Location Optimization Model Research Articles

Selecting pharmacies for COVID-19 testing to ensure access.

Rapid diagnostic testing for COVID-19 is key to guiding social distancing orders and containing emerging disease clusters by contact tracing and isolation. However, communities throughout the US do not yet have adequate access to tests. Pharmacies are already engaged in testing, but there is capacity to greatly increase coverage. Using a facility location optimization model and willingness-to-travel estimates from US National Household Travel Survey data, we find that if COVID-19 testing became available in all US pharmacies, an estimated 94% of the US population would be willing to travel to obtain a test, if warranted. Whereas the largest chain provides high coverage in densely populated states, like Massachusetts, Rhode Island, New Jersey, and Connecticut, independent pharmacies would be required for sufficient coverage in Montana, South Dakota, and Wyoming. If only 1,000 ZIP code areas for pharmacies in the US are selected to provide testing, judicious selection, using our optimization model, provides estimated access to 29 million more people than selecting pharmacies simply based on population density.Supplementary InformationThe online version contains supplementary material available at (10.1007/s10729-020-09538-w).

Develop an optimization model for relief facility location in disaster

Develop an optimization model for relief facility location in disaster

Location Optimization Model of Rural Express Station with Vehicle Routes Consideration

The construction of rural express station (RES) is an important measure to improve the express delivery outlets and save the “last mile” distribution cost. In order to scientifically plan the rural express logistics network, a location optimization model of RES is established considering vehicle routes of the distribution center and the tasks of parcel dispersion and collection. With the help of the model, the following items can be determined, such as the location of RES, the village groups serviced by different express stations, the number of delivery vehicles required by the distribution center, the route of each delivery vehicle and the optimal average daily cost of the distribution system. The model is applied to RES location problem in a certain town, and a feasible solution is obtained.

혼합정수계획법을 활용한 전시상황에서의 효율적인 급수분배계획

In wartime situations securing water resources is one of the most important factors for operational success and the military establishes a plan to supply high-quality drinking water over and above the standard requirement in a wartime distribution system. The distribution of water supply is made in accordance with the water quality regulations for the supplied drinking water and the water quality test is tested periodically to ensure consistency. Nevertheless, the possibility of contamination of drinking water always exists and the drinking water pollution in wartime is a very important issue that has a serious impact on sustaining combat capability. In this study, an integrated optimization model of water purification equipment location and water supply distribution is proposed in order to efficiently supply drinking water to combat units. Through the numerical analysis using examples we show the validity and applicability of the proposed models.

An MI-SDP Model for Optimal Location and Sizing of Distributed Generators in DC Grids That Guarantees the Global Optimum

This paper deals with a classical problem in power system analysis regarding the optimal location and sizing of distributed generators (DGs) in direct current (DC) distribution networks using the mathematical optimization. This optimization problem is divided into two sub-problems as follows: the optimal location of DGs is a problem, with those with a binary structure being the first sub-problem; and the optimal sizing of DGs with a nonlinear programming (NLP) structure is the second sub-problem. These problems originate from a general mixed-integer nonlinear programming model (MINLP), which corresponds to an NP-hard optimization problem. It is not possible to provide the global optimum with conventional programming methods. A mixed-integer semidefinite programming (MI-SDP) model is proposed to address this problem, where the binary part is solved via the branch and bound (B&B) methods and the NLP part is solved via convex optimization (i.e., SDP). The main advantage of the proposed MI-SDP model is the possibility of guaranteeing a global optimum solution if each of the nodes in the B&B search is convex, as is ensured by the SDP method. Numerical validations in two test feeders composed of 21 and 69 nodes demonstrate that in all of these problems, the optimal global solution is reached by the MI-SDP approach, compared to the classical metaheuristic and hybrid programming models reported in the literature. All the simulations have been carried out using the MATLAB software with the CVX tool and the Mosek solver.

A MIQP model for optimal location and sizing of dispatchable DGs in DC networks

The allocation and dimensioning of distributed generators (DGs) in direct current (DC) power grids were addressed in this study by using a mixed-integer quadratic programming (MIQP) formulation. The MIQP model corresponded to an approximation of the mixed-integer nonlinear programming (MINLP) model that represents this problem correctly. The proposed MIQP had, for its objective function, the minimization of the power losses; as constraints, it had power balance, voltage regulation, distributed generation capacity, and the number of DGs available, among others. The general algebraic modeling system (GAMS) was employed for solving the proposed MIQP as well as the MINLP formulation. Simulation results for one DC network with 21 nodes and another with 69 revealed that the proposed MIQP model obtains high-quality results regarding the locations of the generators, the objective function, and the power dispatch in comparison to the exact MINLP model and metaheuristic techniques recently reported in specialized literature.

Hierarchical faulted line section location method for low‐voltage active distribution network considering information distortion

Distortion of fault monitoring information is an important factor that affects the accuracy of faulted line section location in low-voltage active distribution networks (ADNs). This paper proposes a faulted line section location method that considers the layered solution for monitoring information distortion, to improve the accuracy and efficiency of fault location in low-voltage ADNs. A multi-target fault section location optimization model that considers information distortion, multipoint faults, and multiple information distortion types is formulated. A combination of information distortion factors is introduced to represent various types of information distortion and to transform the original optimization model into an unconstrained 0-1 programming problem. A hierarchical fault location algorithm for segmenting the distribution network is designed to solve the low accuracy and efficiency of direct solutions for fault location models resulting from a large number of active distribution line sections. Simulation results show that the fault location method considering information distortion effectively guarantees the accuracy and solution efficiency of faulted line section location of low-voltage ADN.

Design of a location and transportation optimization model including quality of service using constrained multinomial logit

The design of an integrated network with decisions about tactical transportation and strategic locations is complicated and challenging. In addition to the need to consider cost issues, the consumers’ preferences will also have a significant impact on the resulting network. We propose an integrated transportation and location optimization model for designing logistic networks. Our model uses a hybrid iterative heuristic based on a genetic algorithm and a constrained multinomial logit, which includes consumers’ preferences and quality of service variables. Our results show relevant differences when considering, along with network costs, parameters related to the consumers: travel distance, congestion, waiting time, and service time.

Conjugated mathematical model for optimal location of industrial objects

The urgent problem related to solving the problems of monitoring and predicting the ecological state of the air basin in industrial regions is considered in the paper. It provides a brief review of scientific publications devoted to these problems. A mathematical model has been developed to study, predict and monitor the concentration of harmful substances in the atmosphere. The model takes into account weather and climate conditions, soil erosion, physicomechanical properties of aerosol particles, and other factors affecting the process under consideration as a whole; it is designed for optimal location of newly constructed production facilities.

Location and Capacity Selection Method for Electric Thermal Storage Heating Equipment Connected to Distribution Network Considering Load Characteristics and Power Quality Management

High-permeability distributed wind power and photovoltaic systems are connected to the distribution network, which exacerbates the volatility and uncertainty of the distribution network. Furthermore, with the increasing demand of heating in winter and environmental protection, the wide use of electric thermal storage heating equipment (ETSHE) can promote distributed renewable energy utilization. However, an unplanned ETSHE connection to the distribution network may cause serious power quality problems. A new method of equipment location and capacity is proposed, which considered the improvement of power quality and load demand characteristics of the distribution network. First, based on heat load portrait technology, the node’s thermal load classification prediction was carried out to provide the data basis for the model solution. Second, the multi-objective optimal location and capacity programming model including harmonic distortion rate, voltage deviation, voltage fluctuation, and ETSHE cost was established. Then, the system nodes were preprocessed based on the sensitivity analysis method to reduce the number of installation nodes to be selected, and a feasible alternative set of installation nodes for the optimal configuration model of ETSHE could be obtained. Finally, the improved multi-objective particle swarm optimization algorithm was used to solve the model, and the data envelope analysis method was used to evaluate the power quality of each access scheme. The analysis of the numerical example shows that it can not only satisfy the user′s heat demand, but also effectively improve the power quality by rationally planning the location and capacity of ETSHE, which achieves the safe and efficient utilization of energy.

An optimization model for electric vehicle charging infrastructure planning considering queuing behavior with finite queue length

• An optimization model was proposed to deploy the optimal locations and capacities of charging infrastructure under charging queuing behavior with finite queue length. • The M / M / S / N queuing model was adopted to restrict finite queue length and finite charging service capacity of each charging station. • The quantity of chargers allocated at each station was set as variable. • The sensitivity analysis was conducted to illustrate the impact of key parameters on various cost components and optimal results. As clean energy vehicles, electric vehicles (EVs) have been paid unprecedented attention in dealing with serious energy crises and heavy tailpipe emission in recent years. Due to its limited battery range and long charging time, it's significant to reasonably determine the locations and capacities of EV charging infrastructure. There are two research gaps in existing researches: unrealistically assuming the infinite queuing length based on the M / M /1 or M / M / S queuing model and lacking the research on variable quantities of chargers allocated at different charging stations. To fill up these gaps, we propose an optimal location model to determine the optimal locations and capacities of EV charging infrastructure to minimize the comprehensive total cost, which considers the charging queuing behavior with finite queue length and various siting constrains. And the results show that (1) the proposed model has a good performance in determining the optimal locations and capacities of EV charging infrastructure (i.e. the optimal locations of charging stations, the optimal quantities of chargers installed at each charging station, the optimal allowable maximum queue length and maximum capacity of each charging station); (2) the quantity of chargers and allowable maximum queue length at each charging station are consistent with the distribution densities of existing charging stations at these locations; (3) the two parameters of unit value of time and unit distance cost have a more significant impact on the total cost. Therefore, the total cost can be effectively reduced by appropriately increasing the quantity of chargers at each charging station and the distribution density of charging stations.

Multi-coverage optimal location model for emergency medical service (EMS) facilities under various disaster scenarios: a case study of urban fluvial floods in the Minhang district of Shanghai, China

Abstract. Emergency medical service (EMS) response is extremely critical for pre-hospital lifesaving when disaster events occur. However, disasters increase the difficulty of rescue and may significantly increase the total travel time between dispatch and arrival, thereby increasing the pressure on emergency facilities. Hence, facility location decisions play a crucial role in improving the efficiency of rescue and service capacity. In order to avoid the failure of EMS facilities during disasters and meet the multiple requirements of demand points, we propose a multi-coverage optimal location model for EMS facilities based on the results of disaster impact simulation and prediction. To verify this model, we explicitly simulated the impacts of fluvial flooding events using the 1-D–2-D coupled flood inundation model FloodMap. The simulation results suggested that even low-magnitude fluvial flood events resulted in a decrease in the EMS response area. The integration of the model results with a geographical-information-system (GIS) analysis indicated that the optimization of the EMS locations reduced the delay in emergency responses caused by disasters and significantly increased the number of rescued people and the coverage of demand points.

Optimal Location and Capacity of the Distributed Energy Storage System in a Distribution Network

Given the current situation of large-scale energy storage system (ESS) access in distribution network, a practical distributed ESS location and capacity optimization model is proposed. Firstly, a weighted voltage sensitivity is proposed to select the grid-connected node set of ESS. On this basis, the distributed ESS location model is established, which aims at reducing voltage deviation and active power loss of the distribution network. Then, an ESS partition method based on the improved flame propagation model is proposed, and the partition results are obtained by constructing the flammability of nodes, the wind direction of flame propagation, speed of flame propagation and other indicators. Based on partition results, the capacity optimization model is established with the maximum annual net income of energy stored in the partition as the objective function. Finally, the improved IEEE-33 bus distribution network is used to demonstrate the effectiveness and feasibility of the proposed model.

Optimal multi-objective distributed generation location and capacity by elite strategy genetic algorithm considering timing characteristics

In this paper, a distributed generation location and capacity optimization model considering the probability of scenario occurrence is established. The optimization objective is to minimize the total cost of investment, annual power loss of distribution network and node voltage deviation. The improved genetic algorithm with elitist retention mechanism is used to solve the model. The IEEE33 system is used to show the location and constant capacity of the distributed power supply under different conditions. It shows that the reasonable and optimized configuration of the distributed power supply can obtain better voltage quality and minimize the cost function, which verifies the effectiveness of the proposed model.

Optimization of recyclable MSW recycling network: A Chinese case of Shanghai

The establishment of recycling network is critical to improve municipal solid waste (MSW) management. However, how to determine the best locations for the recycling stations and recycling centers remains to be solved. Under such a circumstance, this study aims to forecast the MSW generation and develop a cost-based location optimization model using p-median method so that the optimal scale and location of recycling centers can be identified. Shanghai, with an ambitious plan for promoting MSW recycling at the city level, was selected as a case study city. Results show that Shanghai’s MSW generation rate will be about 3% from 2017 to 2020. Regional distribution analysis shows that the downtown areas have higher intensity for MSW generation due to high population density and consumption level. Fourteen regional recycling centers were identified to be the optimal places for establishing recycling centers. The achievement of this scenario can lead to the lowest total cost of 144 million Chinese Yuan. Moreover, the optimal results may change if unit transportation cost and unit scale cost are changed. For instance, the optimal numbers of recycling centers will increase with the increase of unit transportation cost or decrease of unit scale cost. Finally, model limitations and policy recommendations are raised by considering the local realities.

Agglomeration or separation: Store patterns through an optimal location model

The purpose of this paper is to show how different location patterns of stores emerge as a result of competition between retailers selling similar goods. Our model assumes the interactions between stores arise from the customer’s behavior. Two aspects were taken into account in characterizing customer’s choices: first, that the decisions depend on the total expected cost of buying the product under consideration; second, that there is consumer heterogeneity in regards to the reservation price each is willing to pay for each good. Retailers choose location and price as to maximize their total profit. Numerical evaluations show that reservation price distributions are determinant in the optimal location and in the behavior of equilibrium prices, which can increase, decrease or have a non monotonic behavior as the number of stores at the same location increases.

An exact MINLP model for optimal location and sizing of DGs in distribution networks: A general algebraic modeling system approach

This paper addresses the classical problem of optimal location and sizing of distributed generators (DGs) in radial distribution networks by presenting a mixed-integer nonlinear programming (MINLP) model. To solve such model, we employ the General Algebraic Modeling System (GAMS) in conjunction with the BONMIN solver, presenting its characteristics in a tutorial style. To operate all the DGs, we assume they are dispatched with a unity power factor. Test systems with 33 and 69 buses are employed to validate the proposed solution methodology by comparing its results with multiple approaches previously reported in the specialized literature. A 27-node test system is also used for locating photovoltaic (PV) sources considering the power capacity of the Caribbean region in Colombia during a typical sunny day. Numerical results confirm the efficiency and accuracy of the MINLP model and its solution is validated through the GAMS package.

Relaxed convex model for optimal location and sizing of DGs in DC grids using sequential quadratic programming and random hyperplane approaches

This report addresses the problem of optimal location and sizing of constant power sources (distributed generators (DGs)) in direct current (DC) networks for improving network performance in terms of voltage profiles and energy efficiency. An exact mixed-integer nonlinear programming (MINLP) method is proposed to represent this problem, considering the minimization of total power losses as the objective function. Furthermore, the power balance per node, voltage regulation limits, DG capabilities, and maximum penetration of the DG are considered as constraints. To solve the MINLP model, a convex relaxation is proposed using a Taylor series expansion, in conjunction with the transformation of the binary variables into continuous variables. The solution of the relaxed convex model is constructed using a sequential quadratic programming approach to minimize the linearization error using the Taylor series method. The solution of the relaxed convex model is used as the input for a heuristic random hyperplane method that facilitates the recovery of binary variables that solve the original MINLP model. Two DC distribution feeders, one having 21 and the other having 69 nodes, were used as test systems. Simulation results were obtained using the MATLAB/quadprog package and contrasted with the large-scale nonlinear solvers available for General algebraic modeling system (GAMS) software metaheuristic optimization approaches to demonstrate the robustness and effectiveness of our proposed methodology.

Seeing the Night Sky

Abstract. Clear, dark night skies are harder to see now than ever before, and it will only become more difficult as people continue to move into heavily light polluted and expanding urban areas. Dark Sky Parks offer a place where anyone can go to experience true dark skies, observing the stars and other celestial bodies in conditions unencumbered by artificial light and other sources of pollution. An atlas of these Dark Sky Parks will raise awareness about their existence and locations with the goal of education and outreach. Observatories may be utilized with a similar outcome; however, they need to be located in close proximity to large populations but far enough away to optimize dark skies. This research presents an approach for mapping Dark Sky Parks in the United States through the ongoing production of Seeing the Night Sky: An Atlas of Dark Sky Parks, and a related GIS location optimization model to identify potential observatory locations in a defined study area based on land availability, slope, presence of water/floodplain, proximity to populated places, light pollution, elevation, and transportation infrastructure.

Analyzing the relationship between stadium location and attendance: A location modeling of Major League Baseball (MLB)

The location of a sports facility is one of the significant factors in economically operating and maintaining the facility. The present study used a location theory model to examine the influence of the Major League Baseball (MLB) stadium location on attendance (N=348) for the 2006-2017 MLB regular seasons, taking into consideration the population, median income, and distance between the stadium and the population center of counties nearby the stadium. The optimal location model was determined as the inverse proportion of the squared distance of the first nearest county, and location significantly influenced the attendance (p<.05). Then, based on the results of the location model, the current study analyzed the relationship between the MLB attendance and other attendance determinants by using hierarchical linear modeling. Among 14 different determinants, six variables (i.e., stadium capacity, ticket price, season, as well as the home team’s quality, payroll, and star players) were revealed in the findings to have a significant influence on the MLB attendance (p<.05).