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.     

De Moivre's Poisson Approximation to the Binomial

In his first work on probability, written in 1711, Abraham De Moivre looked at the problem of finding the number of trials required in a binomial experiment to achieve a probability of 1/2 of finding at least some given number of successes. He looked at two cases: when the probability of success  p  = 1/2 and when  p  is small but  n , the number of trials, is large. In the latter case, unlike other problems that he solved in probability, De Moivre never revealed his method of solution. We explore the solution that De Moivre originally suggests and find that his method does not work. We explore other numerical solutions and put forward the suggestion that De Moivre relied on a very cumbersome and tedious method of solution based on his earlier work on series in the 1690s. Since his method was neither quick nor mathematically elegant, he never revealed the method that he used to obtain his numerical solutions.     

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.     

Option Contracts in Supply Chains

This paper considers optimal contracts in supply chains that consist of   n ≥ 2  firms and face a potential investment hold-up problem. We show that option contracts may solve the incentive problems. First, we provide case-study evidence for the use of option contracts in the semiconductor industry. As our second contribution, we generalize the earlier option contract approach by introducing continuous quantities. Third, we extend the setting to n parties. For long supply chains, the first-best allocation can be achieved if there is a particular order of renegotiations .     

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.     

A credibility-based multi-objective temporary logistics hub location-allocation model for relief supply and distribution under uncertainty

Disaster response operations revolve around uncertainties. While uncertainties arising due to randomness can be avoided for post-disaster location problem, those arising because of impreciseness may persist long after the disaster's occurrence. Despite the uncertainties and lack of sufficient information about the extent of the damage, disaster response facilities must be established quickly after the occurrence of the disaster. Moreover, the decisions of whether to open, where to locate, and when to open disaster response facilities are based on the amount and quality of information available during the decision-making period. To address these issues, we develop a multi-objective location-allocation model for relief supply and distribution that accounts for the imprecise and time-varying nature of different parameters and time-varying coverage, while also accommodating the subjective attributes necessary to enable establishment and operation of the temporary logistics hubs (TLHs). A credibility-based fuzzy chance-constrained programming model is employed to account for the impreciseness inherent in predicting parameter values during disaster response. The results show where, when, and how many TLHs to open and how to allocate relief supplies. Meanwhile, the sensitivity analysis provides a broader understanding of the impact of limiting the number of TLHs as well as the confidence level and the spread of the symmetric triangular fuzzy numbers on the attainment of the model objectives.     

蚂蚁算法在复杂性运输路径问题中的应用——多车场多车型路径问题

车辆路径问题中,行驶路线往往取决于一系列约束条件,如配送中心个数,货物需求量,交发货时间,车辆容量限制等。要想达到一定的目标,如路程最短,费用最小,时间尽量少,车辆尽量少等,就得借劲于合适的算法去解决实际的问题。蚂蚁算法在解决著名的旅行商（TSP）问题上已取得了很好的成效,目前已陆续渗透到其他问题的求解上。文章主要针对多车场多车型车辆路径问题,用蚁群算法以及蚁群算法的优化算法去解决一些实际问题。     

Reliable design of a congested disaster relief network: A two-stage stochastic-robust optimization approach

The preparedness of humanitarian relief networks can be enhanced by pre-positioning resources in strategic locations and using them when disasters strike, a strategy that gives rise to a two-stage planning problem. This paper presents a novel two-stage stochastic-robust optimization approach for integrated planning of pre- and post-disaster positioning and allocation of relief resources, while taking into consideration the uncertainty about demand for relief services and disruptions in the relief facilities and the transportation network. The proposed approach enables planners to effectively use limited historical data and imperfect experts’ opinions to obtain robust solutions while avoiding the over-conservatism of classical robust optimization methods. The objective sought is to minimize the expected total time victims need to receive assistance, including both access time to facilities and waiting/service time in them. Congestion in relief facilities is accounted for by modeling them as queuing systems and penalizing waiting time. A decomposition method based on column-and-constraint generation is implemented to solve the problem, whereas the nonlinear terms corresponding to queuing in the second-stage problem are handled using a direct search procedure. Applicability of the proposed approach is demonstrated through a real case study and the numerical results are analyzed to draw managerial insights.     

Location and service mix decisions for a managed health care network

For managers of managed health care organizations, the problem of designing a competitive multiple facility network cannot be solved by existing mathematical models. This paper thus presents a nonlinear integer model for determining a facilities design strategy that embodies the economic tradeoffs encompassed in a competitive strategy: minimizing cost and maximizing market share. The integrated location and service mix model determines the number, location and service offerings of facilities that maximize profitability in a two-level hierarchical referral delivery network where an organization's market share is represented by a multiplicative competitive interaction model. To demonstrate the usefulness of the proposed integrated model, a series of problems is solved by an interchange heuristic and compared to the solutions derived by a simpler approach that ignores market competition.     

野营保障仓库选址优化研究

首先分析战时野营保障仓库选址规划现状和存在的问题,在结合野营保障仓库选址原则的基础上,根据MATLAB工具中最优化规划问题的计算机算法,创建了基于最大最小化问题野营保障仓库选址优化模型,最后通过实例进行了验证分析,为提高我军野营保障仓库选址的精确性和科学性探索了新方法,为增强我军基于体系作战的基建营房保障能力进行了有益尝试。     

Generalized two-sample U-statistics for clustered data

In this paper we investigate two-sample U -statistics in the case of clusters of repeated measurements observed on individuals from independent populations. The observations on the i -th individual in the first population are denoted by     , 1 ≤  i  ≤  m , and those on the k -th individual in the second population are denoted by     , 1 ≤  k  ≤  n . Given the kernel φ ( x ,  y ), we define the generalized two-sample U -statistic by
We derive the asymptotic distribution of U _{m , n} for large sample sizes. As an application we study the generalized Mann–Whitney–Wilcoxon rank sum test for clustered data.     

Siting a facility in continuous space to maximize coverage of a region

Siting facilities in continuous space such that continuously distributed demand within a region is optimally served is a challenging location problem. This problem is further complicated by the non-convexity of regions typically encountered in practice. In this paper a model for maximizing the service coverage of continuously distributed demand through the location of a single service facility in continuous space is proposed. To address this problem, theoretical conditions are established and associated methods are proposed for optimally siting a service facility in a region (convex or non-convex) with uniformly distributed demand. Through the use of geographic information systems (GIS), the developed approach is applied to identify facility sites that maximize regional coverage provided limitations on facility service ability.     

Het probleem van de ruïnering der spelers

The gambler's ruin.
When a single trial has two possible outcomes A and B, with probabilities p and q( p +q= 1), a succession of these trials forms a so-called Bernoulli chain. The well-known result for the probability of n times A and m times B is
In this article we consider the ruin problem, in which the initial capitals of the gamblers are a and b, respectively. In stead of a Bernoulli chain we then have a Markoff chain, with coefficients that are less simple than the ordinary binomial coefficients.
A more general expression (formula 1) is obtained for the probability distribution of the gambler's profit after a certain number of games, provided none of them became ruined beforehand. The probability for ruin after a certain number of games is a special case, similar to the results of Lagrange, Laplace and others, but appears in a form, more suitable for numerical calculations.
Some other results, obtained through the same method as developed in this paper are indicated.     

一次性消耗的应急系统资源调度问题研究

文章研究了一次性消耗的应急资源调度问题,将参与应急的出救点数目最少和应急开始时间最短同时作为优化目标,首先给出了参与应急出救点数目取值范围的判定定理,然后将问题转化为出救点数一定条件下的应急开始时间最早的单目标优化问题,从而得到一组Pareto最优解。并从理论上证明了求解方法的有效性和正确性。     

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.     

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.     

停车位的供需矛盾及其解决方略

针对我国城市停车供需矛盾突出这一问题,从深层次分析原因,认为应该从城市可持续发展的高度,结合机动化发展战略,在立法、公共政策和技术标准制定,以及停车设施规划、建设和管理等方面,系统地提出解决问题的对策;在倡导"公交优先"的同时,应提出限制私人轿车拥有和使用的政策;对城市公共停车设施应进行统筹规划,统一建设,并将城市公共停车设施作为公共物品纳入城市交通基础设施建设;城市停车设施应以公共停车设施为主,严格限制专用停车设施和商品化停车泊位,以提高城市停车设施的利用率。     

The number of securities giving the maximum return in the presence of transaction costs

An essential element of any realistic investment portfolio selection is the consideration of transaction costs. Our purpose, in this paper, is to determine the maximum return and the corresponding number of securities to buy giving such return, whenever practical constraints features related to budget, buy-in thresholds, and transaction costs are taken into consideration. Dealing with the portfolio selection and optimization problem in the point of view of individual investors, we will arrive to get an analytic result, leading to a new and simple alternative solution to heuristic algorithms. Moreover, this result can be considered as another approach to integer optimization.     

Location-allocation problem for intra-transportation system in a big company by using meta-heuristic algorithm

This paper presents the location-allocation problem of parking facilities in Mobarakeh Steel Company. The aim is to find the optimal location for the parking facilities and allocate travels between departments to each parking facility. To optimize the cost and facing the transportation demands of all departments, a mathematical model is designed and solved by a commercial software package. Also, the number of vehicles allocated to each parking facility is determined. A hybrid meta-heuristic algorithm combining a genetic algorithm with parallel simulated annealing is developed which can be used even in more complicated structure of the problem. The results show that this hybrid algorithm is highly efficient in solving this kind of problems.     

A multiobjective modeling approach to locating incinerators

The location of hazardous material incineration facilities is an important problem due to the environmental, social, and economic impacts that they impose. The costs associated with the facilities and the risks placed on nearby populations are important concerns as are the distributions of these costs and risks. This paper introduces a mixed-integer, multiobjective programming approach to identify the locations and capacities of such facilities. The approach incorporates a Gaussian dispersion model and a multiobjective optimization model in a GIS-based interactive decision support system that planners can access via the Internet. The proposed approach is demonstrated via a case study in central Portugal where the national government has decided to locate a large facility for the incineration of hazardous industrial waste. Due to intense local and national opposition, construction of the facility has been delayed. The system has been designed so that it can be used by decision makers with no special training in dispersion modeling, multiobjective programming, or GIS.