Covering Location Problem Research Articles

A family of models in support of realistic drug interdiction location decision‐making

AbstractLong‐standing federal drug‐control policy aims to reduce the flow of narcotics into the USA, in part by intercepting cocaine shipments en route from South American production regions to North American consumer markets. Drug interdiction efforts operate over a large geographic area, containing complex drug trafficking networks in a dynamic environment. The extant interdiction models in the operations research and location science literature do not realistically model the objectives of and constraints on the interdiction forces, and therefore counterdrug organizations do not employ those models in their decision‐making processes. This article presents three new models built on the maximal covering location problem (MCLP): the maximal covering location problem for interdiction (MCLP‐I), multiple‐demand maximal covering location problem (MD‐MCLP), and multiple‐type maximal covering location problem (MT‐MCLP). These are novel formulations that permit multiple types of demands and facilities to be covered, and the utility of these formulations is demonstrated in the context of counterdrug operations. Optimal interdiction locations are determined within the geography of the Central American transit zone, using a coupled GIS and optimization framework. The results identify the optimal interdiction locations for known or estimated drug shipments and can constrain those optimal locations by differentiating among drug traffickers, the types of interdiction resources, and agency jurisdictions. This research both demonstrates the flexibility in designing alternative interdiction scenarios and presents novel covering models that may be extended to other application areas and operational contexts.

On the Parameterized Complexity of the Expected Coverage Problem

The Maximum Covering Location Problem (MCLP) is a well-studied problem in the field of operations research. Given a network with positive or negative demands on the nodes, a positive integer k, the MCLP seeks to find k potential facility centers in the network such that the neighborhood coverage is maximized. We study the variant of MCLP where edges of the network are subject to random failures due to some disruptive events. One of the popular models capturing the unreliable nature of the facility location is the linear reliability ordering (LRO) model. In this model, with every edge e of the network, we associate its survival probability 0 ≤ pe ≤ 1, or equivalently, its failure probability 1 − pe. The failure correlation in LRO is the following: If an edge e fails then every edge e^{prime } with p_{e^{prime }} leq p_{e} surely fails. The task is to identify the positions of k facilities that maximize the expected coverage. We refer to this problem as Expected Coverage problem. We study the Expected Coverage problem from the parameterized complexity perspective and obtain the following results. 1. For the parameter pathwidth, we show that the Expected Coverage problem is W[1]-hard. We find this result a bit surprising, because the variant of the problem with non-negative demands is fixed-parameter tractable (FPT) parameterized by the treewidth of the input graph. 2. We complement the lower bound by the proof that Expected Coverage is FPT being parameterized by the treewidth and the maximum vertex degree. We give an algorithm that solves the problem in time 2^{{mathcal {O}}({textbf {tw}} log {varDelta })} n^{{mathcal {O}}(1)}, where tw is the treewidth, Δ is the maximum vertex degree, and n the number of vertices of the input graph. In particular, since Δ ≤ n, it means the problem is solvable in time n^{{mathcal {O}}({textbf {tw}})} , that is, is in XP parameterized by treewidth.

Optimizing the Spatial Location of Street Lights in Belle Isle, Michigan

Improved street lighting can provide better use of public space and helps to promote safety while driving or walking. In terms of balancing benefits and impacts, on the basis of cost saving, this research adopts two prominent mathematical models, the maximal coverage location problem and the location set covering problem, to optimize street light locations. By comparing with the currently installed lights following the rule of thumb, the mathematical models in this research achieve the effect of saving electric energy while meeting residents’ traffic safety needs and living conditions. Furthermore, the models can provide greater coverage of illumination using the same amount of energy.

Upgrading edges in the maximal covering location problem

We study the upgrading version of the maximal covering location problem with edge length modifications on networks. This problem aims at locating p facilities on the vertices (of the network) so as to maximise coverage, considering that the length of the edges can be reduced at a cost, subject to a given budget. Hence, we have to decide on: the optimal location of p facilities and the optimal edge length reductions.This problem is NP-hard on general graphs. To solve it, we propose three different mixed-integer formulations and a preprocessing phase for fixing variables and removing some of the constraints. Moreover, we strengthen the proposed formulations including valid inequalities. Finally, we compare the three formulations and their corresponding improvements by testing their performance over different datasets.

Set Covering Model Using Greedy Heuristic Algorithm to Determine The Temporary Waste Disposal Sites in Palembang

Optimizing the facility location has a vital role in providing services to the community. This study aims to determine the Temporary Waste Disposal Site (TWDS) in Sako District, Palembang City. The distance data between each TWDS in Sako District is used to formulate the Set Covering model, consisting of the Set Covering Location Problem (SCLP) model and the p-Median Problem model. The classical approach is made by solving both models using Lingo 18.0 software. The Greedy Heuristic algorithm is used as the heuristic approach. Based on the results and discussion, Sako District consists of 4 Villages and 9 TWDS. The SCLP and p-Median Problem models with LINGO 18.0 software and the Greedy Heuristic algorithm show a difference. The study results suggest using the optimal solution resulting from the Greedy Heuristic algorithm because it can meet all requests in Sako District. Research shows that there are six optimal TWDS in Sako District. However, several locations are still not optimal, so it is recommended that there are an additional 14 new TWDS facilities in Sako District to serve all requests.

A Multi-objective variable neighborhood search for the maximal covering location problem with customer preferences

A Multi-objective variable neighborhood search for the maximal covering location problem with customer preferences

Advanced Network Connectivity Features and Zonal Requirements in Covering Location Problems

Advanced Network Connectivity Features and Zonal Requirements in Covering Location Problems

A robust linear model for the maximum expected coverage location problem considering the relative coverage

Emergency medical services (EMS) stations reduce mortality and irreparable damage from injuries through the timely treatment of patients. After performing the initial measures at the scene of the accident, if necessary, they transfer the patient to the hospital. In such cases, the goal is to save human lives. Thus, suggestions and solutions that can improve the performance of these centers are very welcome. One of the most important parameters in providing high-quality EMS is the timing of these services. Therefore, the location of these centers plays a key role in diminishing the response time to demand. In that regard, the location of these centers in cities, especially large and densely populated cities, is very important. In this study, in order to answer the mentioned questions, a linear mathematical model based on the maximum expected coverage model is presented. In this model, by considering the relative coverage conditions, the best locations in the city, as well as the coverage of demand points and distance traveled by the vehicles will be obtained. Furthermore, robust optimization (RO) is used to provide better situations for the operation of the model. Finally, according to the results, it is found that the proposed model has a better resolution time than nonlinear models and is also able to solve cases with high input data. The proposed model is implemented in District 10 of Tehran, Iran.

Could Petrol Stations Play a Key Role in Transportation Electrification? A GIS-Based Coverage Maximization of Fast EV Chargers in Urban Environment

To achieve net-zero in the transportation sector, there is a need to deploy public electric vehicle (EV) fast chargers to boost customer confidence. Currently, charge point operators and EV manufacturers focus on deploying chargers to cover highway networks and the progress in urban environments is inadequate. This is becoming an obstacle for potential EV buyers who do not have access to dedicated chargers or cannot afford expensive EVs with larger battery packs. Since mainstream combustion engine vehicle drivers are accustomed to using petrol stations, this paper examines the suitability of such sites as candidate locations to deploy fast chargers. Spatial analysis is carried out by comparing their coverage performance with existing locations of the fast chargers. More specifically, the location problem is modelled as a maximum coverage location problem (MCLP) and solved using a geographic information system (GIS) based platform. The spatial optimization problem is solved using a linear-programming relaxation based MCLP algorithm developed in Python. Five cities with growing populations, namely San Clara, CA, Salt Lake City, UT, Raleigh, NC, Denver, CO, and Los Angeles, CA, are chosen as case studies. The location analysis is carried out with two demand metrics (population and road traffic) using actual GIS data collected from public authorities. The results show that deploying fast chargers at existing fuel stations significantly increases the coverage needed for EVs. This study will provide useful insights into EV fast charging station planning in urban cities, as the related research is still in its infancy.

Equalizing the spatial accessibility of emergency medical services in Shanghai: A trade-off perspective

Planning public services needs to promote equal access across geographic areas and between demographic groups. However, most location-allocation models emphasize efficiency such as minimal travel burden or maximal demand coverage while omitting the equality issue. This case study optimizes the emergency medical service (EMS) in Shanghai from a trade-off perspective by comparing two models. One is the 2-step optimization (2SO) model that uses the maximum covering location problem (MCLP) to site new facilities and then a quadratic programming (QP) method to optimize capacities, the other performs location selection and capacity optimization simultaneously through greedy optimization (GO). There are several findings from various simulation scenarios. First, the GO model is more effective in optimizing equality, but the 2SO model offers a more balanced approach by covering more people within the mandatory response time while improving access equality. Secondly, solutions of both models change as demands and travel costs vary over time and call for dynamic adjustment of resource allocation. Thirdly, it is important to coordinate EMS with other agencies to ensure reasonable road connectivity and make contingency plans in events such as floods, earthquakes and other natural disasters.

Maximum Coverage Location Model for Fire Stations with Top Corporate Risk Locations

The fire station location is a critical decision to optimize the coverage level as measured in terms of the response time. This paper focuses on optimizing the coverage problem, especially in the fire protection field, with new model features to incorporate realistic business challenges such as location criticality and secondary coverage. We extend the deterministic Maximum Coverage Location Problem to account for Top Corporate Risk locations being covered by different fire stations as primary and secondary coverage. To deal with the response time uncertainty arising in practice, we propose a new binary linear problem based on the Maximum Expected Covering Location Problem. By exploiting the model structural characteristics, we prove that the model complexity can be substantially reduced to yield an efficient solution. In the numerical experiments, we use a real case study with five years of historical data. The optimization results of the models yield a priority ranking of the fire stations to open and show the value of incorporating the coverage uncertainty. Finally, we also compare our model with uncertainty with the standard scenario-based optimization to extend the numerical results.

Probabilistic Set Covering Location Problem in Congested Networks

This paper focuses on designing a facility network, taking into account that the system may be congested. The objective is to minimize the overall fixed and service capacity costs, subject to the constraints that for any demand the disutility from travel and waiting times (measured as the weighted sum of the travel time from a demand to the facility serving that demand and the average waiting time at the facility) cannot exceed a predefined maximum allowed level (measured in units of time). We develop an analytical framework for the problem that determines the optimal set of facilities and assigns each facility a service rate (service capacity). In our setting, the consumers would like to maximize their utility (minimize their disutility) when choosing which facility to patronize. Therefore, the eventual choice of facilities is a user-equilibrium problem, where at equilibrium, consumers do not have any incentive to change their choices. The problem is formulated as a nonlinear mixed-integer program. We show how to linearize the nonlinear constraints and solve instead a mixed-integer linear problem, which can be solved efficiently.

A multi-objective formulation of maximal covering location problem with customers’ preferences: Exploring Pareto optimality-based solutions

The maximal covering location problem (MCLP) is a well-known combinatorial optimization problem with several applications in emergency and military services as well as in public services. Traditionally, MCLP is a single objective problem where the objective is to maximize the sum of the demands of customers which are served by a fixed number of open facilities. In this article, a multi-objective MCLP is proposed where each customer has a preference for each facility. The multi-objective MCLP with customers’ preferences (MOMCLPCP) deals with the opening of a fixed number of facilities from a given set of potential facility locations and then customers are assigned to these opened facilities such that both (i) the sum of the demands of customers and (ii) the sum of the preferences of the customers covered by these opened facilities are maximized. A Pareto-based multi-objective harmony search algorithm (MOHSA), which utilizes a harmony refinement strategy for faster convergence, is proposed to solve MOMCLPCP. The proposed MOHSA is terminated based on the stabilization of the density of non-dominated solutions. For experimental purposes, 82 new test instances of MOMCLPCP are generated from the existing single objective MCLP benchmark data sets. The performance of the proposed MOHSA is compared with the well-known non-dominated sorting genetic algorithm II (NSGA-II), and it has been observed that the proposed MOHSA always outperforms NSGA-II in terms of computation time. Moreover, statistical tests show that the objective values obtained from both algorithms are comparable.

Spatial optimization of multiple biomass utilization for large-scale bioelectricity generation

This study developed a geographical information system-based methodology to maximize the environmental and economic efficiency of large-scale energy plants using different types of biomass. As a precursor to the optimization modelling, multi-criteria spatial analyses and then transport cost optimization are applied taking into account spatial biomass availability and existing road networks, in order to identify optimal biomass energy plant sites for different combinations of biomass types. A geographical information system integrated with a capacitated maximal covering location problem model was employed to assign biomass supply points to biomass energy plants. Capacity limits of the plants and a defined maximum transportation distance were taken into consideration. The resulting information was used to examine major challenges in establishing a large-scale biomass energy plant, biomass supply logistics, environment cost and anticipated traffic congestion. A sensitivity analysis was also carried out to review the influence of plant capacity and maximum transportation distance on economic and environmental sustainability. The proposed methodology was employed utilizing agricultural and forest residues for bioelectricity generation in Queensland, Australia. It was found that 100% bagasse had the highest eco-efficiency for bioelectricity generation from multiple biomass combinations. In contrast, the combination of 70% sawmill residues and 30% forest harvest residues showed the lowest level of traffic congestion (2 trucks per hour). In addition, the impact of traffic congestion of bulky sugarcane residues can be reduced by adding forest residues to the biomass supply. The advantages of the resulting solution are further enhanced when social impacts such as energy security, new income opportunities and job creation are taken into account in addition to the sustainability aspects.

Nash equilibrium sorting genetic algorithm for simultaneous competitive maximal covering location with multiple players

In this article, a new genetic algorithm (GA), called the Nash equilibrium sorting genetic algorithm (NESGA,) is introduced to identify Nash equilibria for the competitive maximal covering location problem with two and three competitors, which is a combinatorial game theory problem where it is computationally intractable to enumerate all decision options of the competitors. Although GAs are widely used in combinatorial optimization, their applications to non-cooperative, simultaneous games have been limited owing to challenges in guiding the evolutionary search to Nash equilibria, which are not necessarily on the Pareto front of the search space and cannot be found by current multi-objective GAs. A novel fitness assignment strategy is proposed to help the NESGA to converge to multiple Nash equilibria. Computational experiments show that the NESGA can discover multiple Nash equilibria in a single run and outperform other game-theoretic GAs.

Extended Maximal Covering Location and Vehicle Routing Problems in Designing Smartphone Waste Collection Channels: A Case Study of Yogyakarta Province, Indonesia

Most people will store smartphone waste or give it to others; this is due to inadequate waste collection facilities in all cities/regencies in Indonesia. In Yogyakarta Province, there is no electronic waste collection facility. Therefore, an e-waste collection network is needed to cover all potential e-waste in the province of Yogyakarta. This study aims to design a collection network to provide easy access to facilities for smartphone users, which includes the number and location of each collection center and the route of transporting smartphone waste to the final disposal site. We proposed an extended maximal covering location problem to determine the number and location of collection centers. Nearest neighbor and tabu search are used in forming transportation routes. The nearest neighbor is used for initial solution search, and tabu search is used for final solution search. The study results indicate that to facilitate all potential smartphone waste with a maximum distance of 11.2 km, the number of collection centers that must be established is 30 units with three pick-up routes. This research is the starting point of the smartphone waste management process, with further study needed for sorting, recycling, repairing, or remanufacturing after the waste has been collected.

Enhanced coverage by integrating site interdependencies in capacitated EMS location models

In order to allocate limited resources in emergency medical services (EMS) networks, mathematical models are used to select sites and their capacities. Many existing standard models are based on simplifying assumptions, including site independency and a similar system-wide busyness of ambulances. In practice, when a site is busy, a call is forwarded to another site. Thus, the busyness of each site depends not only on the rate of calls in the surrounding area, but also on interactions with other facilities. If the demand varies across the urban area, assuming an average system-wide server busy fraction may lead to an overestimation of the actual coverage. We show that site interdependencies can be integrated into the well-known Maximum Expected Covering Location Problem (MEXCLP) by introducing an upper bound for the busyness of each site. We apply our new mathematical formulation to the case of a local EMS provider. To evaluate the solution quality, we use a discrete event simulation based on anonymized real-world call data. Results of our simulation-optimization approach indicate that the coverage can be improved in most cases by taking site interdependencies into account, leading to an improved ambulance allocation and a faster emergency care.

Identifying locations for new bike-sharing stations in Glasgow: an analysis of spatial equity and demand factors

ABSTRACT Worldwide bike-sharing systems are growing in popularity as an alternative, environmentally friendly mode of transportation. As cities seek to further develop bike-sharing programmes, it is important to consider how systems should expand to simultaneously address existing inequalities in accessibility, and best serve demand. In this paper, we determine ideal locations for future bike-sharing stations in Glasgow, Scotland, by integrating demand modelling with accessibility considerations. We began by analysing the spatio-temporal trends of bike-sharing usage, and assessed the spatial equity of access to stations in Glasgow. To identify important determinants of bike-sharing demand, we ran an ordinary least squares regression model using bike sharing trip data from Nextbike Glasgow. We then quantifiably measured the level of spatial accessibility to stations by applying the two-step floating catchment area (2SFCA) methodology and ran a GIS weighted overlay analysis using the significant determinants of station demand. Lastly, we combined the demand and accessibility results to determine where new stations should be located using a maximum covering location problem (MCLP) that maximized the population served. Our results show that distance from transit stations, distance from downtown, employment rates, and nearby cycling lanes are significant factors affecting station-level demand. Furthermore, levels of spatial access were found to be highest primarily in the centre and eastern neighbourhood of Glasgow. These findings aided in determining areas to prioritize for future station locations, and our methodology can easily be applied to other bike-share programmes with adjustments according to varying aims for system expansion.

A variable neighborhood search for the budget-constrained maximal covering location problem with customer preference ordering

A variable neighborhood search for the budget-constrained maximal covering location problem with customer preference ordering

Solving Classic Discrete Facility Location Problems Using Excel Spreadsheets

There are a variety of discrete facility location models that have practical relevance for operations management and management science courses. Integer linear programming (ILP) is the standard technique for solving such problems. An alternative approach that is often conceptually appealing to students is to pose the problem as one of finding the best possible subset of p facilities out of n possible candidates. I developed an Excel workbook that allows students to interactively evaluate the quality of different subsets, to run a VBA macro that finds the optimal subset, or to solve an ILP formulation that finds the optimal subset. Spreadsheets are available for five classic discrete location models: (1) the location set-covering problem, (2) the maximal covering location problem, (3) the p-median problem, (4) the p-centers problem, and (5) the simple plant location problem. The results from an assignment in a master’s-level business analytics course indicate that the workbook facilitates a better conceptual understanding of the precise nature of the discrete facility location problems by showing that they can be solved via enumeration of all possible combinations of p subsets that can be drawn from n candidate locations. More important, students directly observe the superiority of ILP as a solution approach as n increases and as p approaches n/2.