Inventory control under temporal demand heteroscedasticity

This paper studies an inventory control problem when the variance of demand is time-varying and exhibits temporal heteroscedasticity. We use a first-order autoregressive process to characterize the dynamic changes in the level of demand over time and a GARCH(1, 1) structure to describe the changes in the variance of demand. Under these demand settings, we quantify the effect of a temporal heterogeneous variance on inventory performance for a system controlled via an order-up-to-level policy. We show that the effect of temporal heteroscedasticity on the forecasting accuracy can be additively decomposed from the total forecasting error variance. The decomposition is used to derive the absolute and relative cost deviations when the temporal heteroscedasticity is ignored. The relationship of these cost deviations to demand autocorrelation and replenishment leadtime is investigated. Computational results show that ignoring temporal heteroscedasticity can increase firm’s inventory costs by as much as 30% when demand autocorrelation is highly positive.     

An inventory model for slow moving items subject to obsolescence

In this paper, we consider a continuous review inventory system of a slow moving item for which the demand rate drops to a lower level at a known future time instance. The inventory system is controlled according to a one-for-one replenishment policy with a fixed lead time. Adapting to lower demand is achieved by changing the control policy in advance and letting the demand take away the excess stocks. We show that the timing of the control policy change primarily determines the tradeoff between backordering penalties and obsolescence costs. We propose an approximate solution for the optimal time to shift to the new control policy minimizing the expected total cost during the transient period. We find that the advance policy change results in significant cost savings and the approximation yields near optimal expected total costs.     

Optimal control of a finite-capacity inventory system with setup cost and lost sales

One of the most fundamental results in inventory theoryis the optimality of (s, S) policy for inventory systems withsetup cost. This result is established based on a key assumptionof infinite production/ordering capacity. Several studies haveshown that, when there is a finite production/ordering capacity,the optimal policy for the inventory system is very complicatedand indeed, only partial characterization for the optimal policyis possible. In this paper, we consider a continuous reviewinventory system with finite production/ordering capacity andsetup cost, and show that the optimal control policy for thissystem has a very simple structure. We also develop efficientalgorithms to compute the optimal control parameters.     

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.     

Analysis of event-based, single-server nonstationary simulation responses using classical time-series models

In this article, we present a metamodeling methodology for analyzing event-based, single-server nonstationary simulation responses that is based on the use of classical ARIMA (or SARIMA) time-series models. Some analytical results are derived for a Markovian queue and are used to evaluate the proposed methodology. The use of the corresponding procedure is illustrated on a traffic example from the simulation literature. Some conclusions are drawn and recommendations for further work are stated.     

Confidence-based optimisation for the newsvendor problem under binomial,Poisson and exponential demand

We introduce a novel strategy to address the issue of demand estimation in single-item single-period stochastic inventory optimisation problems. Our strategy analytically combines confidence interval analysis and inventory optimisation. We assume that the decision maker is given a set of past demand samples and we employ confidence interval analysis in order to identify a range of candidate order quantities that, with prescribed confidence probability, includes the real optimal order quantity for the underlying stochastic demand process with unknown stationary parameter(s). In addition, for each candidate order quantity that is identified, our approach produces an upper and a lower bound for the associated cost. We apply this approach to three demand distributions in the exponential family: binomial, Poisson, and exponential. For two of these distributions we also discuss the extension to the case of unobserved lost sales. Numerical examples are presented in which we show how our approach complements existing frequentist—e.g. based on maximum likelihood estimators—or Bayesian strategies.     

Time series analysis

Current univariate and multivariate time series modelling procedures are reviewed. Areas of disagreement are discussed, such as the choice of a forecasting method, whether to use time series analysis or econometrics for economic data, the merits of prior seasonal adjustment, and the advisability of prewhitening in multivariate modelling. Some recent developments in model identification, estimation and model criticism are described. It is argued that too little attention has been paid to allowing for departures from the model; this leads to a discussion of exploratory and robust techniques. Finally, it is pointed out that little has been done on modelling positive and discrete-valued time series of importance in OR such as lifetimes and counts; some recent proposals are described.     

Forecasting life expectancy: Evidence from a new survival function

We propose a new survival function to forecast life expectancies at various ages. The proposed model comprises the youth-to-adulthood component and the old-to-oldest-old component. It is able to closely fit adult survivorship of the US men and women in the period from 1950 to 2010. We find evidence that the forecasting performance of life expectancies by the proposed model compares favorably with those obtained from the popular Lee–Carter model (1992) and the shifting logistic model proposed by Bongaarts (2005).     

岩土工程位移时间序列的组合预测研究

将组合预测方法用于岩土工程位移时间序列预测.结合实际观测数据,分别建立位移时间序列预测的GM(1,1)模型、Verhulst模型和趋势曲线模型.采用极小误差法确定各单一模型的权重,建立组合预测模型.应用表明,组合预测的精度高,为岩土工程位移预测提供了一种实用、可靠的方法.     

上证综指和深圳成指的可预测性分析

本文讨论了赫斯特指数的计算方法和R／S分析法在股市时间序列中的应用,表明了上证综指和深圳成指的可预测性。     

Application of time series analysis and modern control theory to the cement plant

Cement plant process is full of internal noise sources and feedback loops. Therefore, statistical approach is required to understand its dynamic characteristics. Time series analysis has been applied to some important subprocesses of a cement plant process. These are the vertical mill process, calcining process and clinker cooling process. Based on the AR models of these, a set of optimum controllers have been designed by modern control theory. Successful results of application are reported in this paper. A method of determining optimal production level is also discussed.     

MODELING THE EFFECT OF SEA SURFACE TEMPERATURE ON SEA TURTLE NESTING ACTIVITIES BY INVESTIGATING SEASONAL TRENDS

ABSTRACT. In the present study, a series of models have been developed in order to investigate the effect of sea water temperature upon the nesting activities of marine turtles. Autoregressive integrated moving average (ARIMA) models, ARIMA models with transfer functions and regression models were developed for forecasting variations in the breeding activity of loggerheads, nesting at the island of Zakynthos, West Greece. Identification and development of the models was determined by the use of several statistical criteria. Weekly data series of sea turtles emerging attempts and number of nests laid were analyzed and compared with sea surface temperature (SST) data series. Our results indicate that whether SST data were included in the ARIMA models with transfer functions and the regression models that developed to describe both emergence data and number of nests, tended to improve fitting and forecasting accuracy. Data series of the number of nests laid was further correlated with observation of emergence data. Adding the effect of previous and current year nesting attempts and including SST data resulted to higher forecasting accuracy and fitting performance.     

Forecasting item-level demands: an analytical evaluation of top-down versus bottom-up forecasting in a production-planning framework

Rajesh Piplani School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore Email: vish{at}pmail.ntu.edu.sg Received on 12 January 2007. Accepted on 19 November 2007. We compare the performance of top–down (TD) and bottom–up(BU) strategies for forecasting the demand of an item that belongsto a product family. The TD strategy forecasts the sum of theitem demands and distributes it to the individual item basedupon the historical demand proportion of each item in the family.The BU strategy forecasts each item demand individually usingthe historical demand data for the particular item. All theitem demands, which may be correlated with each other, are assumedto follow a first-order univariate moving average process. Asis common in a production-planning environment, the forecastingunder both strategies is carried out using the exponential smoothingtechnique. We show that the performance of the two forecastingstrategies is nearly identical, regardless of the coefficientof correlation between the item demands, the items' proportionin the family and the coefficient of the serial correlationterm of the demand process. We further investigate the relativeperformance of the two strategies when a fixed (rather thanthe optimal) smoothing constant is used for forecasting thedemand under both strategies.     

Assessing the effect of advertising expenditures upon sales: A Bayesian structural time series model

We propose a robust implementation of the Nerlove‐Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a countrywide fast‐food franchise network with its weekly sales. Due to the flexibility and modularity of the model, it is well suited to generalization to other markets or situations. Its Bayesian nature facilitates incorporating a priori information reflecting the manager's views, which can be updated with relevant data. This aspect of the model will be used to support the decision of the manager on the budget scheduling of the advertising firm across time and channels.     

A Turing Test of Bootstrap Scenarios

Scenario generation can be an important part of the training of human decision makers. A good scenario generation method should be able to generate large numbers of realistic scenarios. When the scenarios take the form of univariate stationary time series, the moving blocks bootstrap has the potential to be a good automatic scenario generator. However, one must determine the proper bootstrap block length. We have developed a method of setting the block length based on the distribution of a statistic computed from zero crossing counts. To test whether this way of setting the block length results in realistic scenarios, we performed two Turing tests. These visualization experiments confirmed that, when a bootstrap is optimally tuned, it is difficult for sophisticated subjects to identify a bootstrap sample plotted among several real samples. The main visual defects in moving blocks bootstrap samples are sudden jumps at block boundaries and repeating patterns.     

Inventory returns and special sales in a lot-size system with constant rate of deterioration

The problem of returning or of selling the inventory excess to optimal stock level is considered for deteriorating items. Two inventory models, viz. the infinite and the finite horizon models, are developed, in which the deterioration is assumed to be a constant fraction of the on hand inventory. Both the models are developed under the assumptions of instantaneous delivery and no shortages. When there is no deterioration, the developed models are related to the corresponding inventory models for non-deteriorating items. Examples are given to illustrate the derived results.     

组合预测方法在旅游经济分析预测中的应用

应用组合预测方法,对浙江省旅游业主要指标的统计数据建立数学模型,对旅游经济发展进行现状分析和前景预测,并探讨了旅游经济对社会经济发展的影响、研究表明所建模型具有很好的拟合精度,较好的刻画了浙江省旅游经济的发展过程,这将为研究和调控旅游经济发展趋势提供有益的参考依据.     

Aggregation of spectral density estimators

Given stationary time series data, we study the problem of finding the best linear combination of a set of lag window spectral density estimators with respect to the mean squared risk. We present an aggregation procedure and prove a sharp oracle inequality for its risk. We also provide simulations demonstrating the performance of our aggregation procedure, given Bartlett and other estimators of varying bandwidths as input. This extends work by P. Rigollet and A. Tsybakov on aggregation of density estimators.     

Forecasting stock index price based on M-factors fuzzy time series and particle swarm optimization

In real time, one observation always relies on several observations. To improve the forecasting accuracy, all these observations can be incorporated in forecasting models. Therefore, in this study, we have intended to introduce a new Type-2 fuzzy time series model that can utilize more observations in forecasting. Later, this Type-2 model is enhanced by employing particle swarm optimization (PSO) technique. The main motive behind the utilization of the PSO with the Type-2 model is to adjust the lengths of intervals in the universe of discourse that are employed in forecasting, without increasing the number of intervals. The daily stock index price data set of SBI (State Bank of India) is used to evaluate the performance of the proposed model. The proposed model is also validated by forecasting the daily stock index price of Google. Our experimental results demonstrate the effectiveness and robustness of the proposed model in comparison with existing fuzzy time series models and conventional time series models.