Repeated SPRT charts for monitoring INAR(1) processes

Poisson integer valued autoregressive (INAR) models have been proposed for modeling correlated count data. Poisson lognormal (PLN) INAR models extend their use to overdispersed contexts. In this paper, we will propose the use of a repeated Sequential Probability Ratio Test (SPRT) procedure to detect change in first‐order INAR and PLN INAR models. We consider change in the mean, the autocorrelation parameter, and the overdispersion parameter. Simulation results show the repeated SPRT procedure performs favorably relative to previously proposed CUSUM procedures that are based on either the observations themselves or residuals of the observations from predicted values. A dataset on invasive insect species is used to illustrate the repeated SPRT procedure.     

Time series count data models: an empirical application to traffic accidents

Count data are primarily categorised as cross-sectional, time series, and panel. Over the past decade, Poisson and Negative Binomial (NB) models have been used widely to analyse cross-sectional and time series count data, and random effect and fixed effect Poisson and NB models have been used to analyse panel count data. However, recent literature suggests that although the underlying distributional assumptions of these models are appropriate for cross-sectional count data, they are not capable of taking into account the effect of serial correlation often found in pure time series count data. Real-valued time series models, such as the autoregressive integrated moving average (ARIMA) model, introduced by Box and Jenkins have been used in many applications over the last few decades. However, when modelling non-negative integer-valued data such as traffic accidents at a junction over time, Box and Jenkins models may be inappropriate. This is mainly due to the normality assumption of errors in the ARIMA model. Over the last few years, a new class of time series models known as integer-valued autoregressive (INAR) Poisson models, has been studied by many authors. This class of models is particularly applicable to the analysis of time series count data as these models hold the properties of Poisson regression and able to deal with serial correlation, and therefore offers an alternative to the real-valued time series models. The primary objective of this paper is to introduce the class of INAR models for the time series analysis of traffic accidents in Great Britain. Different types of time series count data are considered: aggregated time series data where both the spatial and temporal units of observation are relatively large (e.g., Great Britain and years) and disaggregated time series data where both the spatial and temporal units are relatively small (e.g., congestion charging zone and months). The performance of the INAR models is compared with the class of Box and Jenkins real-valued models. The results suggest that the performance of these two classes of models is quite similar in terms of coefficient estimates and goodness of fit for the case of aggregated time series traffic accident data. This is because the mean of the counts is high in which case the normal approximations and the ARIMA model may be satisfactory. However, the performance of INAR Poisson models is found to be much better than that of the ARIMA model for the case of the disaggregated time series traffic accident data where the counts is relatively low. The paper ends with a discussion on the limitations of INAR models to deal with the seasonality and unobserved heterogeneity.     

Newsvendor decisions under supply uncertainty

We analyse the impact of supply uncertainty on newsvendor decisions. First, we derive a solution for a newsvendor facing stochastic supply yield, in addition to stochastic demand. While earlier research has considered independent uncertainties, we derive the optimal order quantity for interdependent demand and supply and provide a closed-form solution for a specific copula-based dependence structure. This allows us to give insights into how dependence impacts the newsvendor’s decision, profit and risk level. In addition to the theory, we present experimental results that show how difficult newsvendor decisions under supply uncertainty are for human subjects. In our experiment, the control group replicated a well-known newsvendor experiment, whereas the test group faced additional supply yield uncertainty. Comparison of these results shows that under low-profit condition, subjects are able to incorporate supply uncertainty quite well in their decisions. Under high-profit condition, the deviation from the optimum is much more significant. We discuss this asymmetry and also propose some ways to improve newsvendor decision-making.     

Testing for Poisson arrivals in INAR(1) processes

In the framework of integer-valued autoregressive processes of order 1 [INAR(1)], two new tests for the null hypothesis of Poisson-distributed innovations are developed. The tests focus on time reversibility, as this feature is shown to be satisfied exclusively by Poisson INAR(1) processes. The necessary asymptotic variances are explicitly calculated using the joint cumulants of these processes. The finite-sample behavior of the test statistics and the power of the tests are investigated in a simulation study. The results show that the newly developed tests perform better than existing ones in certain situations.     

A new bivariate integer-valued GARCH model allowing for negative cross-correlation

Univariate integer-valued time series models, including integer-valued autoregressive (INAR) models and integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, have been well studied in the literature, but there is little progress in multivariate models. Although some multivariate INAR models were proposed, they do not provide enough flexibility in modeling count data, such as volatility of numbers of stock transactions. Then, a bivariate Poisson INGARCH model was suggested by Liu (Some models for time series of counts, Dissertations, Columbia University, 2012), but it can only deal with positive cross-correlation between two components. To remedy this defect, we propose a new bivariate Poisson INGARCH model, which is more flexible and allows for positive or negative cross-correlation. Stationarity and ergodicity of the new process are established. The maximum likelihood method is used to estimate the unknown parameters, and consistency and asymptotic normality for estimators are given. A simulation study is given to evaluate the estimators for parameters of interest. Real and artificial data examples are illustrated to demonstrate good performances of the proposed model relative to the existing model.     

Effective Control Charts for Monitoring the NGINAR(1) Process

In recent years, there has been a growing interest in the control of autocorrelated count data. Existing results focus on the Poisson integer‐valued autoregressive (INAR) process, but this process cannot deal with overdispersion (variance is greater than mean), which is a common phenomenon in count data. We propose to control the autocorrelated count data based on a new geometric INAR (NGINAR) process, which is an alternative to the Poisson one. In this paper, we use the combined jumps chart, the cumulative sum chart, and the combined exponentially weighted moving average chart to detect the shift of parameters in the process. We compare the performance of these charts for the case of an underlying NGINAR(1) process in terms of the average run lengths. One real example is presented to demonstrate good performances of the charts. Copyright © 2015 John Wiley & Sons, Ltd.     

A Two‐Sided Cumulative Sum Chart for First‐Order Integer‐Valued Autoregressive Processes of Poisson Counts

Count data processes are often encountered in manufacturing and service industries. To describe the autocorrelation structure of such processes, a Poisson integer‐valued autoregressive model of order 1, namely, Poisson INAR(1) model, might be used. In this study, we propose a two‐sided cumulative sum control chart for monitoring Poisson INAR(1) processes with the aim of detecting changes in the process mean in both positive and negative directions. A trivariate Markov chain approach is developed for exact evaluation of the ARL performance of the chart in addition to a computationally efficient approximation based on bivariate Markov chains. The design of the chart for an ARL‐unbiased performance and the analyses of the out‐of‐control performances are discussed. Copyright © 2012 John Wiley & Sons, Ltd.     

Impact on inventory costs with consolidation of distribution centers

The consolidation of Distribution Centers (DCs) is a new trend in global logistics management, with a reduction in inventory costs often being cited as one of the main benefits. This paper uses an analytical modeling approach to study the impact on facility investment and inventory costs when several DCs are consolidated into a central DC. In particular, our model suggests that consolidation leads to lower total facility investment and inventory costs if the demands are identically and independently distributed, or when they follow independent but possibly nonidentical Poisson processes. This agrees with the conclusion of the classical EOQ and newsvendor models. However, we show by an example that, for general stochastic demand processes, the total facility investment and inventory costs of a consolidated system can be infinitely worse off than that of a decentralized system. This arises mainly because the order replenishment fixed cost yields a cost component proportional to the square root of the mean value of the demand, while the demand uncertainty yields a cost component proportional to the standard deviation of the demand. Whether consolidation is cost effective or not depends on the trade-off between these two components, as indicated by an extensive numerical study. We also propose an algorithm that solves for a distribution system with the total facility investment and inventory costs within √2 of the optimal.     

An innovative air-conditioning load forecasting model based on RBF neural network and combined residual error correction

Accurate air-conditioning load forecasting is the precondition for the optimal control and energy saving operation of HVAC systems. They have developed many forecasting methods, such as multiple linear regression (MLR), autoregressive integrated moving average (ARIMA), grey model (GM) and artificial neural network (ANN), in the field of air-conditioning load prediction. However, none of them has enough accuracy to satisfy the practical demand. On the basis of these models existed, a novel forecasting method, called ‘RBF neural network (RBFNN) with combined residual error correction’, is developed in this paper. The new model adopts the advanced algorithm of neural network based on radial basis functions for the air-conditioning load forecasting, and uses the combined forecasting model, which is the combination of MLR, ARIMA and GM, to estimate the residual errors and correct the ultimate foresting results. A study case indicates that RBFNN with combined residual error correction has a much better forecasting accuracy than RBFNN itself and RBFNN with single-model correction.     

The inventory costs of common mis-specification of demand-forecasting models

In inventory planning, the use of exponential smoothing to forecast demand or the assumption that demand over consecutive time periods is i.i.d. is commonplace. In practice, these forecasting approaches are often invoked without justifying their appropriateness. In this paper we assert that, in many situations, the demand process may be different from that implicit in these commonly applied forecasting methods. In particular, we consider demand generated by a general ARM A process. For such a process, we derive expressions for the comparison of the steady-state sum of holding cost and stockout cost per unit time that results from using the correct forecasting model with that which results from the two commonly-used models mentioned above. This comparison indicates that correctly identifying the demand process is warranted and that popular efforts in batch-size reduction increase the benefits of doing so.     

Short-term forecasting of electricity prices in the colombian electricity market

The restructuring of the electricity-generating industry from protected monopoly to an open competitive market has presented producers with a problem scheduling generation: finding the optimal bidding strategy to maximise their profits. In order to solve this scheduling problem, a reliable system capable of forecasting electricity prices is needed. This work evaluates the forecasting capabilities of several modelling techniques for the next-day-prices forecasting problem in the Colombian market, measured in USD/MWh. The models include exogenous variables such as reservoir levels and load demand. Results show that a segmentation of the prices into three intervals, based on load demand behaviour, contribute to an important standard deviation reduction. Regarding the models under analysis, Takagi?Sugeno?Kang models and ARMAX models identified by means of a Kalman filter perform the best forecasting, with an error rate below 6%.     

Optimization of autoregressive,exogenous inputs-based typhoon inundation forecasting models using a multi-objective genetic algorithm

Three types of model for forecasting inundation levels during typhoons were optimized: the linear autoregressive model with exogenous inputs (LARX), the nonlinear autoregressive model with exogenous inputs with wavelet function (NLARX-W) and the nonlinear autoregressive model with exogenous inputs with sigmoid function (NLARX-S). The forecast performance was evaluated by three indices: coefficient of efficiency, error in peak water level and relative time shift. Historical typhoon data were used to establish water-level forecasting models that satisfy all three objectives. A multi-objective genetic algorithm was employed to search for the Pareto-optimal model set that satisfies all three objectives and select the ideal models for the three indices. Findings showed that the optimized nonlinear models (NLARX-W and NLARX-S) outperformed the linear model (LARX). Among the nonlinear models, the optimized NLARX-W model achieved a more balanced performance on the three indices than the NLARX-S models and is recommended for inundation forecasting during typhoons.     

Minimizing response time in a two-stage supply chain system with variable lead time and stochastic demand

We consider customer response time minimization in a two-stage system facing stochastic demand. Traditionally, the objective of representative mathematical models is to minimize costs related to production, inventory holding, and shortage. However, the highly competitive market characterized by impatient customers warrants the inclusion of costs related to customer waiting. Therefore we investigate a supply chain system in an uncertain demand setting that encompasses customer waiting costs as well as traditional plant costs (i.e. production and inventory costs). A representative expected cost function is derived and the closed form optimal solution is determined for a general demand distribution. We also provide examples to illustrate results for some common probability distributions. Our results indicate significant cost savings under certain assumptions when comparing solutions from the proposed model to the traditional newsvendor order/production quantity.     

The bullwhip effect under different information-sharing settings: a perspective on price-sensitive demand that incorporates price dynamics

Information sharing has been shown previously in the literature to be effective in reducing the magnitude of the bullwhip effect. Most of these studies have focused on a particular information-sharing setting that assumes demand follows an autoregressive process. In this paper, we contribute to the literature by presenting a price-sensitive demand model and a first-order autoregressive pricing process that is coupled to the optimal order-up-to inventory policy and the optimal minimum mean-squared error forecasting technique. We compare a no information-sharing setting – in which only the first stage of the supply chain observes end-customer demands and market prices, and upstream echelons must base their forecasts on downstream incoming orders – with two information-sharing settings, end-demand and order information and end-demand information. In the case of end-demand and order information, upstream echelons develop their forecasts and plan their inventories based on the end-customer demand, price information, and downstream orders. With end-demand information, upstream echelons use only end-customer demands and market prices to conduct their forecasting and planning. We derive the analytical expressions of the bullwhip effect with and without information sharing, quantify the impact of information sharing on the reduction of the bullwhip effect associated with end-demand and order information and end-demand information, and explore the optimal information setting that could most significantly restrain the bullwhip effect. Our analysis suggests that the value of these two information-sharing settings can be high, especially when the pricing process is highly correlated over time or when the product price sensitivity coefficient is small. Moreover, we find that the value of adopting end-demand and order information is always greater than that of end-demand information.     

Improved CUSUM monitoring of Markov counting process with frequent zeros

There has been a growing interest in monitoring processes featuring serial dependence and zero inflation. The phenomenon of excessive zeros often occurs in count time series because of the advancement of quality in manufacturing process. In this study, we propose three control charts, such as the cumulative sum chart with delay rule (CUSUM‐DR), conforming run length (CRL)‐CUSUM chart, and combined Shewhart CRL‐CUSUM chart, to enhance the performance of monitoring Markov counting processes with excessive zeros. Numerical experiments are conducted based on integer‐valued autoregressive time series models, for example, zero‐inflated Poisson INAR and INARCH, to evaluate the performance of the proposed charts designed for the detection of mean increase. A real example is also illustrated to demonstrate the usability of our proposed charts.     

Value of a put option to the risk-averse newsvendor

In this paper we consider an extension of the single-period inventory model with stochastic demand where a put option can be purchased to reduce losses resulting from low demand. The newsvendor not only chooses the order quantity but also determines the “strike price” and/or the “strike quantity” of the put option. As the buyer of the put option, the newsvendor pays the option writer an amount that equals the expected option payoff plus a risk premium and receives from the option writer the strike price (adjusted for salvage value) for each unit that the demand falls below the strike quantity. The newsvendor is risk-averse and attempts to maximize an expected utility function. We show that: (i) the same order quantity maximizes the expected profit with or without the option; and (ii) the strike price and strike quantity do not affect the newsvendor's maximum expected profit but they do affect the variance of the profit. We use concepts from stochastic dominance theory to prove the following result: if the newsvendor uses the expected profit maximizing order quantity and if she has a quadratic utility function, then maximizing her expected utility is equivalent to minimizing the variance of the profit. Sensitivity analysis results indicate that under poor economic conditions (low sale price/high purchase cost) it may not be optimal to purchase the option. We also find that when the option writer assumes a higher risk/return for the random option payoff (that he pays the newsvendor) the newsvendor can reduce her profit uncertainty by choosing the strike price or strike quantity optimally.     

How a competing environment influences newsvendor ordering decisions

We conduct an experimental study on the decision biases in a scenario in which two newsvendors compete for a common market. If stock-out occurs at one newsvendor, the unsatisfied demand is reallocated to the competitor. Following the existing theory, an experiment of competing games with high- and low-profit settings is conducted with a control experiment of a standard newsvendor scenario for reference. The results indicate that compared with the single scenario, a competing environment can cause participants to significantly increase their ordering levels in the high-profit group and increase their ordering oscillations in the low-profit group. In addition, we propose a behavioural model by combining the logit choice rule and mental accounting. The model fits the experimental data satisfactorily, and the estimation of the parameters indicates that the participants in the high-profit group tend to ignore distractions from competitors, while the participants in the low-profit group are highly influenced by their competitors. Observations from this study suggest that managers should pay careful attention to different profit-margin products in a competing environment.     

Forecast of trademark applications in Switzerland

Trademark offices which run according to principles of new management have an inherent need for dependable forecasting data in planning capacity and service levels. We wanted to find out whether there are factors which positively or negatively influence customers to register trademarks in Switzerland. Lacking literature on the idiosyncrasies of trademark filing behavior, we developed our own forecasting model adapted from those in other fields. It included timelines for trademark applications and corresponding classes over a 9-year period (1992–2001) and internal events which might possibly influence filing.The forecast is based on state space models with and without explanatory variables. We used a standard model with trend, season and random components, then added variables for external interventions and finally, added a model for regressors. The result was a statistical model which produced reliable forecasting over an 18-month period. It compares well to four other forecasting methods. Reliability was improved slightly by adding economic variables such as the Dow Jones Industrial Average, SPI, SMI and the Swiss Consumer Index.     

Some recent theory for autoregressive count time series

In this paper an overview is given over recent theoretical developments in autoregressive count time series. The focus is on generalized autoregressive models where the autoregressive structure is incorporated via a link function. Starting from an ordinary autoregressive model the difficulties in extending standard theory of statistical inference to count time series are highlighted. Special attention is given to the issues of ergodicity and asymptotic theory of estimation. Two main approaches are mentioned, a perturbation approach and the use of a weak dependence concept. The main emphasis is on the former. Linear as well as log-linear and nonlinear models are treated. It is argued that the developed theory forms a necessary basis for modelling and application of these count time series. The setting of the paper is one of simple models and conditional distributions of Poisson type. But it is claimed that the framework is general enough to handle many extensions with an accompanying flexibility in applications of these models.     

Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty

In this article, we investigate the newsvendor problem in a joint ordering and pricing setting in the presence of option contracts under demand uncertainty. At the beginning of a single selling season, the newsvendor who faces additive stochastic demand can obtain goods through two ways: ordering from a firm or purchasing and exercising call options. Single ordering (ordering from a firm only or purchasing and exercising call options only) and mixed ordering (ordering from a firm and purchasing and exercising call options simultaneously) cases are investigated. We find that the newsvendor’s optimal pricing and ordering strategies exist and are unique for both cases, respectively. In addition, when both cases are available, mixed ordering is the newsvendor’s optimal ordering policy. If only single ordering is available, the newsvendor prefers ordering from a firm when demand risk is low, while enjoys purchasing and exercising call options when demand risk is high. We also find that with option contracts, the newsvendor’s optimal order quantity and maximum expected profit are all decreasing in the option price and exercise price of product, while the optimal retail price in terms of option price and exercise price of product are intricate. Moreover, we show that, mixed ordering is more capable to deal with supply price volatility risk.