Weekly scheduling models for traveling therapists

This paper presents a series of models that can be used to find weekly schedules for therapists who provide ongoing treatment to patients throughout a geographical region. In all cases, patient-appointment times and visit days are known prior to the beginning of the planning horizon. Variations in the models include single vs. multiple home bases, homogeneous vs. heterogeneous therapists, lunch break requirements, and a nonlinear cost structure for mileage reimbursement and overtime. The single home base and homogeneous therapist cases proved to be easy to solve and so were not thoroughly investigated. This left two cases of interest: the first included only lunch breaks while the second added nonlinear overtime and mileage reimbursement costs. For the first case, 40 data sets were solved, each consisting of either 15 or 20 therapists and between roughly 300 and 540 patient visits over five days. For each instance, we were able to obtain the minimum cost of providing residential healthcare services using a commercial solver. The results showed that CPU time increases more rapidly than total cost as the total number of visits grows. For the second case, which was much more difficult, it was necessary to develop heuristics to find good solutions quickly. Results for 5- through 20-therapist instances are presented and compared to the linear programming relaxation lower bounds. In the first of two parametric analyses, the tradeoff between the number of therapists on staff and the cost of providing service was examined. In the second, a similar tradeoff was explored between cost can the number of home bases used by the therapists.     

用Excel规划求解报亭选址问题

报亭的选址问题是一类目标优化问题,从采用精确重心方法来求解的数学模型来看,此目标问题是一个迭代型规划问题,不能直接用常规的Excel规划方法来求解。文中通过引入过渡变量来逐步进行迭代求解。在每一步通过比较前后2对坐标之间的误差,在有限的时间与迭代次数内,求解到了地址目标。求解结果与手工计算的相吻合。     

基于网络均衡模型的仓库规划研究

网络均衡模型作为研究供应链的一种新的工具应用日益广泛.本文以供应链均衡模型为基础,利用网络的均衡流量建立每个仓库的决策模型,从而解决整个供应链仓库规划问题,综合提出一种新的解决仓库问题的方法,最后给出一个数值算例.通过利用网络均衡模型可以得到量化的仓库容量的解,同时又考虑自建和租赁两种情况,因此方法有很强的实用性.     

基于ATIS下的鲁棒连续交通网络设计问题

考虑基于ATIS下的连续交通网络设计问题,假定网络上交通需求不确定,但属于一个有界椭球闭集,应用鲁棒优化的方法建立基于ATIS下的连续交通网络设计的鲁棒模型,然后应用需求生成的算法求解此模型,数值算例表明鲁棒设计方案更加可靠。     

Sequential decisions under uncertainty and the maximum theorem

For sequential decision problems in which the decision-maker observes a process of state variables and chooses an adapted process of action variables, the paper defines a topology on the space of measures of processes of state variables which ensures the applicability of Berge's maximum theorem to the decision-maker's optimal behavior. The topology controls for the information available to the decision-maker at each decision date. The paper also discusses the implications of the analysis for the dynamic-programming approach to sequential decision-making under uncertainty, and for equilibrium existence proof strategies in sequential-market models and games.     

能量项链问题的解法探讨

通过引入程序设计竞赛中的有趣题目,有利于激发学生的学习兴趣,提高学生的实践能力。文章利用动态规划方法的一个典型例子"矩阵连乘问题"解决了一道经典的竞赛题目"能量项链问题"。分析了两个问题的相似性和相异性,得到了能量项链问题的求解方法。     

随机仓库布局问题模型与算法研究

通过讨论随机条件下仓库布局问题．建立了随机仓库布局问题机会约束规划模型,并设计出基于随机模拟的禁忌搜索算法求解模型,最后利用算例来验证算法的有效性。     

不确定环境下回收网络选址-库存最优策略研究

基于中国废旧产品回收网络的特点,分析了由制造商、综合回收中心、当地回收点、消费者构成的回收网络,并对其选址-库存策略进行了研究。提出了一个随机规划模型,针对不同的情景进行了分析,并通过敏感性分析,得出回收周期、当地回收点和消费者之间的距离对总的废旧产品回收成本的影响,为回收商制定回收决策提供了一定的理论依据。     

电动自行车电池逆向物流网络优化设计研究

针对电动自行车电池回收网络不完善,电池回收处理流程不科学的问题,以我国现有电动自行车销售网点为基础,以企业构建电动自行车电池逆向物流网络的总成本最小为目标,建立电动自行车电池逆向物流的非线性混合整数规划网络模型,通过LINGO 11.0软件对该模型进行求解,以确定废旧电池回收中心、处理中心数量和位置。最后,通过算例验证模型的有效性。     

EXCEL规划求解功能在运输问题中的应用

在日常生活和企业生产经营过程中,人们经常要将某些物品从一个地方运输到另外一个地方,这就产生了运输问题。如何在运输问题日益复杂的情况下,使运输成本费用更为节约,就成为目前运输问题研究的重点。文章主要采用excel的规划求解功能对运筹学中的产销平衡的运输问题进行应用研究,并举例加以说明。     

Home care routing and scheduling problem with teams’ synchronization

The demand for home care (HC) services has steadily been growing for two main types of services: healthcare and social care. If, for the former, caregivers' skills are of utter importance, in the latter caregivers are not distinguishable in terms of skills. This work focuses social care and models caregivers' synchronization as a means of improving human resources management. Moreover, in social care services, several visits need to be performed in the same day since patients are frequently alone and need assistance throughout the day. Depending on the patient's autonomy, some tasks have to be performed by two caregivers (e.g. assist bedridden patients). Therefore, adequate decision support tools are crucial for assisting managers (often social workers) when designing operational plans and to efficiently assign caregivers to tasks. This paper advances the literature by 1) considering teams of one caregiver that can synchronize to perform tasks requiring two caregivers (instead of having teams of two caregivers), 2) simultaneously modelling daily continuity of care and teams' synchronization, and 3) associating dynamic time windows to teams' synchronizations introducing scheduling flexibility while minimize service and travel times. These concepts are embedded into a daily routing and scheduling MIP model, deciding on the number of caregivers and on the number and type of teams to serve all patient tasks. The main HC features of the problem, synchronization and continuity of care, are evaluated by comparing the proposed planning with the current situation of a home social care service provider in Portugal. The results show that synchronization is the feature that most increases efficiency with respect to the current situation. It evidences a surplus in working time capacity by proposing plans where all requests can be served with a smaller number of caregivers. Consequently, new patients from long waiting lists can now be served by the “available” caregivers.     

供应商选择问题的模糊机会约束规划模型

论文以模糊机会约束规划的方法处理供应商选择问题（VSP）。在市场需求量为模糊变量,同时成本、质量、交付时间三个目标以一定的置信水平成立的前提下,提供了一种帮助决策者进行供应商供货量分配的方法,并给出模型的混合智能通用算法。     

考虑批量订货的易腐农产品配送中心选址方法

为提高物流管理绩效、降低物流运作成本,考虑到配送中心的批量订货和作业能力限制,建立了易腐农产品配送中心选址问题的0-1整数非线性规划模型,并利用Lingo 9.0软件进行了模型求解.利用该模型可以确定配送中心的位置和各配送中心与零售店之间的配送关系,并可得到配送中心的订货周期和订货批量.最后,通过算例验证了模型的有效性.     

基于改进Dijkstra算法的最短路算法

Dijkstra算法是求解最短路径问题的经典算法。在现如今的城市交通网络中,经常需要寻求两个地点之间的最短距离,减少运输时间。本文将Dijkstra算法与C语言相结合,对Dijkstra算法进行改进,根据实际网络图的情况,建立了相应的数学模型,运用C语言编程,在给定的网络图中,实现了只需确定起始点和终点,就可以直接输出最短路径和最短距离的功能。在有多个相同最短路径的情况下,会将多个最短路径一起输出,在搜索到终点时,立即跳出,结束循环。在一般情况下,无需对所有点进行迭代,提高了效率。这种方法可以应用到现在的物流运输中,以此来节约时间,降低成本。     

不确定OD需求下混合交通网络设计的鲁棒优化模型

假定OD需求是不确定的,但它属于一个有界多面体,应用鲁棒优化的方法对不确定OD需求下混合网络设计问题进行了研究,建立了基于用户均衡的混合网络设计的极小极大模型,并采用需求生成的算法求解不确定OD需求下混合网络设计的鲁棒对应模型。数值算例的结果表明应用鲁棒优化方法得到的混合网络设计方案不仅更加符合实际,而且较传统确定性的混合网络设计方案具有更高的可靠性。     

PROBABILISTIC MODELING OF WORKFORCE-BASED DISRUPTIONS AND INPUT–OUTPUT ANALYSIS OF INTERDEPENDENT RIPPLE EFFECTS

This paper extends the formulation of the input–output model to account for events that cause time varying and probabilistic workforce disruptions. One example of such an event is a pandemic, because the rates with which it affects the working population vary from period to period and are coupled with uncertainties. To address such complexities, the paper develops two extensions: (i) a method of translating unavailable workforce into a measure of sector productivity disruption, and (ii) a simulation framework to account for the possible variations in economic output losses. These extensions are implemented via a MATLAB program to simulate a pandemic scenario in the Commonwealth of Virginia.