The Vehicle Scheduling Problem with Multiple Vehicle Types

The vehicle scheduling problem is specified in terms of a set of tasks to be executed with a fleet of multiple vehicle types. The purpose of this paper is to formulate the problem and to show that the heuristic and exact methods developed for the vehicle scheduling problem with time windows and with a single type of vehicle can be extended in a straightforward fashion to the multiple-vehicle-types problem.     

多级运载火箭动态级间分离的Monte Carlo仿真

提出了研究多级运载火箭级间冷、热分离的计算公式．利用Monte Carlo仿真，考虑箭体分离时，采用远离正常设计值的参数去评估分离失败的风险．分析了各种扰动，如动态不平衡，剩余推力，分离机构引起的分离扰动，以及冷、热分离未对准的影响，得到分离箭体不会发生碰撞的条件．结果表明，当前设计满足分离要求．     

免疫算法在车辆调度问题中的应用

免疫算法是模仿生物体高度进化、复杂的免疫系统仿生的一种智能化启发式算法。本文根据车辆调度问题的具体情况，应用免疫算法解决车辆调度中路线安排问题，并提出了一种基于分组匹配的亲和力的计算方法。实验结果表明，免疫算法能有效地应用于车辆调度中路线安排问题。     

Method of Moments Using Monte Carlo Simulation

Abstract

We present a computational approach to the method of moments using Monte Carlo simulation. Simple algebraic identities are used so that all computations can be performed directly using simulation draws and computation of the derivative of the log-likelihood. We present a simple implementation using the Newton-Raphson algorithm with the understanding that other optimization methods may be used in more complicated problems. The method can be applied to families of distributions with unknown normalizing constants and can be extended to least squares fitting in the case that the number of moments observed exceeds the number of parameters in the model. The method can be further generalized to allow “moments” that are any function of data and parameters, including as a special case maximum likelihood for models with unknown normalizing constants or missing data. In addition to being used for estimation, our method may be useful for setting the parameters of a Bayes prior distribution by specifying moments of a distribution using prior information. We present two examples—specification of a multivariate prior distribution in a constrained-parameter family and estimation of parameters in an image model. The former example, used for an application in pharmacokinetics, motivated this work. This work is similar to Ruppert's method in stochastic approximation, combines Monte Carlo simulation and the Newton-Raphson algorithm as in Penttinen, uses computational ideas and importance sampling identities of Gelfand and Carlin, Geyer, and Geyer and Thompson developed for Monte Carlo maximum likelihood, and has some similarities to the maximum likelihood methods of Wei and Tanner.     

The multi-level Monte Carlo finite element method for a stochastic Brinkman Problem

We present the formulation and the numerical analysis of the Brinkman problem derived in Allaire (Arch Rational Mech Anal 113(3): 209–259,1990. doi:10.1007/BF00375065, Arch Rational Mech Anal 113(3): 261–298, 1990. doi:10.1007/BF00375066) with a lognormal random permeability. Specifically, the permeability is assumed to be a lognormal random field taking values in the symmetric matrices of size $d\times d$ , where $d$ denotes the spatial dimension of the physical domain $D$ . We prove that the solutions admit bounded moments of any finite order with respect to the random input’s Gaussian measure. We present a Mixed Finite Element discretization in the physical domain $D$ , which is uniformly stable with respect to the realization of the lognormal permeability field. Based on the error analysis of this mixed finite element method (MFEM), we develop a multi-level Monte Carlo (MLMC) discretization of the stochastic Brinkman problem and prove that the MLMC-MFEM allows the estimation of the statistical mean field with the same asymptotical accuracy versus work as the MFEM for a single instance of the stochastic Brinkman problem. The robustness of the MFEM implies in particular that the present analysis also covers the Darcy diffusion limit. Numerical experiments confirm the theoretical results.     

多车场多车型车辆调度问题及其遗传算法

研究多车场多车型车辆调度问题,建立了一种基于最小配送费用的数学模型,模型的配送费用在考虑基本运输费的基础上又引入了司机的工资支出,包括基本工资和加班费.在多车场多车型车辆调度模型中,一辆车可以为多个客户服务,但一个客户只能由一辆车提供服务.根据模型的这些特点,提出了一种新的染色体混合编码方案和遗传操作策略,从而借助遗传算法成功实现了模型的求解.数值仿真结果验证了算法的可行性.     

多行程带时间窗口的车辆调度问题研究

为了提高车辆的使用率,企业往往会安排车辆在单位周期内,执行多次配送任务.为了研究多行程带时间窗口的车辆配送(VRPTW)中的车辆调度问题.模型以车辆的固定费用、车辆行驶过程中的等待费用、司机的工作小时费最小为目标,同时也融合了司机在执行不同路线时,由于熟悉的过程所弓I起的费用.通过对路线的时间窗口性质的分析,建立了调度问题的模型.     

客户终生价值的蒙特卡罗分析

客户终生价值分析是客户关系管理研究的重要课题．但现有的研究只限于于期望值分析，而忽略了客户价值的风险。本文使用贝叶斯方法及蒙特卡罗方法分析客户终生价值及客户资产，可以得到个体客户终生价值和客户资产的后验分布样本。分析的结果揭示了具有相近期望价值的客户，其风险可能存在较大差异，为客户选择决策提供了依据。     

Parallel Markov chain Monte Carlo Simulation by Pre-Fetching

In recent years, parallel processing has become widely available to researchers. It can be applied in an obvious way in the context of Monte Carlo simulation, but techniques for “parallelizing” Markov chain Monte Carlo (MCMC) algorithms are not so obvious, apart from the natural approach of generating multiple chains in parallel. Although generation of parallel chains is generally the easiest approach, in cases where burn-in is a serious problem, it is often desirable to use parallelization to speed up generation of a single chain. This article briefly discusses some existing methods for parallelization of MCMC algorithms, and proposes a new “pre-fetching” algorithm to parallelize generation of a single chain.     

基于蒙特卡罗模拟的上海铜期货保证金研究

基于VaR技术的保证金计算方法被视为保证金制度发展的趋势,蒙特卡罗模拟则被用来解决传统VaR模型对价格波动极端状况时的低估问题。根据基于蒙特卡罗模拟的保证金算法对上海期货交易所铜期货保证金水平的实证结果,模拟的保证金算法能够适应铜期货合约风险管理的需求,保证金水平反映了市场风险状况,也有效的降低了投资者交易成本。铜期货合约现行静态保证金收取方式亟需改进,5%保证金比例总体偏高,但在市场剧烈波动时又略显不足。综合考虑反馈检验,投资者交易成本,以及模型的计算时间,EGARCH-T是最佳的铜期货保证金模拟算法。     

Exact Simulation of Jump-Diffusion Processes with Monte Carlo Applications

We introduce a novel algorithm (JEA) to simulate exactly from a class of one-dimensional jump-diffusion processes with state-dependent intensity. The simulation of the continuous component builds on the recent Exact Algorithm (Beskos et al., Bernoulli 12(6):1077–1098, 2006a). The simulation of the jump component instead employs a thinning algorithm with stochastic acceptance probabilities in the spirit of Glasserman and Merener (Proc R Soc Lond Ser A Math Phys Eng Sci 460(2041):111–127, 2004). In turn JEA allows unbiased Monte Carlo simulation of a wide class of functionals of the process’ trajectory, including discrete averages, max/min, crossing events, hitting times. Our numerical experiments show that the method outperforms Monte Carlo methods based on the Euler discretization.     

An Integer Programming Approach to the Vehicle Scheduling Problem

This paper describes an integer programming formulation of the vehicle scheduling problem and illustrates how such a formulation can be extended to incorporate restrictions on work load, coverage and service that occur in real world vehicle scheduling problems. The integer programme is solved using the Revised Simplex method, additional constraints being introduced to retain integrality during convergence. The feasible region of this integer programme is initially restricted so that only routes constructed through sets of radially contiguous locations are considered. The effect of relaxing these over-constraints is explored. The method is demonstrated on fifteen problems ranging in size from 21 to 100 locations and the results generally show an improvement on previously published results. This is particularly true of the larger problems. This method compares favourably with other methods in computational efficiency.     

The Use of Straight Line Distances in Solutions to the Vehicle Scheduling Problem

This paper is concerned with the use of straight-line distances in algorithms concerned with the solution of the vehicle scheduling problem (V.S.P.). An empirical test is carried out to see whether transport operating cost between two points can be estimated from the corresponding straight-line distance, as often assumed in V.S.P. algorithms which have a cost-minimising objective. The use of variance in V.S.P. algorithms is also discussed, especially in relation to travelled times on links and limits on goods vehicle drivers' hours.     

基于蒙特卡罗模拟的供应链风险估计研究

以市场需求波动风险为例,基于蒙特卡罗模拟研究了供应链风险估计问题.首先,对市场需求波动风险及其损失度量进行理论分析,利用市场需求波动风险情境下的供应链系统库存成本损失来度量市场需求波动风险的损失.其次,选择供应链末端需求为蒙特卡罗方法待模拟的随机变量,基于需求建立了市场需求波动风险概率测度模型和风险损失度量模型,确定了市场需求波动风险概率和风险损失为需求的相关量.然后,通过实例的仿真求解验证了模型.最后,给出了利用本模型方法进行供应链风险估计时需要注意的问题及进一步研究的问题.研究表明:蒙特卡罗方法对供应链风险估计具有较强的鲁棒性.     

基于Matlab的Poisson分布随机数的Monte carlo模拟

给出了三种随机模拟:Poisson分布随机数的方法,用Matlab7.0软件实现了对Poisson分布随机数的随机模拟,并用随机模拟的方法解决了商品销售、母鸡下蛋等实际应用问题.