Sequential facility location with distance dependent demand

Systems providing identical service to many population centers frequently face the issue of where to locate the next retail outlet, branch, store, etc. In such systems the demand for the facilities' service depends mainly on the distance between facilities and customers. It is assumed that there are already m facilities located on a network to respond to the demand at the nodes. The paper addresses the problems of finding a location on the network for the (m +1 )st facility corresponding to a given total expected demand and of determining which demand points will be served by which facility. Also the range of the total expected demand values that can be realized along each link in the m +1 facility system is determined. Examples and a discussion of the results are provided.     

Reconfiguring a set of coverage-providing facilities under travel time uncertainty

We study networks of facilities that must provide coverage under conditions of uncertainty with respect to travel times and customer demand. We model this uncertainty through a set of scenarios. Since opening new facilities and/or closing existing ones is often quite expensive, we focus on optimal re-configuration of the network, that is finding a facility set that achieves desired thresholds with respect to expected and minimal coverage, while retaining as many of the existing facilities as possible. We illustrate our model with an example of Toronto Fire Service. We demonstrate that relocating just a few facilities can have the same effect as opening a similar number of new ones. We develop exact and approximate solution approaches and test them with computational experiments. Algorithm based on Tabu Search (with certain novel components) appears to be particularly successful for this problem. We also analyze the multi-objective version of the problem, where the expected and minimum coverage levels are treated as objectives in addition to the objective of maximizing the number of pre-existing facilities in the final location set.     

Data center supply chain configuration design: A two-stage decision approach

Data centers are special-purpose facilities that enable customers to perform cloud based real-time online transactions and rigorous computing operations. Service levels of data center facilities are characterized by response time between query and action, which to a large extent depends on data center location and data travel distance. Another aspect of service level is resource up-time availability, which is determined by data center configuration. Data center location and configuration decisions are, therefore, of great significance to ensure uninterrupted operations in customers of manufacturing and service industries relying on cloud-based computing resources. In this study, following a grid-based location approach, we present two mixed integer linear programming models for capacitated single-source data center location-allocation problems. The first model provides optimal locations, capacities and configurations of data centers, and allocation of demands to open facilities when there is no existing facilities in the region. Our second model considers the decision problem of meeting new demand when the existing demand is met by the already opened facilities. We term these newly arrived demand as replication demand, which results either from emergence of new users of existing customers at distant locations in the future, or as a means of increasing data resilience by creating data replication as a backup. To solve the decision problem for meeting primary and replication demand optimally, we propose a two-stage decision algorithm. The algorithm provides optimal locations, capacities and configurations for new data centers, capacity addition decisions to the existing facilities and subsequent allocation of demands. Both models and solution algorithm are implemented using AMPL programming language and solved with CPLEX solver. The models are found to be scalable and capable to provide high quality solutions in reasonable time.     

The flow-refueling location problem for alternative-fuel vehicles

Beginning with Hodgson (Geogr.Anal.22(1990) 270), several researchers have been developing a new kind of location-allocation model for “flow capturing.” Instead of locating central facilities to serve demand at fixed points in space, their models aim to serve demand consisting of origin-destination flows along their shortest paths. This paper extends flow-capturing models to optimal location of refueling facilities for alternative-fuel (alt-fuel) vehicles, such as hydrogen fuel cells or natural gas. Existing flow-capturing models assume that if a flow passes just one facility along its path, it is covered. This assumption does not carry over to vehicle refueling because of the limited range of vehicles. For refueling, it may be necessary to stop at more than one facility in order to successfully refuel the entire path, depending on the vehicle range, the path length, and the node spacing. The Flow Refueling Location Model (FRLM) optimally locates p refueling stations on a network so as to maximize the total flow volume refueled. This paper presents a mixed-integer programming formulation for the nodes-only version of the problem, as well as an algorithm for determining all combinations of nodes that can refuel a given path. A greedy-adding approach is demonstrated to be suboptimal, and the tradeoff curve between number of facilities and flow volume refueled is shown to be nonconvex.     

Evaluating spatial service and layout efficiency of municipal Wi-Fi facilities for SmartCity planning: A case study of Wuhan city,China

This paper explores an approach to evaluating spatial service and layout efficiency of municipal Wi-Fi facilities for cyber infrastructure planning in the construction of a smart city. Based on the equilibrium principle that Wi-Fi services supply should meet the spatial demand for recreation, urgency, and security, two evaluation models were built. In the first model, the spatial service efficiency of Wi-Fi facilities is measured by a mean ratio of three types of demand spaces covered by Wi-Fi service. In the other model, spatial layout efficiency of each Wi-Fi facility is calculated by a demand load indicator - the sum of the three types of demand space's ratios of served quantity to the average quantity it should carry, and then assessed by relationship with its adjacent facilities. Corresponding statistical methods and analysis processes were also designed using the function modules found in ArcGIS software. The approach was applied to Wuhan city in 2016. After overlaying influence areas of 688 Wi-Fi facilities with demand spaces of 137 access points for recreation, 1200.99 km roads for urgency, 121.54 km² regions for security, the results show that there exists a spatial disequilibrium between supply and demand of Wi-Fi service in Wuhan due to lack of comprehensive planning. Specifically, there are 67 points, 700.76 km roads, and 42.59 km² regions of demand spaces covered by Wi-Fi service, with service efficiencies of 48.91%, 58.35%, and 35.04% respectively and an overall spatial service efficiency of 47.43%. Among all the Wi-Fi facilities, there are 481 carrying saturated demand, 3 straying from the centre of demand space, and 204 redundant. The overall spatial layout efficiency of Wi-Fi facilities is 43.01%. The conclusion is that the dense and massive redundant Wi-Fi facilities should be optimized, especially in the centre areas along the confluence of Yangtze and Han rivers and new Wi-Fi facilities supplemented in other ill-equipped areas. Since many metropolitan cities experience the same problem, this novel approach will find wide application in the future and offer improved evaluation strategies for researchers and policymakers.     

On the optimal number of scale points in graded paired comparisons

In market research, it is common practice to measure individuals’ brand or product preference through graded paired comparisons (GPCs). One important decision concerns the (odd) number of scale points (e.g., five, seven, nine, or eleven) that has to be assigned to either brands or products in each pair. Using data from an experiment with 122 students, we assessed the extent to which GPCs with a higher number of scale points (requiring more cognitive effort) really outperform GPCs with a smaller number of scale points (requiring less cognitive effort). Our data analyses have shown that one may reduce the (odd) number of scale points from eleven to nine or seven, depending on what minor compromises one is willing to make. The detailed psychometric results presented in this paper are useful to applied researchers as they help them in making well-informed decisions on the number of scale points in a GPC task.     

基于成本分析的集装箱码头堆场起重机优化研究

优化配置集装箱码头堆场面积和堆场起重机,对提高码头资源利用率,降低码头运作成本,提高港口竞争力具有重要的意义。文章使用成本模型研究了进口集装箱堆场每个BAY堆存集装箱和堆场起重机的优化配置．并通过一个案例说明了该方法运用的可行性。     

Facility location under demand uncertainty: Response to a large-scale bio-terror attack

In the event of a catastrophic bio-terror attack, major urban centers need to efficiently distribute large amounts of medicine to the population. In this paper, we consider a facility location problem to determine the points in a large city where medicine should be handed out to the population. We consider locating capacitated facilities in order to maximize coverage, taking into account a distance-dependent coverage function and demand uncertainty. We formulate a special case of the maximal covering location problem (MCLP) with a loss function, to account for the distance-sensitive demand, and chance-constraints to address the demand uncertainty. This model decides the locations to open, and the supplies and demand assigned to each location. We solve this problem with a locate-allocate heuristic. We illustrate the use of the model by solving a case study of locating facilities to address a large-scale emergency of a hypothetical anthrax attack in Los Angeles County.     

Commentary on facility location in the presence of congested regions with the rectilinear distance metric

This paper is a commentary on the work of Butt and Cavalier (Socio-Econ. Plann. Sci. 31(2) (1997) 103), a paper that was published in an earlier issue of this journal. With the aid of an example problem, we demonstrate that the set of gridlines proposed by them to find the rectilinear least cost path between two points in the presence of convex polygonal congested regions is inadequate. We proceed to prove its adequacy for the case of rectangular congested regions in which the edges of the rectangles are parallel to the travel directions. In wake of the difficulties of the general problem, we consider a specific example of a convex quadrilateral congestion region and a pair of external origin and destination points. Finally, we revisit the example shown in Butt and Cavalier's paper and present a mixed integer linear programming formulation that determines the optimal locations of the entry and exit points for this example.     

Gradual location set covering with service quality

Location set covering models were first described in the early 1970s. In their simplest form, they minimize the number of facilities necessary to completely cover a set of customers in some given space, where covering means providing service within a predetermined distance. This paper considers extensions of the basic model that soften the covered/not covered dichotomy and replace it with gradual covering. The models discussed in this work include the quality of service as a criterion. The models are formulated and compared with each other with respect to their size and features. A small series of computational tests concludes the paper.     

Pre-positioning of relief items in humanitarian logistics considering lateral transhipment opportunities

The main objective of this study is to investigate the inclusion of lateral transhipment opportunities into the humanitarian relief chain and to examine the effect of different parameters on minimizing the average distance travelled per item while serving the beneficiaries. Direct shipment model (DT), lateral transhipment model (LTSP) and maritime lateral transhipment model (MLTSP) are developed and compared between each other by using a real life earthquake scenario prepared for the city of Istanbul by JICA (Japanese International Cooperation Agency). Developed mathematical models decide on the locations and number of disaster relief facilities, quantity of relief items to hold at those facilities, and quantity of lateral transhipment between the facilities. Vulnerability of the roads and heterogeneous capacitated facilities are also considered. It can be concluded that both LTSP and MLTSP models gave better results than DT model and lateral transhipment option helps beneficiaries to obtain relief items faster and with higher service level.     

A facility location problem with clients' preference orderings

The Simple Plant Location Problem (SPLP) consists in identifying a pattern of facilities among a set of potential sites so that the sum of the costs for opening the facilities and for supplying a group of geographically dispersed clients therefrom is minimized. It is posited in this framework that the locator rules on the allocation of the clients to the facilities. When the clients are free to decide upon which facility they will attend, their choices do not necessarily match the most economical supply pattern from the point of view of the locator. We suppose here that each client has a preference ordering on the list of potential sites whereby he determines his allocation out of any set of open facilities. This preference ordering depends on characteristics of the client, of the sites, and of the trip between the client's location and the sites. Mathematically, we translate the orderings into a set of constraints to be appended to the SPLP. This new problem, termed SPLPO, has a wide range of applications as shown by a series of examples. We present an algorithm for solving the SPLPO and extensive computational experiments are reported.     

Consistent graphs with signed points

A signed graph is obtained from a graph when each line is given either a positive or a negative sign. We now define a marked graph analogously by signing the points of a graph. In both of these the sign of a cycle is the product of the signs of the lines or points, respectively. In a balanced signed graph or in a consistent marked graph, every cycle is positive. Our object is to investigate consistent marked graphs. It is shown that if such a graph has both positive and negative points, it cannot be highly connected; more precisely, it is not 3-connected. We conclude with a series of constructions which show that a given consistent marked graph can often be reduced to smaller ones.     

Capacitated heuristic program for multiactivity, multi-facility system designs

Multi-activity, multi-facility design systems occur in a wide variety of industrial and service applications: e.g.: regional health care centers with configurations of activities at each center, and multi-echelon inventory distribution systems. The problem in designing such systems is to determine from a candidate set of possible locations what facility locations should be opened and what types of activities should be carried out at each of the open facilities. This article presents an efficient heuristic procedure for such a problem.The heuristic procedure described can be used to solve both the uncapacitated and the capacitated problems where capacity is expressed in terms of the number of activities which can be supported by the facilities.Extensive computational experience with the heuristic is presented. The performance of the heuristic is compared against optimal solutions and the results look very encouraging.     

The maximal covering location problem with accessibility indicators and mobile units

We study the Maximal Covering Location Problem with Accessibility Indicators and Mobile Units that maximizes the facilities coverage, the accessibility of the zones to the open facilities, and the spatial disaggregation. The main characteristic of our problem is that mobile units can be deployed from open facilities to extend the coverage, accessibility, and opportunities for the inhabitants of the different demand zones. We formulate the Maximal Covering Location Problem with Accessibility Indicators and Mobile Units as a mixed-integer linear programming model. To solve larger instances, we propose a matheuristic (combination of exact and heuristic methods) composed of an Estimation of Distribution Algorithm and a parameterized Maximal Covering Location Problem with Accessibility Indicators and Mobile Units integer model. To test our methodology, we consider the Maximal Covering Location Problem with Accessibility Indicators and Mobile Units model to cover the low-income zones with Severe Acute Respiratory Syndrome Coronavirus 2 patients. Using official databases, we made a set of instances where we considered the poverty index, number of population, locations of hospitals, and Severe Acute Respiratory Syndrome Coronavirus 2 patients. The experimental results show the efficiency of our methodologies. Compared to the case without mobile units, we drastically improve the coverage and accessibility for the inhabitants of the demand zones.     

The spatial structure of production with a Leontief technology

The structure of the optimal spatial pattern of production is studied when there are interdependencies among production units which can be described by a Leontief technology, and when there is a single marketplace of final demand, the CBD. Transportation cost is proportional to distance. It is shown that the various goods are produced in rings which can be ranked by distance from the CBD independently of the levels of final demand. Furthermore shipment of goods for meeting intermediate and final demand can only be in the direction of the CBD and no shipment of goods towards the periphery can occur. A finite algorithm is given for the construction of the optimal pattern and for determining a system of f.o.b. prices and land rents which sustain it as a competitive equilibrium.     

A simple model for predicting the number of servers necessary to cover a region

A simple regression model is developed to estimate the number of servers necessary to cover a region. Data for the model were obtained within a research design that included five replications of 180 experimental conditions. A total of 300 rectangular regions were generated, and a set covering location problem was solved for each region using three distance metrics. Statistical results established coverage radius, compactness, and the number of nodes in the region to be significant factors. The resulting regression model was applied to a South Carolina county. Its estimates are seen to be very close to the number of units needed to cover. The model is shown to be a convenient technique for quickly estimating the number of servers while exhibiting an error distribution that is conservatively biased towards overestimation. This last property is desirable for public emergency services.     

A Hybrid model for locating new emergency facilities to improve the coverage of the road crashes

We propose an emergency facility-locating model aimed at increasing the coverage of emergency demand throughout the city. The proposed model takes into account the status and location of the emergency facilities in the network and identifies locations suitable for the construction of new facilities. Here, Data Envelopment Analysis (DEA) and Maximum Coverage Location Problem (MCLP) have been combined in a single model. To do so, design problem and evaluation problem are considered concurrently to maximize the efficiency of services provided by emergency facilities across the city in response to the demand. Moreover, the total emergency demand in each district was considered in relation to the population density, the fatal, injurious, and property damage only (PDO) crashes. The coverage area of each emergency facility was assumed to be proportional to the average ambulance speed in the surrounding road network during rush hours. The available budget was included in the model to let the model function under various fiscal conditions. Model input variables consisted of average number of mortalities, injuries and PDO crashes as well as the population density of each urban district. The output variables of the model included the coverage share of proposed emergency centers and hospitals equipped with ambulances. The model was tested on the network of Tehran (Iran). It is recommended to add the location of some emergency centers and hospitals to the network. Moreover, the results showed that ten urban districts had efficiency problem in provision of emergency services.     

Random utility demand models and service location

This paper considers the problem of the optimal location of facilities when the demand behavior is described by a random utility choice model. By means of duality theory of mathematical programming, it is shown how a wide family of such problems can be mapped into an entropy maximizing problem, which is usually easy to solve numerically. Theory and methods are discussed in details for the problem of locating a single type of facilities, and the extension to some kinds of systems with many types of facilities is outlined.     

A socio-economic optimization model for blood supply chain network design during the COVID-19 pandemic: An interactive possibilistic programming approach for a real case study

In uncertain circumstances like the COVID-19 pandemic, designing an efficient Blood Supply Chain Network (BSCN) is crucial. This study tries to optimally configure a multi-echelon BSCN under uncertainty of demand, capacity, and blood disposal rates. The supply chain comprises blood donors, collection facilities, blood banks, regional hospitals, and consumption points. A novel bi-objective Mixed-Integer Linear Programming (MILP) model is suggested to formulate the problem which aims to minimize network costs and maximize job opportunities while considering the adverse effects of the pandemic. Interactive possibilistic programming is then utilized to optimally treat the problem with respect to the special conditions of the pandemic. In contrast to previous studies, we incorporated socio-economic factors and COVID-19 impact into the BSCN design. To validate the developed methodology, a real case study of a Blood Supply Chain (BSC) is analyzed, along with sensitivity analyses of the main parameters. According to the obtained results, the suggested approach can simultaneously handle the bi-objectiveness and uncertainty of the model while finding the optimal number of facilities to satisfy the uncertain demand, blood flow between supply chain echelons, network cost, and the number of jobs created.