better results in terms of percentage of coverage and computation time to find the solutions in almost all the cases. The proposed GA-based approach with local refinement is also found to outperform the other existing methods for most of the small as well as large instances of MCLP.

A Two-Phase Optimization Method for Solving the Multi-Type Maximal Covering Location Problem in Emergency Service Networks

This study introduces the Multi-Type Maximal Covering Location Problem (MTMCLP) that arises from the design of emergency service networks, and represents a generalization of the well-known Maximal Covering Location Problem (MCLP). Differently from the basic MCLP, several types of incidents and emergency units are considered and hierarchy of emergency units of different types is assumed in the MTMCLP. The numbers of available emergency units of each type are limited to some constants. The objective of the MTMCLP is to choose locations for establishing emergency units of each type, such that the total number of covered incidents is maximized. In order to provide a decision maker with optimal solutions in an efficient manner, a two-phase optimization approach to the MTMCLP is designed. In the first phase, a variant of Reduced Variable Neighborhood Search (RVNS) is applied to quickly find a high-quality solution. The obtained RVNS solution is used as a good starting point for the Linear Programming method in the second phase, which returns the optimal solution to the MTMCLP. All constructive elements of the proposed two-phase method, denoted as RVNS-LP, are adapted to the characteristics of the considered problem. The RVNS-LP approach is evaluated on real-life instances obtained from two networks of police units in Montenegro and Serbia, and randomly generated test instances of larger dimensions. Experimental evaluation shows that the proposed RVNS-LP reached all optimal solutions on all real-life test instances in very short CPU time. On generated test instances, the RVNS-LP also returned optimal solutions in all cases, within short running times and significant time savings compared to CPLEX solver. The mathematical model and the proposed two-phase optimization method may be applicable in the design and management of various emergency-service networks.DOI: http://dx.doi.org/10.5755/j01.itc.46.1.13853

GRASP and hybrid GRASP-Tabu heuristics to solve a maximal covering location problem with customer preference ordering

In this study, a maximal covering location problem is investigated. In this problem, we want to maximize the demand of a set of customers covered by a set of p facilities located among a set of potential sites. It is assumed that a set of facilities that belong to other firms exists and that customers freely choose allocation to the facilities within a coverage radius. The problem can be formulated as a bilevel mathematical programming problem, in which the leader locates facilities in order to maximize the demand covered and the follower allocates customers to the most preferred facility among those selected by the leader and facilities from other firms. We propose a greedy randomized adaptive search procedure (GRASP) heuristic and a hybrid GRASP-Tabu heuristic to find near optimal solutions. Results of the heuristic approaches are compared to solutions obtained with a single-level reformulation of the problem. Computational experiments demonstrate that the proposed algorithms can find very good quality solutions with a small computational burden. The most important feature of the proposed heuristics is that, despite their simplicity, optimal or near-optimal solutions can be determined very efficiently.

Optimal allocation for electric vehicle charging stations using Trip Success Ratio

This paper proposes a new model for optimally allocating Plug–in Electric Vehicle (PEV) Charging Stations (CSs) in the network. The model considers Trip Success Ratio (TSR) in order to enhance CS accessibility for PEV drivers. Diversity of usage and different driving habits are considered in the presented model, as well as different trip types (In-city, Highway). The allocation model has two stages: modeling TSR to estimate Charging Station Service Range (CSSR), and the CS allocation stage. In the first stage, the service range of charging stations has been estimated using TSR with consideration of the uncertainty of trip distances (In-city, Highway) and the uncertainty in the Remaining Electric Range (RER) of PEVs. The estimated CSSR is utilized in the CS allocation stage in order to optimize the CS location set that covers the network with a certain guaranteed TSR level. The allocation problem has been formulated as the Maximum Covering Location Problem (MCLP) in order to make the optimal decision for allocating CSs in the network.

Optimizing the configuration of precipitation stations in a space-ground integrated sensor network based on spatial-temporal coverage maximization

The two major rainfall observation techniques, ground-based measurements and remote sensing, have distinct coverage characteristics. Large-scale spatial coverage and long-term temporal coverage cannot be achieved simultaneously by using only ground-based precipitation stations or space-borne sensors. Given the temporal discontinuity of satellite coverage and limited ground-based observation resources, we propose a method for siting precipitation stations in conjunction with satellite-based rainfall sensors to maximize the total spatial-temporal coverage of weighted demand in a continuous observation period. Considering the special principles of deploying precipitation stations and the requirement for continuous coverage in space and time, a time-continuous maximal covering location problem (TMCLP) model is introduced. The maximal spatial coverage range of a precipitation station is determined based on the minimum density required and the site-specific terrain conditions. The coverage of a satellite sensor is calculated for each time period when it passes overhead. The polygon intersection point set (PIPS) is refined to identify finite candidate sites. By narrowing the continuous search space to a finite dominating set and discretizing the continuous observation period to sequential sub-periods, the siting problem is solved using the TMCLP model and refined PIPS. According to specific monitoring purposes, different weighting schemes can be used to evaluate the coverage priority of each demand object. The Jinsha River Basin is selected as the study region to test the proposed method. Satellite-borne precipitation radar is used to evaluate the satellite coverage. The results show that the proposed method is effective for precipitation station configuration optimization, and the model solution achieves higher coverage than the real-world deployment. The applicability of the proposed method, site selection criteria, deployment strategies in different observation modes, and the impacts of different weighting schemes are also discussed.