Fixed or variable demand? Does it matter when locating a facility?

In most competitive location models available in the literature, it is assumed that the demand is fixed independently of market conditions. However, demand may vary depending on prices, distances to the facilities, etc., especially when the goods are not essential. Taking variable demand into consideration increases the complexity of the problem and, therefore, the computational effort needed to solve it, but it may make the model more realistic. In this paper, a new planar competitive location and design problem with variable demand is presented. By using it, it is shown numerically for the first time in the literature that the assumption of fixed demand influences the location decision very much, and therefore the selection of the type of demand (fixed or variable) must be made with care when modeling location problems. Finally, two methods are presented to cope with the new model, an exact interval branch-and-bound method and an evolutionary algorithm called UEGO (Universal Evolutionary Global Optimizer).     

针对存在传染效应突发事件的资源布局问题研究

本文针对一类具有传染效应的突发事件建立资源布局模型。具有传染效应的突发事件是指在某地区发生事件,在其周围一定距离内的其他地区也会发生同类事件。对初始发生事件供应不同的资源将影响到其他地区的资源需求,因此整个地区的资源需求表现为多个需求组合。本文建立的模型考虑到某个地点发生事件带来的多种资源需求组合,将问题分为两个阶段进行分析,并同时考虑选址和资源配置来满足该地区发生事件需求以及引发的其他地区的资源需求。针对此模型,构造两层的禁忌搜索算法,并在最后给出算例。     

考虑空间随机需求的急救站点选址规划

随着人民生活水平的提高和人口老龄化加剧，公众对急救医疗服务的要求越来越高。为保证急救需求的响应及时性，急救站点的选址规划问题受到广泛关注。急救站点选址的依据是需求的分布，然而现有研究未能充分考虑急救需求在空间分布上的随机性影响，通常将其空间分布简化为若干个集中需求点，或将规划空间划分为若干矩形网格，然而这种需求刻画过于粗略，导致需求覆盖水平的计算不够准确，影响配置方案的有效性。针对该问题，本研究应用高斯混合模型解决了急救需求的空间分布刻画问题，创新性地提出基于高斯混合聚类的站点选址规划方法，考虑急救需求时空随机性，建立了相应的机会约束规划模型。实际数据的验证分析表明，该选址方法能够显著减少服务延误时间和次数，保证急救服务的响应及时性。     

A FACILITY LOCATION PROBLEM WITH DISTANCE-DEPENDENT DEMAND

This paper examines network systems where demand for the services of a facility originates at the nodes of the network and its magnitude depends on the shortest distance to a service-providing facility. Service systems with such features include bank branches, fastfood outlets, and grocery stores. With the assumption that demand is a Poisson-distributed random variable whose mean is an exponentially decreasing function of distance, possible locations based on two important performance measures are characterized: the expected value and the variance of the demand. Two procedures are proposed: one to find the locations with the minimum and maximum expected demand and the other to find the location(s) that provide a given level of expected demand. The procedures are illustrated by two examples.     

Facility Location: A Robust Optimization Approach

In this research, we apply robust optimization (RO) to the problem of locating facilities in a network facing uncertain demand over multiple periods. We consider a multi‐period fixed‐charge network location problem for which we find (1) the number of facilities, their location and capacities, (2) the production in each period, and (3) allocation of demand to facilities. Using the RO approach we formulate the problem to include alternate levels of uncertainty over the periods. We consider two models of demand uncertainty: demand within a bounded and symmetric multi‐dimensional box, and demand within a multi‐dimensional ellipsoid. We evaluate the potential benefits of applying the RO approach in our setting using an extensive numerical study. We show that the alternate models of uncertainty lead to very different solution network topologies, with the model with box uncertainty set opening fewer, larger facilities. Through sample path testing, we show that both the box and ellipsoidal uncertainty cases can provide small but significant improvements over the solution to the problem when demand is deterministic and set at its nominal value. For changes in several environmental parameters, we explore the effects on the solution performance.     

Temporary Hubs for the Global Vehicle Supply Chain in Humanitarian Operations

We model the global vehicle supply chain of an International Humanitarian Organization (IHO) with a dynamic hub location model across monthly periods. We use actual vehicle data from the International Federation of the Red Cross to feed our model and provide insights into IHO secondary support demand. We find that secondary support demand for items such as vehicles is different from primary beneficiary demand for items such as water and food. When considering disaster response and development program demand simultaneously (disaster cycle management), our results illustrate that keeping a lean centralized hub configuration with an option for temporary hubs in mega disaster locations can reduce overall supply chain costs over a long time horizon. We also show that it is possible to structure a supply chain to take operational advantage of earmarked funding. This research lays the groundwork for using optimization models to analyze disaster cycle management.     

A Bicriterion Maximal Covering Location Formulation Which Considers the Satisfaction of Uncovered Demand

There have been many applications of the maximal covering location problem (MCLP). An underlying assumption of the MCLP is that demand not covered (i.e., not within a prespecified maximal distance of a facility) is not served. This may be an unrealistic assumption in many location planning scenarios, especially in the public sector. For example, in cases such as fire protection or ambulance service, calls not technically covered will still be serviced. The MCLP, however, does not consider the distances or travel times necessary to service such demand. This paper presents a bicriterion locational covering model which explicitly considers the travel distance or time necessary to service demand not within the maximal covering distance of a facility. The model may be used to generate noninferior (Pareto optimal) siting configurations which demonstrate the inherent trade-offs between a siting scheme designed to maximize total coverage and one designed to minimize total travel time for uncovered demand to reach its nearest facility. In addition, it is shown that for any particular weighting scheme on the two objectives, the problem can be solved as a p-median problem; a problem for which several efficient solution methods exist.     

Updating Inventories of Substitutable Resources in Response to Forecast Updates

We show simple yet optimal results to update the inventory/capacity levels, expected profit, fill rates, and service levels of substitutable resources in response to an updating of the mean demand forecasts for the resources. We find that a change in the mean demand of one resource does not affect the optimal inventory level of any other resource. The results are obtained for demands with location‐scale distribution, and for a revenue structure satisfying a triangle property such that the manager will always use the inventory of a resource to meet her own demand first before using it for substitution. The results for updating the performance measures also extend to managers who maintain non‐optimal inventory/capacity levels. Implications for procurement, sales and operational planning, and multi‐store operations are discussed.     

The flow refueling location problem with load flow control

Battery electric vehicles as well as renewable energy are two key factors that can contribute significantly to sustainable development within the transportation and the energy sector. However, the market introduction of these technologies results in new challenges, especially with regard to the interaction between both sectors. So far, neither location models for charging stations nor load flow models for the electrical grid consider these interactions sufficiently. Thus, an integration of planning problems from both sectors is needed in order to exploit potential synergies and to avoid negative impacts.In this paper, we present such an integrated planning approach to locate charging infrastructure for battery electric vehicles considering interactions with the electrical grid. Herein, we combine a charging station location model and a power flow model with integrated energy stores. We aim at determining a network configuration that satisfies the charging demand of battery electric vehicles, herein maximizing the benefits and minimizing the negative impacts resulting from the interactions of the two sectors. To demonstrate the benefit of our integrated planning approach, we apply it to an illustrative case and present results of a sensitivity analysis. We derive managerial insights regarding the interdependencies of the number of sited charging stations and the installed storage capacity based on renewable energy generation and charging demand.     

Management of school locations allowing for free school choice

Nearly without exception, we find in literature (school) location models with exogenously given demand. Indeed, we know from a large number of empirical studies that this assumption is unrealistic. Therefore, we propose a discrete location model for school network planning with free school choice that is based on simulated utility values for a large average sample. The objective is to maximize the standardized expected utility of all students taking into account capacity constraints and a given budget for the school network. The utility values of each student for the schools are derived from a random utility model (RUM). The proposed approach is general in terms of the RUM used. Moreover, we do not have to make assumptions about the functional form of the demand function. Our approach, which combines econometric and mathematical methods, is a linear 0–1 program although we consider endogenous demand by a highly non-linear function. The proposed program enables practicing managers to consider student demand adequately within their decision making. By a numerical investigation we show that this approach enables us to solve instances of real size optimally – or at least close to optimality – within few minutes using GAMS/Cplex.     

带时间窗装卸货问题的改进多策略分组编码遗传算法

通过研究求解PDPTW的分组编码遗传算法（GGA）及多策略分组编码遗传算法（MSGGA），改进了GGA中的交叉算子及MSGGA中的路径调整策略，提出了易位组合交叉算子、单车路径重排策略及需求对换策略。求解了400个客户点的标准算例集，其中4个算例lc2_4_3、lrc1_4_1、lrc2_4_2和lrc2_4_3的行驶总路程有所减少。     

The facility location problem with Bernoulli demands

This paper presents the facility location problem with Bernoulli demands. In this capacitated discrete location stochastic problem the goal is to define an a priori solution for the locations of the facilities and for the allocation of customers to the operating facilities that minimizes the sum of the fixed costs of the open facilities plus the expected value of the recourse function. The problem is formulated as a two-stage stochastic program and two different recourse actions are considered. For each of them, a closed form is presented for the recourse function and a deterministic equivalent formulation is obtained for the case in which the probability of demand is the same for all customers. Numerical results from computational experiments are presented and analyzed.     

OPTIMIZING AND SATISFICING IN STOCHASTIC COST-VOLUME-PROFIT ANALYSIS

This paper examines some of the implications of introducing penalties for output not equalling demand by employing a general stochastic model for a firm facing an uncertain demand with a known probability density function. Several alternative objectives of the firm are considered: (1) maximization of expected profits; (2) maximization of the probability of achieving a particular target level of profits; and (3) maximization of target profits, given a target level of the probability of their being achieved. It is shown that the resulting probability density function of profits is not well defined. The shape and location of the function depend on the relative magnitudes of the model parameters and the output decision. Several important implications of this result for cost-volume-profit analysis are discussed.     

Location and reliability problems on a line: Impact of objectives and correlated failures on optimal location patterns

In this paper we study a class of locations models where facilities are not perfectly reliable and failures may be correlated. We analyze problems with Median and Center objectives under complete and incomplete customer information regarding the state of facilities. The goal is to understand how failure probabilities, correlations, availability of information, and problem objective affect the optimal location patterns. In particular, we want to find analytical confirmations for location patterns observed in numerical experiments with network location models. To derive closed-form analytical results the analysis is restricted to a simple (yet classic) setting: a 2-facility problem on a unit segment, with customer demand distributed uniformly over the segment (results can be extended to other demand distributions as well). We derive explicit expressions for facility trajectories as functions of model parameters, obtaining a number of managerial insights. In addition we provide the decomposition of the optimal cost into the closed form components corresponding to the cost of travel, the cost of facility unreliability and the cost of incomplete information. Most of the theoretical insights are confirmed via numerical experiments for models with larger (3–5) number of facilities.     

OPTIMAL ALLOCATION OF RECOVERABLE ITEMS*

Allocation of at most n recoverable items among m demand locations is considered. Items are assumed to be demanded singly and independently and are eventually returned to the demand location. If a stockout occurs, the demand is lost and a penalty corresponding to lost profit is assessed. The allocation that minimizes the sum of expected stockout costs plus holding costs is readily obtained. An example involving allocation of rental cars among outlets is solved in detail.     

基于手机定位数据的突发事件下道路修复和物资配送集成优化研究

应急道路的修复是突发事件发生后有效开展物资配送的前提,而道路修复和物资配送二者集成研究极大地提高整个应急救援效率。但是由于灾害的突发性和不确定性,决策者很难立即获取充分的灾情信息,尤其是灾民分布情况、位置、灾害影响和物资需求等信息。传统的获取灾情信息的方法通常是通过救援人员的现场报导和调查,卫星图像等,阻碍了救援活动的迅速开展,效率低下。手机等移动设备的普及和广泛应用,使得手机定位数据为灾害情况下的应急救援提供了更加快捷的信息获取手段,大大提高了应急救援的效率。本文基于手机定位数据,同时结合道路修复和物资配送二者的相互关系,建立了混合整数线性规划模型,通过手机定位数据获取灾民分布情况、位置、灾害影响和物资需求等信息,实现精准道路修复和物资配送的决策,并设计了相应的启发式求解算法。最后通过算例仿真验证了模型和算法的有效性,同时将手机定位数据下的救援结果与缺少手机定位数据的常规救援结果进行比较分析,验证了文章所提出的手机定位数据的应用在应急救援方面的优势。     

Planning ambulatory health care delivery systems

This paper develops an optimal ambulatory health care delivery system for a community, by determining the optimal number, size and location of health centers. The demand for ambulatory health care services is given. The objective is to maximize the difference between the benefits of the patients receiving treatment and the total cost of the system. Utilization of facilities, which is a function of distance, is expressed in terms of benefits and incorporated into the cost-benefit analysis. The model is illustrated by a numerical example.     

基于二阶段随机规划的城市医疗废弃物回收网络设计

城市医疗废弃物日益增加,且回收需求量受诸多因素的影响,难以准确预测,假定回收需求为确定值的医疗废弃物网络优化设计不能与实际需求相匹配。本文考虑了离散随机参数环境下,医疗回收网络设计中选址规划、分配计划及运输规划的协同优化问题,建立了以选址成本、运输成本最小为目标,设施与车辆能力限制为约束的二阶段随机规划模型。根据模型特点,设计了基于Benders decomposition的求解算法,同时,设计了一系列加速技术用于提高算法的求解效率。最后,以国内某城市医疗回收网络为背景设计算例,检验本文模型和求解策略的可行性和有效性。结果表明：相比确定性规划,随机规划的解能够节约总成本,结合一系列加速技术的Benders decomposition方法比CPLEX与纯的Benders decomposition更有优势。     

基于消费者搜寻成本的商圈形成机理研究

基于Nelson搜寻成本节约相关理论,通过引入购物成本、品味搜寻成本Ι、品味搜寻成本ΙΙ以及区位搜寻成本等概念,在深入阐释消费者搜寻与购物行为基础上,构建了消费者商圈搜寻期望经济学模型。研究结果表明:第一,商圈商品所能提供的满意度随消费者对商品要求提高或商圈内搜寻新店成本减小而增加;第二,孤立企业商品所能提供的满意度随消费者对商品要求提高、商圈内企业数量增加或商圈内搜寻新店成本减小而增加;第三,商品的区位搜寻成本,以及商圈到孤立企业间距离的影响则由商圈与孤立企业各自所能提供商品的满意度比较情况而决定。同时,结合徐家汇商圈形成案例的分析对以上结论进行了进一步探讨与分析。     

设施失灵风险下不确定需求应急定位-路径鲁棒优化研究

为抵御突发灾害对路网造成的破坏性和设施失灵风险,降低系统成本,并快速完成应急救援任务,本文考虑到受灾点物资需求量的不确定和风险对救援系统的影响,采用直升机进行物资运送以规避路径风险。建立了最小化应急物流系统总成本和物资到达需求点总救援时间为双目标的应急物流定位-路径鲁棒优化模型,基于相对鲁棒优化方法处理需求不确定,采用偏差鲁棒优化思想描述设施失灵风险损失,采用遗传算法进行求解。通过对三个算例进行数据仿真实验,证明了相对鲁棒优化方法在处理需求不确定和偏差鲁棒优化方法在处理设施失灵风险方面的有效性,进而为解决应急设施点的开设和救援物资的安全及时准确配送,增强应急物流系统的风险应对能力提供了有效的方法。