An analysis of p-median location problem: Effects of backup service level and demand assignment policy

Any solution to facility location problems will consider determining the best suitable locations with respect to certain criteria. Among different types of location problems, involving emergency service system (ESSs) are one of the most widely studied in the literature, and solutions to these problems will mostly aim to minimize the mean response time to demands. In practice, however, a demand may not be served from its nearest facility if that facility is engaged in serving other demands. This makes it a requirement to assign backup services so as to improve response time and service quality. The level of backup service is a key, strategic-level planning factor, and must be taken into consideration carefully. Moreover, in emergency service operations conducted in congested demand regions, demand assignment policy is another important factor that affects the system performance. Models failing to adopt sufficient levels of backup service and realistic demand assignment policies may significantly deteriorate the system performance.Considering the classic p-median problem (pMP) location model, this paper investigates the effects of backup service level, demand assignment policy, demand density, and number of facilities and their locations on the solution performance in terms of multiple metrics. For this purpose, we adopt a combined optimization and simulation approach. We will first modify the classic pMP to account for distances to backup services. Next, we employ a discrete event simulation to evaluate the performance of location schemes obtained from the deterministic mathematical model. Our results provide insights for decision-makers while planning ESS operations.     

Optimizing capacity,pricing and location decisions on a congested network with balking

In this paper, we consider the problem of making simultaneous decisions on the location, service rate (capacity) and the price of providing service for facilities on a network. We assume that the demand for service from each node of the network follows a Poisson process. The demand is assumed to depend on both price and distance. All facilities are assumed to charge the same price and customers wishing to obtain service choose a facility according to a Multinomial Logit function. Upon arrival to a facility, customers may join the system after observing the number of people in the queue. Service time at each facility is assumed to be exponentially distributed. We first present several structural results. Then, we propose an algorithm to obtain the optimal service rate and an approximate optimal price at each facility. We also develop a heuristic algorithm to find the locations of the facilities based on the tabu search method. We demonstrate the efficiency of the algorithms numerically.     

Capacitated emergency facility siting with multiple levels of backup

In many service systems, the primary objective is to provide continuous service and/or service within a prespecified time interval. In the public sector, emergency service systems fit into this category. In the private sector, systems providing repair service to critical production facilities and computers constitute another example. In these systems, the concept of multiple service facilities providing backup to each other becomes an important element in the design process. In this paper, we study the capacitated facility siting problem with multiple levels of backup coverage. The problem is formulated as a mathematical program; an efficient solution procedure is developed and computational experiments are reported.     

化工园区应急设施区间规划选址模型研究

应急设施选址受应急物资需求量的影响。为优化应急设施选址布局,提高突发事件应急处置能力,以化工园区突发事件为研究背景,对化工园区突发事故下应急设施选址进行研究。考虑到化工园区突发事件的随机性和复杂性、突发事件应急物资需求的不确定性等特点,以应急设施选址安全性最大、经济性和服务效益最好为目标,基于传统确定性应急设施选址模型,构建了不确定需求条件下化工园区应急设施选址区间规划数学模型。模型中应急物资需求量是一个区间值,通过引入区间规划理论和模糊理论对模型进行求解,不仅避免了不确定参数随机概率分布的波动率,而且也降低了模型求解过程中的不确定性。最后,以园区各企业潜在事故为工程背景进行实例分析,得到园区应急设施的布局方案。结果表明,模型的求解效果较好,可为园区应急设施选址决策提供参考依据。     

Location and allocation for distribution systems with transshipments and transportion economies of scale

Locating transshipment facilities and allocating origins and destinations to transshipment facilities are important decisions for many distribution and logistic systems. Models that treat demand as a continuous density over the service region often assume certain facility locations or a certain allocation of demand. It may be assumed that facility locations lie on a rectangular grid or that demand is allocated to the nearest facility or allocated such that each facility serves an equal amount of demand. These assumptions result in suboptimal distribution systems. This paper compares the transportation cost for suboptimal location and allocation schemes to the optimal cost to determine if suboptimal location and allocation schemes can produce nearly optimal transportation costs. Analytical results for distribution to a continuous demand show that nearly optimal costs can be achieved with suboptimal locations. An example of distribution to discrete demand points indicates the difficulties in applying these results to discrete demand problems.     

Optimizing pricing and location decisions for competitive service facilities charging uniform price

In this paper, we present the problem of optimizing the location and pricing for a set of new service facilities entering a competitive marketplace. We assume that the new facilities must charge the same (uniform) price and the objective is to optimize the overall profit for the new facilities. Demand for service is assumed to be concentrated at discrete demand points (customer markets); customers in each market patronize the facility providing the highest utility. Customer demand function is assumed to be elastic; the demand is affected by the price, facility attractiveness, and the travel cost for the highest-utility facility. We provide both structural and algorithmic results, as well as some managerial insights for this problem. We show that the optimal price can be selected from a certain finite set of values that can be computed in advance; this fact is used to develop an efficient mathematical programming formulation for our model.     

The transfer point location problem

In this paper, we introduce the transfer point location problem. Demand for emergency service is generated at a set of demand points who need the services of a central facility (such as a hospital). Patients are transferred to a helicopter pad (transfer point) at normal speed, and from there they are transferred to the facility at increased speed. The general model involves the location of p helicopter pads and one facility. In this paper, we solve the special case where the location of the facility is known and the best location of one transfer point that serves a set of demand points is sought. Both minisum and minimax versions of the models are investigated. In follow up papers we investigate the general model using the results obtained in this paper.     

鲁棒动态设施选址问题的近似算法

设施选址问题是组合优化中重要问题之一。动态设施选址问题是传统设施选址问题的推广,其中度量空间中设施的开设费用和顾客的需求均随着时间的变化而变化。更多地,经典设施选址问题假设所有的顾客都需要被服务。在这个模型假设下,所有的顾客都需要服务。但事实上,有时为服务距离较远的顾客,需要单独开设设施,导致了资源的浪费。因此,在模型设置中,可以允许一些固定数目的顾客不被服务 (带异常点的设施选址问题),此外也可以通过支付一些顾客的惩罚费用以达到不服务的目的 (带惩罚的设施选址问题)。本文将综合以上两种鲁棒设置考虑同时带有异常点和惩罚的动态设施选址问题,通过原始-对偶框架得到近似比为3的近似算法。     

考虑应急设施中断风险与防御的可靠性选址模型研究

为提高应急设施运行的可靠性和抵御中断风险的能力, 研究中断情境下的应急设施选址-分配决策问题。扩展传统无容量限制的固定费用选址模型, 从抵御设施中断的视角和提高服务质量的视角建立选址布局网络的双目标优化模型, 以应急设施的建立成本和抵御设施中断的加固成本最小为目标, 以最大化覆盖服务质量水平为目标, 在加固预算有限及最大最小容量限制约束下, 构建中断情境下应急设施的可靠性选址决策优化模型。针对所构建模型的特性利用非支配排序多目标遗传算法(NSGA-Ⅱ)求解该模型, 得到多目标的Pareto前沿解集。以不同的算例分析和验证模型和算法的可行性。在获得Pareto前沿的同时对不同中断概率进行灵敏度分析, 给出Pareto最优解集的分布及应急设施选址布局网络的拓扑结构。     

The use of simulation in validating a multiobjective EMS location model

A location model is proposed for emergency medical service systems to solve the multiobjective location problem of minimizing mean response time and balancing facility workload. Location solutions generated from the model are tested with simulation and are shown to be quite realistic with regard to mean response time prediction and facility allocation. This efficiency is determined to be directly attributable to workload constraints.     

Local search algorithm for universal facility location problem with linear penalties

The universal facility location problem generalizes several classical facility location problems, such as the uncapacitated facility location problem and the capacitated location problem (both hard and soft capacities). In the universal facility location problem, we are given a set of demand points and a set of facilities. We wish to assign the demands to facilities such that the total service as well as facility cost is minimized. The service cost is proportional to the distance that each unit of the demand has to travel to its assigned facility. The open cost of facility i depends on the amount z of demand assigned to i and is given by a cost function \(f_i(z)\). In this work, we extend the universal facility location problem to include linear penalties, where we pay certain penalty cost whenever we refuse serving some demand points. As our main contribution, we present a (\(7.88+\epsilon \))-approximation local search algorithm for this problem.     

基于改进NSGA-II算法的多级服务设施备用覆盖选址决策模型

为了应对跨区域突发事件过程中受灾点服务差异化需求的问题,建立了应急储备设施点的多级备用覆盖选址决策模型,即一个需求点由多个应急设施提供不同质量水平的服务,并考虑设施繁忙状态下由其他设施点提供服务的状况,使模型更加符合实际应用。首次通过设计分段的染色体编码方式改进NSGA-II算法提升运算效率以更好地解决多目标选址决策问题,将改进方法下得到的Pareto解分布与NSGA-II算法下的仿真结果进行对比分析,结合设施点的部署策略得到不同的空间布局方案。证明了模型的可行性及改进NSGA-II算法在解决设施点多目标选址决策问题时的有效性。     

Incorporating congestion in preventive healthcare facility network design

Preventive healthcare aims at reducing the likelihood and severity of potentially life-threatening illnesses by protection and early detection. The level of participation to preventive healthcare programs is a crucial factor in terms of their effectiveness and efficiency. This paper provides a methodology for designing a network of preventive healthcare facilities so as to maximize participation. The number of facilities to be established and the location of each facility are the main determinants of the configuration of a healthcare facility network. We use the total (travel, waiting and service) time required for receiving the preventive service as a proxy for accessibility of a healthcare facility, and assume that each client would seek the services of the facility with minimum expected total time. At each facility, which we model as an M/M/1 queue so as to capture the level of congestion, the expected number of participants from each population zone decreases with the expected total time. In order to ensure service quality, the facilities cannot be operated unless their level of activity exceeds a minimum workload requirement. The arising mathematical formulation is highly nonlinear, and hence we provide a heuristic solution framework for this problem. Four heuristics are compared in terms of accuracy and computational requirements. The most efficient heuristic is utilized in solving a real life problem that involves the breast cancer screening center network in Montreal. In the context of this case, we found out that centralizing the total system capacity at the locations preferred by clients is a more effective strategy than decentralization by the use of a larger number of smaller facilities. We also show that the proposed methodology can be used in making the investment trade-off between expanding the total system capacity and changing the behavior of potential clients toward preventive healthcare programs by advertisement and education.     

General network design: A unified view of combined location and network design problems

This paper presents a unified framework for the general network design problem which encompasses several classical problems involving combined location and network design decisions. In some of these problems the service demand relates users and facilities, whereas in other cases the service demand relates pairs of users between them, and facilities are used to consolidate and re-route flows between users. Problems of this type arise in the design of transportation and telecommunication systems and include well-known problems such as location-network design problems, hub location problems, extensive facility location problems, tree-star location problems and cycle-star location problems, among others. Relevant modeling aspects, alternative formulations and possible algorithmic strategies are presented and analyzed.     

Competitive facility location and design problem

We develop a spatial interaction model that seeks to simultaneously optimize location and design decisions for a set of new facilities. The facilities compete for customer demand with pre-existing competitive facilities and with each other. The customer demand is assumed to be elastic, expanding as the utility of the service offered by the facilities increases. Increases in the utility can be achieved by increasing the number of facilities, design improvements, or locating facilities closer to the customer.     

The multiple location of transfer points

In this paper, we investigate the location of several transfer points to serve as collector points for customers who need the services of a facility. For example, demand for emergency services by patients is generated at a set of demand points that need the services of a central facility (such as a hospital). Patients are transferred to a helicopter pad (transfer point) at normal speed, and from there they are transferred to the facility at increased speed. The general model involves the location of multiple transfer points and one facility. Locating one transfer point when the set of demand points and the location of the facility are known was investigated in a previous paper by the authors. In this paper, we apply the results of that paper to solve the problem when the location of the facility is known. Both minisum and minimax versions of the models are investigated both in the plane and on the network.     

A multi-objective genetic algorithm for a bi-objective facility location problem with partial coverage

In this study, we present a bi-objective facility location model that considers both partial coverage and service to uncovered demands. Due to limited number of facilities to be opened, some of the demand nodes may not be within full or partial coverage distance of a facility. However, a demand node that is not within the coverage distance of a facility should get service from the nearest facility within the shortest possible time. In this model, it is assumed that demand nodes within the predefined distance of opened facilities are fully covered, and after that distance the coverage level decreases linearly. The objectives are defined as the maximization of full and partial coverage, and the minimization of the maximum distance between uncovered demand nodes and their nearest facilities. We develop a new multi-objective genetic algorithm (MOGA) called modified SPEA-II (mSPEA-II). In this method, the fitness function of SPEA-II is modified and the crowding distance of NSGA-II is used. The performance of mSPEA-II is tested on randomly generated problems of different sizes. The results are compared with the solutions of the most well-known MOGAs, NSGA-II and SPEA-II. Computational experiments show that mSPEA-II outperforms both NSGA-II and SPEA-II.     

考虑需求不确定的多级应急物流设施选址研究

为了对急物流设施选址问题进行合理的研究,建立了包含配送中心、配送点和需求点的多级应急物流网络。基于应急物资需求特点,使用三角模糊数表示应急物资需求的不确定性,同时考虑应急救援成本和应急救援时间两个目标,建立了应急物流设施选址模型。采用去模糊化方法将三角模糊数转化为确定数,利用成本和时间的单目标的最优结果将多目标转化为相对值,再对时间和成本目标进行加权处理,既消除了不同目标之间的单位及数量级差异,还可以进行动态调整。设计了遗传算法对模型进行求解,通过实际算例表明了模型和算法可以有效地解决应急物流设施选址问题。     

Modelling lost demand in competitive facility location

In this paper, we propose a simple new approach to model lost demand (also referred to as elastic demand) in competitive facility location. A ‘dummy’ competing facility that attracts the lost demand is added to the list of competing facilities. All competitive facility location models, regardless of their complexity or assumptions, can be modified to include lost demand and be solved by the same algorithms designed for standard models once the dummy facility is added to the data as an additional competitor.     

Solving a Huff-like competitive location and design model for profit maximization in the plane

A chain wants to set up a single new facility in a planar market where similar facilities of competitors, and possibly of its own chain, are already present. Fixed demand points split their demand probabilistically over all facilities in the market proportionally with their attraction to each facility, determined by the different perceived qualities of the facilities and the distances to them, through a gravitational or logit type model. Both the location and the quality (design) of the new facility are to be found so as to maximise the profit obtained for the chain. Several types of constraints and costs are considered.