Forecasting of compound Erlang demand

Intermittent demand items dominate service and repair inventories in many industries and they are known to be the source of dramatic inefficiencies in the defence sector. However, research in forecasting such items has been limited. Previous work in this area has been developed upon the assumption of a Bernoulli or a Poisson demand arrival process. Nevertheless, intermittent demand patterns may often deviate from the memory-less assumption. In this work we extend analytically previous important results to model intermittent demand based on a compound Erlang process, and we provide a comprehensive categorisation scheme to be used for forecasting purposes. In a numerical investigation we assess the benefit of departing from the memory-less assumption and we provide insights into how the degree of determinism inherent in the process affects forecast accuracy. Operationalised suggestions are offered to managers and software manufacturers dealing with intermittent demand items

Poisson Distributed Individuals Control Charts with Optimal Limits

The conventional method used in attribute control charts is the Shewhart three sigma limits. The implicit assumption of the Normal distribution in this approach is not appropriate for skewed distributions such as Poisson, Geometric and Negative Binomial. Normal approximations perform poorly in the tail area of the these distributions. In this research, a type of attribute control chart is introduced to monitor the processes that provide count data. The economic objective of this chart is to minimize the cost of its errors which is determined by the designer. This objective is a linear function of type I and II errors. The proposed control chart can be applied to Poisson, Geometric and Negative Binomial as the underlying distribution of count data. Control limits in this chart is calculated optimally since it is based on the probability distribution of the data and can detect a directional shift in the process rate. Some numerical results for the optimal design of the proposed control chart are provided. The expected cost of the control chart is compared to that of a one sided c chart. The effects of changing the available parameters on the cost, errors and the optimal limits of the proposed control chart are shown graphically

Performance deterioration modeling and optimal preventive maintenance strategy under scheduled servicing subject to mission time

AbstractServicing is applied periodically in practice with the aim of restoring the system state and prolonging the lifetime. It is generally seen as an imperfect maintenance action which has a chief influence on the maintenance strategy. In order to model the maintenance effect of servicing, this study analyzes the deterioration characteristics of system under scheduled servicing. And then the deterioration model is established from the failure mechanism by compound Poisson process. On the basis of the system damage value and failure mechanism, the failure rate refresh factor is proposed to describe the maintenance effect of servicing. A maintenance strategy is developed which combines the benefits of scheduled servicing and preventive maintenance. Then the optimization model is given to determine the optimal servicing period and preventive maintenance time, with an objective to minimize the system expected life-cycle cost per unit time and a constraint on system survival probability for the duration of mission time. Subject to mission time, it can control the ability of accomplishing the mission at any time so as to ensure the high dependability. An example of water pump rotor relating to scheduled servicing is introduced to illustrate the failure rate refresh factor and the proposed maintenance strategy. Compared with traditional methods, the numerical results show that the failure rate refresh factor can describe the maintenance effect of servicing more intuitively and objectively. It also demonstrates that this maintenance strategy can prolong the lifetime, reduce the total lifetime maintenance cost and guarantee the dependability of system

Parametric, Nonparametric, and Semiparametric Linear Regression in Classical and Bayesian Statistical Quality Control

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a practitioner’s guide to provide a stepby- step application for parametric, nonparametric, and semiparametric methods in profile monitoring, creating an in-depth guideline for novice practitioners. We then consider the commonly used cumulative sum (CUSUM), multivariate CUSUM (mCUSUM), exponentially weighted moving average (EWMA), multivariate EWMA (mEWMA) charts under a Bayesian framework for monitoring respiratory disease related hospitalizations and global suicide rates with parametric, nonparametric, and semiparametric linear models

Forecasting of intermittent demand: A Thesis submitted for the degree of Doctor of Philosophy, Business School, Buckinghamshire Chilterns University College, Brunel University July 2001

This thesis explores forecasting for intermittent demand requirements. Intermittent demand occurs at random, with some time periods showing no demand. In addition, demand, when it occurs, may not be for a single unit or a constant size. Consequently, intermittent demand creates significant problems in the supply and manufacturing environment as far as forecasting and inventory control are concerned. A certain confusion is shared amongst academics and practitioners about how intermittent demand (or indeed any other demand pattern that cannot be reasonably represented by the normal distribution) is defined. As such, we first construct a framework that aims at facilitating the conceptual categorisation of what is termed, for the purposes of this research, “non-normal” demand patterns. Croston (1972) proposed a method according to which intermittent demand estimates can be built from constituent elements, namely the demand size and inter-demand interval. The method has been claimed to provide unbiased estimates and it is regarded as the “standard” approach to dealing with intermittence. In this thesis we show that Croston’s method is biased. The bias is quantified and two new estimation procedures are developed based on Croston’s concept of considering both demand sizes and inter-demand intervals. Consequently the issue of variability of the intermittent demand estimates is explored and finally Mean Square Error (MSE) expressions are derived for all the methods discussed in the thesis. The issue of categorisation of the demand patterns has not received sufficient academic attention thus far, even though, from the practitioner’s standpoint it is appealing to switch from one estimator to the other according to the characteristics of the demand series under concern. Algebraic comparisons of MSE expressions result in universally applicable (and theoretically coherent) categorisation rules, based on which, “non-normal” demand patterns can be defined and estimators be selected. All theoretical findings are checked via simulation on theoretically generated demand data. The data is generated upon the same assumptions considered in the theoretical part of the thesis. Finally, results are generated using a large sample of empirical data. Appropriate accuracy measures are selected to assess the forecasting accuracy performance of the estimation procedures discussed in the thesis. Moreover, it is recognised that improvements in forecasting accuracy are of little practical value unless they are translated to an increased customer service level and/or reduced inventory cost. In consequence, an inventory control system is specified and the inventory control performance of the estimators is also assessed on the real data. The system is of the periodic order-up-to-level nature. The empirical results confirm the practical validity and utility of all our theoretical claims and demonstrate the benefits gained when Croston’s method is replaced by an estimator developed during this research, the Approximation method

Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method

Risk management is crucial when committing investments in electricity markets. Investment projects for the generation of electricity are capital-intensive, in large part irreversible and future performance is subject to high uncertainty. Fortunately, most power generation projects have strategic flexibility for handling uncertainty and for mitigating risks under unfavorable scenarios. Modern corporate finance recognizes Real Option analysis (ROA) as the correct way to value investment projects with these characteristics. Due to both, environmental concerns and escalation of fuel prices, electricity generation from renewable sources has grown dramatically worldwide over the last decade. Renewable investment projects share many of the features mentioned. As such, option valuation methods should be applied to estimate the monetary value of flexibility in renewable energy investments. This work presents an appropriate methodology for assessing the economic value of a photovoltaic power plant under uncertainties. ROA is applied to determine the value of delaying the investment decision while waiting for better market information that would reduce acquisition costs due to progress in solar technology. The flexibility of relocating the solar facility in the future upon the appearance of a more attractive site in terms of cost, network accessibility or regulatory policies is also valued. The problem of option valuation is solved through stochastic simulation combined with recursive approximate dynamic programming techniques. The methodology developed might be used by investors for more efficient decision-making and by regulatory agencies for designing adequate support policies that encourage investment in renewable energy generation.Fil: Pringles, Rolando Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Energía Eléctrica. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; ArgentinaFil: Olsina, Fernando Gabriel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Energía Eléctrica. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; ArgentinaFil: Penizzotto Bacha, Franco Victor. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Juan. Instituto de Energía Eléctrica. Universidad Nacional de San Juan. Facultad de Ingeniería. Instituto de Energía Eléctrica; Argentin

Production and inventory control in complex production systems using approximate dynamic programming.

Production systems focus not only on providing enough product to supply the market, but also on delivering the right product at the right price, while lowering the cost during the production process. The dynamics and uncertainties of modern production systems and the requirements of fast response often make its design and operation very complex. Thus, analytical models, such as those involving the use of dynamic programming, may fail to generate an optimal control policy for modern production systems. Modern production systems are often in possession of the features that allow them to produce various types of product through multiple working stations interacting with each other. The production process is usually divided into several stages, thus a number of intermediate components (WIP) are made to stock and wait to be handled by the next production stage. In particular, development of an efficient production and inventory control policy for such production systems is difficult, since the uncertain demand, system dynamics and large changeover times at the work stations cause significant problems. Also, due to the large state and action space, the controlling problems of modern production systems often suffer from the curse of dimensionality

A study of self-similar traffic generation for ATM networks

This thesis discusses the efficient and accurate generation of self-similar traffic for ATM networks. ATM networks have been developed to carry multiple service categories. Since the traffic on a number of existing networks is bursty, much research focuses on how to capture the characteristics of traffic to reduce the impact of burstiness. Conventional traffic models do not represent the characteristics of burstiness well, but self-similar traffic models provide a closer approximation. Self-similar traffic models have two fundamental properties, long-range dependence and infinite variance, which have been found in a large number of measurements of real traffic. Therefore, generation of self-similar traffic is vital for the accurate simulation of ATM networks. The main starting point for self-similar traffic generation is the production of fractional Brownian motion (FBM) or fractional Gaussian noise (FGN). In this thesis six algorithms are brought together so that their efficiency and accuracy can be assessed. It is shown that the discrete FGN (dPGN) algorithm and the Weierstrass-Mandelbrot (WM) function are the best in terms of accuracy while the random midpoint displacement (RMD) algorithm, successive random addition (SRA) algorithm, and the WM function are superior in terms of efficiency. Three hybrid approaches are suggested to overcome the inefficiency or inaccuracy of the six algorithms. The combination of the dFGN and RMD algorithm was found to be the best in that it can generate accurate samples efficiently and on-the-fly. After generating FBM sample traces, a further transformation needs to be conducted with either the marginal distribution model or the storage model to produce self-similar traffic. The storage model is a better transformation because it provides a more rigorous mathematical derivation and interpretation of physical meaning. The suitability of using selected Hurst estimators, the rescaled adjusted range (R/S) statistic, the variance-time (VT) plot, and Whittle's approximate maximum likelihood estimator (MLE), is also covered. Whittle's MLE is the better estimator, the R/S statistic can only be used as a reference, and the VT plot might misrepresent the actual Hurst value. An improved method for the generation of self-similar traces and their conversion to traffic has been proposed. This, combined with the identification of reliable methods for the estimators of the Hurst parameter, significantly advances the use of self-similar traffic models in ATM network simulation