Forecasting intermittent demand: a comparative study

Methods for forecasting intermittent demand are compared using a large data set from the UK Royal Air Force. Several important results are found. First, we show that the traditional per period forecast error measures are not appropriate for intermittent demand, even though they are consistently used in the literature. Second, by comparing the ability to approximate target service levels and stock holding implications, we show that Croston's method (and a variant) and Bootstrapping clearly outperform Moving Average and Single Exponential Smoothing. Third, we show that the performance of Croston and Bootstrapping can be significantly improved by taking into account that an order in a period is triggered by a demand in that period.     

Forecasting for intermittent demand: the estimation of an unbiased average

The majority of the range of items held by many stockists exhibit intermittent demand. Accurate forecasting of the issue rate for such items is important and several methods have been developed, but all produce biased forecasts to a greater or lesser degree. This paper derives the bias expected when the order arrivals follows a Poisson process, which leads to a correction factor for application in practice. Extensions to some other arrival processes are briefly considered.     

Determining order-up-to levels under periodic review for compound binomial (intermittent) demand

We propose a new method for determining order-up-to levels for intermittent demand items in a periodic review system. Contrary to existing methods, we exploit the intermittent character of demand by modelling lead time demand as a compound binomial process. In an extensive numerical study using Royal Air Force (RAF) data, we show that the proposed method is much better than existing methods at approximating target service levels and also improves inventory-service efficiency. Furthermore, the proposed method can be applied for both cost and service oriented systems, and is easy to implement.     

Periodic control of intermittent demand items: theory and empirical analysis

In this paper we propose a modification to the standard forecasting, periodic order-up-to-level inventory control approach to dealing with intermittent demand items, when the lead-time length is shorter than the average inter-demand interval. In particular, we develop an approach that relies upon the employment of separate estimates of the inter-demand intervals and demand sizes, when demand occurs, directly for stock control purposes rather than first estimating mean demand and then feeding the results in the stock control procedure. The empirical performance of our approach is assessed by means of analysis on a large demand data set from the Royal Air Force (RAF, UK). Our work allows insights to be gained on the interactions between forecasting and stock control as well as on demand categorization-related issues for forecasting and inventory management purposes.     

A new approach of forecasting intermittent demand for spare parts inventories in the process industries

Accurate demand forecasting is of vital importance in inventory management of spare parts in process industries, while the intermittent nature makes demand forecasting for spare parts especially difficult. With the wide application of information technology in enterprise management, more information and data are now available to improve forecasting accuracy. In this paper, we develop a new approach for forecasting the intermittent demand of spare parts. The described approach provides a mechanism to integrate the demand autocorrelated process and the relationship between explanatory variables and the nonzero demand of spare parts during forecasting occurrences of nonzero demands over lead times. Two types of performance measures for assessing forecast methods are also described. Using data sets of 40 kinds of spare parts from a petrochemical enterprise in China, we show that our method produces more accurate forecasts of lead time demands than do exponential smoothing, Croston's method and Markov bootstrapping method.     

Linear combinations of heuristics for examination timetabling

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In this paper, we explore this direction and introduce a new strategy of using linear combinations of heuristics for weighted graphs which model the timetabling problems under consideration. The weights of the heuristic combinations define specific roles that each simple heuristic contributes to the process of ordering vertices. We include specific explanations for the design of our strategy and present the experimental results on a set of benchmark real world examination timetabling problem instances. New best results for several instances have been obtained using this method when compared with other constructive methods applied to this benchmark dataset.     

On universality for linear combinations of L-functions

In the present paper, we consider the universality property in the Voronin sense for certain combinations of L-functions with general Dirichlet series as coefficients. In addition, we present some interesting examples of zeta and L-functions which can be expressed in this form. More precisely, we obtain the universality theorem for zeta functions associated to certain arithmetic functions, zeta functions associated to symmetric matrices and Euler–Zagier double zeta and L-functions.     

Pointwise characterization for combinations of Baskakov operators

In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.     

POINTWISE CHARACTERIZATION FOR COMBINATIONS OF BASKAKOV OPERATIORS

In this paper,we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totkik modulus of smoothness.     

Linear combinations of overlapping variance estimators for simulation

We estimate the variance parameter of a stationary simulation-generated process using a linear combination of overlapping standardized time series (STS) area variance estimators based on different batch sizes. We establish the linear-combination estimator's asymptotic distribution, presenting analytical and simulation-based results exemplifying its potential for improvements in accuracy and computational efficiency.     

Crucial combinations of parts for handwritten alphanumeric characters

A combining approach has been studied previously to integrate different parts of handwritten characters for their analysis and recognition. Perfect combinations, by which the characters can be identified with certainty, are important to pattern analysis and character recognition. However, a large number of possible combinations (e.g., 63 combinations for a character partitioned into six parts), also produce a lot of perfect combinations. Hence, it is necessary to determine which of them are most important. In this paper, we propose a methodology of finding the basic crucial combinations, and algorithms to compute them. Compared with perfect combinations, such basic crucial combinations are most significant to the character distinctiveness. Similarly, the largest confusion regions are also identified.Experimental studies have also been conducted using the 89 most frequently used patterns of 36 alphanumeric handprints, to obtain their basic crucial combinations and largest confusion combinations. The results indicate that the ratio of the number of basic crucial combinations to perfect combinations is only 12.6%, and the ratio of the number of the largest confusion regions to the total confusion combinations is 15.6%.     

On the modeling of demand spill for a stochastic demand system under competition

When customers for a product from N substitutable alternatives find their first choice sold out, they might “spill” to their secondmost preferred product. The existing literature typically assumes an exogenous spill rate. We develop a surprisingly simple model that links the spill rate to economic factors associated with direct demand systems.     

Explicit Voronovskaja-type results for linear combinations of BDT-operators

In this paper we prove an explicit Voronovskaja-type result for linear combinations of the so-called BDT-operators.     

Discrete location for bundled demand points

This paper considers a discrete location problem where the demand points are grouped. We propose a formulation, an enforcement for it, and an associated Lagrangian relaxation, and then we build feasible solutions to the problem from the optimal solutions to the relaxed subproblems. Valid inequalities for the formulation are also identified and added to the set of relaxed constraints. This method produces good feasible solutions and enables us to address large instances of the problem. Computational experiments have been performed with benchmark instances from the literature on related problems.     

Modeling demand management strategies for evacuations

Evacuations are massive operations that create heavy travel demand on road networks some of which are experiencing major congestions even with regular traffic demand. Congestion in traffic networks during evacuations, can be eased either by supply or demand management actions. This study focuses on modeling demand management strategies of optimal departure time, optimal destination choice and optimal zone evacuation scheduling (also known as staggered evacuation) under a given fixed evacuation time assumption. The analytical models are developed for a system optimal dynamic traffic assignment problem, so that their characteristics can be studied to produce insights to be used for large-scale solution algorithms. While the first two strategies were represented in a linear programming (LP) model, evacuation zone scheduling problem inevitable included integers and resulted in a mixed integer LP (MILP) one. The dual of the LP produced an optimal assignment principle, and the nature of the MILP formulations revealed clues about more efficient heuristics. The discussed properties of the models are also supported via numerical results from a hypothetical network example.     

Selecting the best periodic inventory control and demand forecasting methods for low demand items

The (s,S) form of the periodic review inventory control system has been claimed theoretically to be the best for the management of items of low and intermittent demand. Various heuristic procedures have been put forward, usually justified on the basis of generated data with known properties. Some stock controllers also have other simple rules which they employ and which are rarely seen in the literature. Determining how to forecast future demands is also a major problem in the area. The research described in this paper compares various periodic inventory policies as well as some forecasting methods and attempts to determine which are best for low and intermittent demand items. It evaluates the alternative methods on some long series of daily demands for low demand items for a typical spare parts depot.     

Comparative error bound theory for three location models: continuous demand versus discrete demand

We develop a unified error bound theory to compare a given p-median, p-center or covering location model with continuously distributed demand points in R ⁿ to a corresponding given original model of the same type having a finite collection of demand points in R ⁿ . We give ways to construct either a continuous or finite demand point model from the other model and also control the error bound. Our work uses Voronoi tilings extensively, and is related to earlier error bound theory for aggregating finitely many demand points.     

Pointwise direct estimate for combinations of some exponential-type operators

The purpose of this paper is to give the pointwise direct estimate for the combinations of some exponential-type operators.     

Pointwise direct estimate for combinations of some exponential-type operators

The purpose of this paper is to give the pointwise direct estimate for the combinations of some exponential-type operators. Supported by the Zheijiang Provincial Natural Science Foundation of China.