A compound-Poisson Bayesian approach for spare parts inventory forecasting

Abstract Spare parts are often associated with intermittent demand patterns that render their forecasting a challenging task. Forecasting of spare parts demand has been researched through both parametric and non-parametric approaches. However, little has been contributed in this area from a Bayesian perspective, and most of such research is built around the Poisson demand distributional assumption. However, the Poisson distribution is known to have certain limitations and, further, empirical evidence on the inventory performance of Bayesian methods is lacking. In this paper, we propose a new Bayesian method based on compound Poisson distributions. The proposed method is compared to the Poisson-based Bayesian method with a Gamma prior distribution as well as to a parametric frequentist method and to a non-parametric one. A numerical investigation (on 7400 theoretically generated series) is complemented by an empirical assessment on demand data from about 3000 stock keeping units in the automotive sector to analyse the performance of the four forecasting methods. We find that both Bayesian methods outperform the other methods with a higher inventory efficiency reported for the Poisson Bayesian method with a Gamma prior. This outperformance increases for higher demand variability. From a practical perspective, the outperformance of the proposed method is associated with some added complexity. We also find that the performance of the non-parametric method improves for longer lead-times and higher demand variability when compared to the parametric one.

[1]  Joern Meissner,et al.  Spare parts inventory management: New evidence from distribution fitting , 2017, Eur. J. Oper. Res..

[2]  Ruud H. Teunter,et al.  Determining order-up-to levels under periodic review for compound binomial (intermittent) demand , 2010, Eur. J. Oper. Res..

[3]  Katy S. Azoury,et al.  A Comparison of the Optimal Ordering Levels of Bayesian and Non-Bayesian Inventory Models , 1984 .

[4]  M. Z. Babai,et al.  An investigation on bootstrapping forecasting methods for intermittent demands , 2019, International Journal of Production Economics.

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

[6]  M. Z. Babai,et al.  On the performance of adjusted bootstrapping methods for intermittent demand forecasting , 2018, International Journal of Production Economics.

[7]  Rose Baker,et al.  Event count distributions from renewal processes: fast computation of probabilities , 2016, 1610.06157.

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

[9]  Dennis Prak,et al.  Forecasting and Inventory Control with Compound Poisson Demand Using Periodic Demand Data , 2018 .

[10]  Katy S. Azoury.  Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution , 1985 .

[11]  Rob A. Zuidwijk,et al.  On the use of installed base information for spare parts logistics: a revieuw of ideas and industry practice , 2010 .

[12]  Salma Ahmed,et al.  Analysis of Bullwhip effect: A Behavioral Approach , 2019, Supply Chain Forum: An International Journal.

[13]  Aris A. Syntetos,et al.  A note on the demand distributions of spare parts , 2013 .

[14]  Ken R. McNaught,et al.  Using Bayesian Networks to forecast spares demand from equipment failures in a changing service logistics context , 2019, International Journal of Production Economics.

[15]  Alexandre Dolgui,et al.  On the performance of binomial and beta-binomial models of demand forecasting for multiple slow-moving inventory items , 2008, Comput. Oper. Res..

[16]  Ken-iti Sato.  Lévy Processes and Infinitely Divisible Distributions , 1999 .

[17]  Edward A. Silver,et al.  Bayesian Determination of the Reorder Point of a Slow Moving Item , 1965 .

[18]  J. R. De Wit.  Inventory Problems with Slow Moving Items: A Bayesian Approach , 1983 .

[19]  Walid Klibi,et al.  Special dossier: quantifying supply chain resilience , 2018 .

[20]  M. S. Aguir,et al.  Spare parts demand forecasting: a review on bootstrapping methods , 2019, Int. J. Prod. Res..

[21]  Uday S. Karmarkar,et al.  A robust forecasting technique for inventory and leadtime management , 1994 .

[22]  George F. Brown,et al.  A Bayesian approach to demand estimation and inventory provisioning , 1973 .

[23]  M. Z. Babai,et al.  Forecasting intermittent inventory demands: simple parametric methods vs. bootstrapping ☆ , 2015 .

[24]  Aris A. Syntetos,et al.  On the categorization of demand patterns , 2005, J. Oper. Res. Soc..

[25]  R. Watson,et al.  The Effects of Demand-Forecast Fluctuations on Customer Service and Inventory Cost When Demand is Lumpy , 1987 .

[26]  Rommert Dekker,et al.  Inventory control of spare parts using a Bayesian approach: A case study , 1999, Eur. J. Oper. Res..

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

[28]  Konstantinos Nikolopoulos,et al.  Supply chain forecasting: Theory, practice, their gap and the future , 2016, Eur. J. Oper. Res..

[29]  David F. Pyke,et al.  Inventory and Production Management in Supply Chains , 2016 .

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

[31]  J. Boylan,et al.  On the stock control performance of intermittent demand estimators , 2006 .

[32]  Argyrios Syntetos,et al.  Spare parts management: Linking distributional assumptions to demand classification , 2014, Eur. J. Oper. Res..

[33]  Jovan Popovic,et al.  Decision making on stock levels in cases of uncertain demand rate , 1987 .

[34]  M. Z. Babai,et al.  On the empirical performance of some new neural network methods for forecasting intermittent demand , 2020 .

[35]  P. Yelland.  Bayesian forecasting of parts demand , 2010 .

[36]  Andrew W. Howard,et al.  FORECASTING FOR THE ORDERING AND STOCK- HOLDING OF CONSUMABLE SPARE PARTS , 2002 .