基于遗传算法的带时间窗约束车辆路径问题研究

在建立带时间窗约束物流配送路径优化问题数学模型的基础上,构造了求解该问题的遗传算法,并进行了实验计算.计算结果表明,用遗传算法进行物流配送路径优化,可以方便有效地求得问题的最优解或近似最优解.     

On the retention of finished goods inventory when reorder-occurrence is uncertain

Finished goods inventory may accumulate for a variety of reasons in the production of lowdemand or slow-moving items. In this article a simple model is developed and some results are presented to aid in making inventory retention decisions when there exists uncertainty about whether reorders for a slow-moving item will be received in the future. In formulating the model, it is assumed that some excess inventory remains after filling a customer order and that a single reorder for the item is possible. The problem is to determine how long to retain the inventory before disposing of it.The relevant expected costs of retaining some quantity of inventory for a period of time consist of two types: (1) the inventory carrying cost less the salvage value from disposal; and (2) the future production cost incurred due to premature disposal. Using conventional optimization, a relationship for finding the optimal retention period is derived and conditions are identified that ensure that the optimal retention period can be obtained directly from the relationship.To determine the optimal retention period, probability distributions are required for the interarrival time until the reorder occurs and for the reorder quantity. While it seems logical to assume that each item would have its own distributions, this argument leads to a specification problem since the data needed to establish distributions for individual items will generally not be available for slow-moving items. One approach used to overcome this problem in practice is to combine data for a selected group of items and use the combined data to obtain distributions useful for any or all of the items in the group. An example illustrating this approach is provided.     

Inventory control with unknow demand distribution: a slow-mover case

In this paper some tools will be developed for analysing a simple inventory problem of the slow-mover type with the special feature that the probability distribution of the demand interarrival times is unknown. The role of sufficient statistics in decision making is analysed for an arbitrary optimality criterion and particularly for the Bayesian criterion. A computational approach for the case of a Bayesian criterion is presented together with some numerical results.     

Produktiviteitsverhoging bij accountantscontrole door toepassing van gelaagde steekproeven

The auditor's productivity: application of stratified sampling to an auditing problem.
In this paper it is shown that the use of stratified sampling can lead to a considerable saving of costs in auditing operations and thus increases the auditor's productivity.
The sampling method to be described will render it possible to say that the total value of the transactions will not differ more than a fraction φ, given in advance, from the correct total value, apart from a probability not surpassing a preassigned level e, on condition that a certain acceptance criterion is fulfilled. Taking into account the auditing costs, the author gives an optimal sampling design and calculates the savings obtained.
Finally the theoretical results are applied to a population of clerical transactions, with an exponential and a logarithmico-normal distribution respectively.     

Time dependent solution of a queueing problem with correlated batch arrivals and general service time distribution

This paper considers the transient behaviour of queueing problem in which (i) the arrivals occur in batches of variable size (ii) the arrival and no arrival of a batch at two consecutive transition marks are correlated (iii) the service time distribution for each, unit is general with probability density functionD(x). TheLaplace transform of various probability generating functions of queue length are obtained and some particular cases are derived therefrom.     

时变路网无能力约束车辆路径优化

讨论了一类时变路网下的无能力约束车辆配送路径优化问题,建立了基于时变路网的以配送总耗时最短为优化目标的无能力约束车辆配送路径优化模型。提出了基于实时Dijkstra算法的模型求解方法。数值算例表明考虑路网时变特性得到的优化配送方案将更加符合配送实际。     

Optimal lottery

This article proposes an equilibrium approach to lottery markets in which a firm designs an optimal lottery to rank-dependent expected utility (RDU) consumers. We show that a finite number of prizes cannot be optimal, unless implausible utility and probability weighting functions are assumed. We then investigate the conditions under which a probability density function can be optimal. With standard RDU preferences, this implies a discrete probability on the ticket price, and a continuous probability on prizes afterwards. Under some preferences consistent with experimental literature, the optimal lottery follows a power-law distribution, with a plausibly extremely high degree of prize skewness.     

需求受定购数量影响的供应链合同设计问题

本文针对一类市场需求受定购影响的问题提出了最佳合同设计问题。现实生活中上网卡或者高档消费品等特殊商品，数量卖的过多，顾客对该商品的评价下降，从而购买量也会相应下降，因此零售商需要考虑如何制定定购数量和合同形式使得自身利益最大。经对目前各种合同形式的研究，发现buy-back合同是最合适的合同形式，它能够达到供应链最佳协调的效果并能实现利润在供应链伙伴间任意分配。     

Optimal estimates and optimal predictors of finite population characteristics in the presence of nonresponse

Summary When samples from a finite population are studied, for instance by interview, there will usually be some units from which no response is obtained. In this paper optimal predictors of finite population characteristics, when nonresponse is present, are studied. The predictors are studied under simple regression superpopulation models. The optimal predictors are connected to the classical weighted sample estimates which are shown to be maximum likelihood estimates, provided the probability function is fully described by the sampling design. The predictors are compared with respects to their efficiencies for some simple models and a possible explanation to the fact that the poststratification estimate which compensate for nonresponse does no better than the simple estimate, is pointed out.     

Can the random walk model be beaten in out-of-sample density forecasts? Evidence from intraday foreign exchange rates

It has been documented that random walk outperforms most economic structural and time series models in out-of-sample forecasts of the conditional mean dynamics of exchange rates. In this paper, we study whether random walk has similar dominance in out-of-sample forecasts of the conditional probability density of exchange rates given that the probability density forecasts are often needed in many applications in economics and finance. We first develop a nonparametric portmanteau test for optimal density forecasts of univariate time series models in an out-of-sample setting and provide simulation evidence on its finite sample performance. Then we conduct a comprehensive empirical analysis on the out-of-sample performances of a wide variety of nonlinear time series models in forecasting the intraday probability densities of two major exchange rates—Euro/Dollar and Yen/Dollar. It is found that some sophisticated time series models that capture time-varying higher order conditional moments, such as Markov regime-switching models, have better density forecasts for exchange rates than random walk or modified random walk with GARCH and Student-t innovations. This finding dramatically differs from that on mean forecasts and suggests that sophisticated time series models could be useful in out-of-sample applications involving the probability density.     

Investigating design for survival models

The aim of this paper is to derive methodology for designing ‘time to event’ type experiments. In comparison to estimation, design aspects of ‘time to event’ experiments have received relatively little attention. We show that gains in efficiency of estimators of parameters and use of experimental material can be made using optimal design theory. The types of models considered include classical failure data and accelerated testing situations, and frailty models, each involving covariates which influence the outcome. The objective is to construct an optimal design based of the values of the covariates and associated model or indeed a candidate set of models. We consider D-optimality and create compound optimality criteria to derive optimal designs for multi-objective situations which, for example, focus on the number of failures as well as the estimation of parameters. The approach is motivated and demonstrated using common failure/survival models, for example, the Weibull distribution, product assessment and frailty models.     

Preference for equivalent random variables: A price for unbounded utilities

Savage's expected utility theory orders acts by the expectation of the utility function for outcomes over states. Therefore, preference between acts depends only on the utilities for outcomes and the probability distribution of states. When acts have more than finitely many possible outcomes, then utility is bounded in Savage's theory. This paper explores consequences of allowing preferences over acts with unbounded utility. Under certain regularity assumptions about indifference, and in order to respect (uniform) strict dominance between acts, there will be a strict preference between some pairs of acts that have the same distribution of outcomes. Consequently in these cases, preference is not a function of utility and probability alone.     

When the principal knows better than the agent: Subjective evaluations as an optimal disclosure mechanism

When the firm has some private and unverifiable information about an employee’s ability, it can design a subjective evaluation mechanism, whereby payments are tied to evaluations, to communicate such information. In this paper, I investigate how to design an optimal disclosure mechanism for the firm. I characterize the firm’s optimal disclosure policy as a function of the worker’s ability distribution, with the hazard rate function playing a key role. I also demonstrate that with some reasonable restrictions on the ability distribution, the firm’s optimal strategy exhibits a particular pattern: it will reward the best workers aggressively, fire the worst ones, and assign one central rating to the rest. The predictions are consistent with the way firms utilize subjective evaluations in reality.     

基于时间约束的单产品共同配送研究

随着物流业的调整发展．提高物流效率、降低物流成本逐渐成为关注的焦点。有着发达物流业的国家,如德国、美国等的实践已经证实,采用共同配送这一先进的配送模式,将能够改善在物流效率、物流成本方面所凸现的问题。在我国,共同配送体系还不完善,加之客户对于配送时间的要求也越来越高．满足客户时间要求的集约化、协同化配送就成为亟待解决的问题。文章针对这一问题,将“软时间窗”和“硬时间窗”同时引入到共同配送中,建立模型并通过算例分析对理论研究进行了实证。     

When should homeless families get subsidized apartments? A theoretical inquiry

How and when should operators of homeless shelters place families from these shelters into subsidized housing? I apply the tools of contract theory to this problem, especially some approaches that have been taken to optimal unemployment insurance. The problem combines moral hazard and adverse selection. When all families are drawn from the same distribution, placement should occur immediately. When families are heterogeneous, the optimal strategy creates a separating equilibrium. Good searchers self-select into a contract with high probability of immediate placement and no probability of later placement; poorer searchers self-select into a contract with a lower probability of immediate placement but a positive probability of later placement.     

Optimal inventories for repairable redundant systems with aging components

Complex systems that are required to perform very reliably are often designed to be “fault-tolerant,” so that they can function even though some component parts have failed. Often fault-tolerance is achieved through redundancy, involving the use of extra components. One prevalent redundant component configuration is the m-out-of-n system, where at least m of n identical and independent components must function for the system to function adequately.Often machines containing m-out-of-n systems are scheduled for periodic overhauls, during which all failed components are replaced, in order to renew the machine's reliability. Periodic overhauls are appropriate when repair of component failures as they occur is impossible or very costly. This will often be the case for machines which are sent on “missions” during which they are unavailable for repair. Examples of such machines include computerized control systems on space vehicles, military and commercial aircraft, and submarines.An interesting inventory problem arises when periodic overhauls are scheduled. How many spare parts should be stocked at the maintenance center in order to meet demands? Complex electronic equipment is rarely scrapped when it fails. Instead, it is sent to a repair shop, from which it eventually returns to the maintenance center to be used as a spare. A Markov model of spares availability at such a maintenance center is developed in this article. Steady-state probabilities are used to determine the initial spares inventory that minimizes total shortage cost and inventory holding cost. The optimal initial spares inventory will depend upon many factors, including the values of m and n, component failure rate, repair rate, time between overhauls, and the shortage and holding costs.In a recent paper, Lawrence and Schaefer [4] determined the optimal maintenance center inventories for fault-tolerant repairable systems. They found optimal maintenance center inventories for machines containing several sets of redundant systems under a budget constraint on total inventory investment. This article extends that work in several important ways. First, we relax the assumption that the parts have constant failure rates. In this model, component failure rates increase as the parts age. Second, we determine the optimal preventive maintenance policy, calculating the optimal age at which a part should be replaced even if it has not failed because the probability of subsequent failure has become unacceptably high. Third, we relax the earlier assumption that component repair times are independent, identically distributed random variables. In this article we allow congestion to develop at the repair shop, making repair times longer when there are many items requiring repair. Fourth, we introduce a more efficient solution method, marginal analysis, as an alternative to dynamic programming, which was used in the earlier paper. Fifth, we modify the model in order to deal with an alternative objective of maximizing the job-completion rate.In this article, the notation and assumptions of the earlier model are reviewed. The requisite changes in the model development and solution in order to extend the model are described. Several illustrative examples are included.     

Optimal prediction designs in finite discrete spectrum linear regression models

In the paper, we solve the n-point optimal prediction design problem for the simplest nontrivial finite discrete spectrum linear regression models with correlated observations. We show that for all the models in consideration, there exists an optimal prediction design supported on at most three distinct points, which can be computed using one-dimensional optimization. In some cases, an optimal prediction design can be found explicitly.     

Bepaling van de personeelssterkte op kostenbasis*

Determining the optimal number of staff in a department using a method based on costs. How many men do you appoint in a department of a firm? This number can be determined in an optimal way, if the following data are known: - The number of men required per unit of time (may be given as a stochastic quantity). - The mean probability of absence per man in the department (due to illness, holidays etc.). - Wages per man. - Costs (proceeds), if in one unit of time there are less (more) men available than required. Generally the solution will be obtained by an iterative method. However, when the parameters show a certain behaviour it is possible to find the optimum solution by analytical and graphical means.     

Nonparametric maximum likelihood estimation of a probability density via mathematical programming

Based on sample values of a one-dimensional random variable a nonparametric maximum likelihood estimate for the unknown probability density is introduced as the solution of an optimization problem in an appropriate Hilbert space. This solution turns out to be a polynomial spline function, and a complete characterization is given using recent results on the differentiability of the optimal value of a parametrized family of optimization problems. An important feature of this estimate is that its support interval results in a quite natural way from the formulation of the problem and is not fixed in advance. The estimator is shown to have a certain consistency property for a special class of density functions. Numerical results will be given in a subsequent paper.     

Expected Precision of Estimation and Probability of Ruling Out a Hypothesis Based on a Confidence Interval

Interval estimation is an important objective of most experimental and observational studies. Knowing at the design stage of the study how wide the confidence interval (CI) is expected to be and where its limits are expected to fall can be very informative. Asymptotic distribution of the confidence limits can also be used to answer complex questions of power analysis by computing power as probability that a CI will exclude a given parameter value. The CI‐based approach to power and methods of calculating the expected size and location of asymptotic CIs as a measure of expected precision of estimation are reviewed in the present paper. The theory is illustrated with commonly used estimators, including unadjusted risk differences, odds ratios and rate ratios, as well as more complex estimators based on multivariable linear, logistic and Cox regression models. It is noted that in applications with the non‐linear models, some care must be exercised when selecting the appropriate variance expression. In particular, the well‐known ‘short‐cut’ variance formula for the Cox model can be very inaccurate under unequal allocation of subjects to comparison groups. A more accurate expression is derived analytically and validated in simulations. Applications with ‘exact’ CIs are also considered.