Forecasting the Intermittent Demand for Slow-Moving Items

Organizations with large-scale inventory systems typically have a large proportion of items for which demand is intermittent and low volume. We examine different approaches to forecasting for such products, paying particular attention to the need for inventory planning over a multi-period lead-time when the underlying process may be nonstationary. This emphasis leads to consideration of prediction distributions for processes with time-dependent parameters. A wide range of possible distributions could be considered but we focus upon the Poisson (as a widely used benchmark), the negative binomial (as a popular extension of the Poisson) and a hurdle shifted Poisson (which retains Croston’s notion of a Bernoulli process for times between orders). We also develop performance measures related to the entire predictive distribution, rather than focusing exclusively upon point predictions. The three models are compared using data on the monthly demand for 1,046 automobile parts, provided by a US automobile manufacturer. We conclude that inventory planning should be based upon dynamic models using distributions that are more flexible than the traditional Poisson scheme.

[1]  David Barber,et al.  Bayesian Time Series Models , 2011 .

[2]  John E. Boylan,et al.  Judging the judges through accuracy-implication metrics: The case of inventory forecasting , 2010 .

[3]  Rob J. Hyndman,et al.  EXPONENTIAL SMOOTHING AND NON‐NEGATIVE DATA , 2009 .

[4]  Claudia Czado,et al.  Predictive Model Assessment for Count Data , 2009, Biometrics.

[5]  L. Duncan,et al.  Forecasting intermittent demand: a comparative study , 2009, J. Oper. Res. Soc..

[6]  R. Snyder,et al.  Feasible parameter regions for alternative discrete state space models , 2008 .

[7]  Rob J Hyndman,et al.  Forecasting with Exponential Smoothing: The State Space Approach , 2008 .

[8]  A. Raftery,et al.  Strictly Proper Scoring Rules, Prediction, and Estimation , 2007 .

[9]  Roman Liesenfeld,et al.  Time series of count data: modeling, estimation and diagnostics , 2006, Comput. Stat. Data Anal..

[10]  Rob J Hyndman,et al.  Another look at measures of forecast accuracy , 2006 .

[11]  A. Koehler,et al.  Exponential Smoothing Model Selection for Forecasting , 2006 .

[12]  Rob J Hyndman,et al.  Stochastic models underlying Croston's method for intermittent demand forecasting , 2005 .

[13]  Melvin J. Hinich,et al.  Time Series Analysis by State Space Methods , 2001 .

[14]  Anne B. Koehler,et al.  Comments on a patented bootstrapping method for forecasting intermittent demand , 2005 .

[15]  J. Boylan,et al.  The accuracy of intermittent demand estimates , 2005 .

[16]  Gael M. Martin,et al.  Bayesian predictions of low count time series , 2005 .

[17]  T. Willemain,et al.  A new approach to forecasting intermittent demand for service parts inventories , 2004 .

[18]  Brian G. Kingsman,et al.  Forecasting for the ordering and stock-holding of spare parts , 2004, J. Oper. Res. Soc..

[19]  Andréas Heinen,et al.  Modelling Time Series Count Data: An Autoregressive Conditional Poisson Model , 2003 .

[20]  Ralph Snyder,et al.  Forecasting sales of slow and fast moving inventories , 2002, Eur. J. Oper. Res..

[21]  J. Boylan,et al.  On the bias of intermittent demand estimates , 2001 .

[22]  Spyros Makridakis,et al.  The M3-Competition: results, conclusions and implications , 2000 .

[23]  W. Dunsmuir,et al.  On autocorrelation in a Poisson regression model , 2000 .

[24]  Ralph D. Snyder,et al.  Lead time demand for simple exponential smoothing: an adjustment factor for the standard deviation , 1999, J. Oper. Res. Soc..

[25]  Brian G. Kingsman,et al.  Selecting the best periodic inventory control and demand forecasting methods for low demand items , 1997 .

[26]  J. Ord,et al.  Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models , 1997 .

[27]  Kais Hamza,et al.  Some Properties and Generalizations of Non‐negative Bayesian Time Series Models , 1997 .

[28]  J. E. Boylan,et al.  Forecasting intermittent demand: A comparative evaluation of croston's method. Comment , 1996 .

[29]  J. Boylan,et al.  Forecasting for Items with Intermittent Demand , 1996 .

[30]  Neil Shephard,et al.  Generalized linear autoregressions , 1995 .

[31]  T. Willemain,et al.  Forecasting intermittent demand in manufacturing: a comparative evaluation of Croston's method , 1994 .

[32]  A. W. Kemp,et al.  Univariate Discrete Distributions , 1993 .

[33]  Chris Chatfield,et al.  Calculating Interval Forecasts , 1993 .

[34]  Andrew Harvey,et al.  Time Series Models for Count or Qualitative Observations , 1989 .

[35]  E. McKenzie,et al.  Some ARMA models for dependent sequences of poisson counts , 1988, Advances in Applied Probability.

[36]  S. Zeger.  A regression model for time series of counts , 1988 .

[37]  M. Kendall,et al.  Kendall's advanced theory of statistics , 1995 .

[38]  Mohamed Alosh,et al.  FIRST‐ORDER INTEGER‐VALUED AUTOREGRESSIVE (INAR(1)) PROCESS , 1987 .

[39]  M. West,et al.  Dynamic Generalized Linear Models and Bayesian Forecasting , 1985 .

[40]  Euclid,et al.  Advances in Applied Probability , 1981, Journal of Applied Probability.

[41]  A. Vijaya Rao,et al.  A Comment on: Forecasting and Stock Control for Intermittent Demands , 1973 .

[42]  J. D. Croston.  Forecasting and Stock Control for Intermittent Demands , 1972 .

[43]  A. H. Murphy.  A Note on the Ranked Probability Score , 1971 .

[44]  Edward S. Epstein,et al.  A Scoring System for Probability Forecasts of Ranked Categories , 1969 .

[45]  Quenouille Mh,et al.  A relation between the logarithmic, Poisson, and negative binomial series. , 1949 .

[46]  M. H. Quenouille,et al.  A relation between the logarithmic, Poisson, and negative binomial series. , 1949, Biometrics.