An approximation algorithm for a facility location problem with stochastic demands and inventories

We propose a 2-approximation algorithm for a facility location problem with stochastic demands. At open facilities, inventory is kept such that arriving requests find a zero inventory with (at most) some pre-specified probability. Costs incurred are expected transportation costs, facility operating costs and inventory costs.     

最小最大二点集覆盖问题分析及改进算法设计

本文考虑二中心问题的扩展问题-最小最大二点集覆盖问题。给定两个平面点集P₁和P₂,分别包含m和n个点,求两个圆分别覆盖P₁和P₂,并且要求两圆半径与两圆圆心距三者中的最大值最小。本文主要贡献在于分析半径变化过程中两个点集中心包之间最近距离的变化关系,其中中心包是点集所具有的一个特殊几何结构,所得到的结果改进了Huang等人之前给出的结果,并且通过该结果设计相应算法,所得到的算法复杂性是目前最好的。     

Spherical Minimax Location Problem

This paper presents an algorithm for determining a minimax location to service demand points that are equally weighted and distributed over a sphere. The norm under consideration is geodesic. The algorithm presented here is based on enumeration and has a polynomial time complexity.     

暂留Bessel过程的将来极小值及其位置的联合分布

对暂留 Ｂｅｓｓｅｌ过程 Ｘ,令 Ｉ（ｔ）＝ｉｎｆ_s≥tＸ（ｓ）及　ξ（ｔ）＝ｉｎｆ｛ｕ≥ｔ：Ｘ（ｕ）＝Ｉ（ｔ）｝,本文求出了Ｉ（ｔ）,　ξ（ｔ）及Ｘ_t的联合分布。     

An approximate analytical solution of one-dimensional phase change problems in a finite domain

In this paper, we present an approximate analytical solution for solving one dimensional two phase Stefan problem. The finite sine transform technique is used to convert the non dimensional form from a space domain to a wave number domain. Inverse finite sine transform is used to obtain the desired solution. The location of moving interface during freezing process in a finite domain is studied and the result thus obtained are discussed graphically. The whole analysis is presented in a non dimensional form.     

区域分工水平评价的新方法——区位结构熵法

根据区域产业分工理论,运用区位商测定区域专业化程度.然后,基于复杂系统结构熵理论,从产业在区际和区内聚集分布信息出发,融合行业路径和地区路径分析法于一体,提出并证明了可以用区位结构熵全面衡量产业在空间上的分布状况.在此基础上,构建一维区域分工指数,综合测定区域分工水平.最后,以我国工业空间分布为例,例证了该方法是合理的、可行的,具有一定的推广和应用价值.     

会议选址问题的优化模型

国内某公司在各省会城市都设有分支机构,公司每年都有频繁的会议和培训工作需要各地分支机构派人参加,如何在大陆地区31个省会城市里选择一个城市作为会议地址,使得举办会议的成本最低且中转次数最少.建立了该会议选址问题的双目标优化模型,收集处理了有关实际数据,利用网络最短路算法和约束法等得到了该会议选址问题的解.在不考虑中转费用的情况下,得出成本最低且中转次数最少的会议地址是西安;在考虑中转费用的情况下,根据中转费用的不同给出了可供实际决策的最优会议选址方案.     

The minmax regret gradual covering location problem on a network with incomplete information of demand weights

The gradual covering location problem seeks to establish facilities on a network so as to maximize the total demand covered, allowing partial coverage. We focus on the gradual covering location problem when the demand weights associated with nodes of the network are random variables whose probability distributions are unknown. Using only information on the range of these random variables, this study is aimed at finding the “minmax regret” location that minimizes the worst-case coverage loss. We show that under some conditions, the problem is equivalent to known location problems (e.g. the minmax regret median problem). Polynomial time algorithms are developed for the problem on a general network with linear coverage decay functions.     

Probabilistic analysis of geometric location problems

We analyze the behaviour of thek center and median problems forn points randomly distributed in an arbitrary regionA ofR ^d . Under a mild assumption on the regionA, we show that fork≦k(n)=o(n/logn), the objective function values of the discrete and continuous versions of these problems are equal to each otheralmost surely. For the two-dimensional case, both these problems can be solved by placing the centers or medians in an especially simple regular hexagonal pattern (the ‘honeycomb heuristic’ of Papadimitriou). This yields the exact asymptotic values for thek center and median problem, namely, α(|A|/k)^1/2 and β(|A|/k)^1/2, where |A| denotes the volume ofA, α and β are known constants, and the objective of the median problem is given in terms of the average, rather than the usual total, distance. For the 3- and 4-dimensional case, similar results can be obtained for the center problem to within an accuracy of roughly one percent. As a by-product, we also get asymptotically optimal algorithms for the 2-dimensionalp-normk median problem and for the twin problems of minimizing the maximum number of vertices served by any center and similarly for maximizing the minimum.     

供应商不确定情景下药品物流多中心选址优化研究

根据国家4+7药品带量集中采购评审标准,基于药品生产企业生产质量、供应能力、相关资质和同类药品参标结果等数据进行梳理和分析,针对药品供应商不确定情景下药品物流多中心选址问题,构建药品物流整体费用最优的多中心选址模型,设计多阶段改进禁忌搜索算法,最后通过4+7带量集中采购具体算例对模型和算法进行验证,结果显示该模型和算法是可行和有效的。