Enhancement of Intermittent Demands in Forecasting for Spare Parts Industry

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1 Indian Journal of Science and Technology, Vol 8(25), DOI: /ijst/2015/v8i25/53374, October 2015 ISSN (Print) : ISSN (Online) : Enhancement of Intermittent Demands in Forecasting for Spare Parts Industry B. Vasumathi 1* and A. Saradha 2 1 Department of Computer Science and Applications, PGP College of Arts and Science, Namakkal , Tamil Nadu, India 2 Department of Computer Science and Technology, Institute of Road and Transport Technology, Erode , Tamil Nadu, India Abstract The standard method to forecast intermittent demand is Croston s Method. This method is available in ERP type solution such as SAP and specialized forecasting software packages (e.g., Forecast Pro), and often applied in practice 6. In this paper, two forecasting methods, Croston s Method and a New Method (Bisection of Croston s Method), are compared. Two kinds of spare parts were chosen for the analysis. By using a modified Croston s Method, we forecast the average of last two demands over a fixed lead time. The mean square errors are shown to meet the theoretical and practical requirements of intermittent demand. Based on these measures, the best statistical summary can be obtained. The out-of-sample comparison results indicate superior performance of the New Method. In addition, the results show that the mean square error is a well-behaved accuracy measures for intermittent demand. Methods/Statistical Analysis: Croston s Method was implemented for forecasting irregular demands. Bisection Numerical method was compared with existing Croston s Method. The results are based on the Mean Square Error Values (MSE) values. Results/Findings: Bisection Method showed MSE Values of Proposed Method is lesser than the MSE values of Existing Method. Conclusion/Application: 'Bisection Method ' can be a better method to predict the Production of Spare Parts Industries. Keywords: Bisection Method, Crostons Method, Mean Square Error, Spare Parts 1. Introduction Forecasting is a method for translating past experience into estimates of the future. There are two types of forecasting methods. i.e., Quantitative method and Qualitative method (Figure 1, Table 1). Croston s Method (CR) has been shown to be appropriate in dealing with intermittent demand items. Croston 1 presented a method that separates the forecasts in two parts; in time between withdrawals or demand and demand size. The forecasts are updated only when there is a demand. The usefulness of Croston s Method is verified by e.g., by Willemain et al 7. Syntetos and Boylan recommended an adjustment of the Croston s Method due to a systematic error notified by Syntetos and Boylan 2. In this paper a New Method proposed to calculate the intermittent demands in forecasting. Calculate the average of last two demands for the input to the calculation; it will produce the better result than the original Croston s Method. It is necessary to examine and evaluate the performance of the forecast. Silver et al. 8 point out; no single measure is universally best. Wallstrom et al. 6 point out; Still, evaluations of forecasting performances are done using only one measure of the forecasting errors. The most common measures are Mean Absolute Deviation (MAD) or Mean Square Error (MSE). This paper studies and compares original Croston s Method 1 and New Method. Both the methods are applied * Author for correspondence

2 Enhancement of Intermittent Demands in Forecasting for Spare Parts Industry to the same real data that have varied intermittent demand. It is to show that the New Method produce the better MSE values than the original method. data to indicate the period in which the forecast is needed. After selecting the data, apply the appropriate statistical methods to calculate the forecast value. Before selecting the statistical method, consider the resources available in the organization as well as the complexity of the problem. Next, conduct the forecast by analyzing the availability of historical data. To determine the accuracy of forecasting data appropriate tool can be applied. 2. Forecasting Methods Figure 1. Forecasting techniques. Figure 2. Forecasting process. Forecasting process begins with collection of historical Table 2. Statistical methods for forecasting Sl. No Statistical Methods Formula 1. Moving Average Ft = MA(n) = 2. Single exponential Ft+1=α X t+(1-α) Ft smoothing 3. Weighted moving Ft+1 = average 4. Croston s Method Zt+1=α X t+(1-α) Zt-1 Pt+1=α G t+(1-α) Pt-1 Ft+1= Zt+1 / Pt+1 5. Syntetos Boylan Approximation Ft+1 = 1 6. Bootstrap method 1-take an observed sample, 2-observed can be extracted, 3-calculate T for every bootstrap sample 7. Binomial method N = x1 + x2 with: x1 =. n 8. Poisson method Pd,T,x = PCUMd, T,x = 9. Grey prediction model + (k) = b Table 1. Forecating methods Sl. Qualitative Methods Quantitative Methods No 1. Characteristics Based on human judgment, opinions; subjective and non Based on mathematics; quantitative in nature mathematical. 2. Strengths Can incorporate latest changes in the environment and inside information. Consistent and objective; able to consider much information and data at one time. 3. Weaknesses Can bias the forecast and reduce forecast accuracy Often quantifiable data are not available. Only as good as the data on which they are based 2 Vol 8 (25) October Indian Journal of Science and Technology

3 B. Vasumathi and A. Saradha 3. Literature Review on Croston s Method The pioneer work by Croston 1 demonstrates that the use of classical methods of exponential smoothing on intermittent demand items generates high forecasting errors and, as a consequence, unnecessarily high safety inventories. Croston 1 proposes an alternative method which separates the estimation of intervals between demands of the amounts demanded in each occurrence. Johnston and Boylan 9 compared forecasting made through exponential smoothing to the ones made through Croston s Method, and concluded that the latter is superior when the average interval between demands is greater than 1.25 time periods (time bucket). Syntetos and Boylan 2 pointed out a bias in the original Croston s model and proposed a correction that gave rise to the SBA (Syntetos-Boylan Approximation) model. Ghobbar and Friend 10 compared 13 forecasting techniques to aircraft parts demand and proved the superiority of the techniques: weighted moving average, double exponential smoothing (Holt), and Croston s Method. Similar results were presented by Regattieri et al 11. Eaves and Kingsman 12 evaluated spare parts demand forecasting techniques in the case of British airforce (RAF), including SBA and Croston s Method, and demonstrated the superiority of the SBA method to a certain service level. Willemain, Smart and Schwarz 13 developed forecasting models for intermittent demands, using the bootstrapping technique to assess the demand distribution during lead-time, considering autocorrelation and introducing small demand variations to the original series (jittering). Comparing the new model to Croston s Method and exponential smoothing, they concluded that the first provides better results, especially for small historical series. Hua et al. 14 used bootstrapping together with regression analysis in demand forecasting of parts in the petrochemical industry and showed the advantages of the proposed model. Gutierrez, Solis and Mukhopadhyay 15 presented a forecasting model based on neural networks which proved to be superior to the exponential smoothing, SBA and Croston s Methods. Li and Kuo 16 developed the Enhanced Fuzzy Neural Network (EFNN) method, which uses the fuzzy logic, in connection with the Analytical Hierarchical Process (AHP) and genetic algorithms. Li and Kuo 16 showed that the model provides better results using 14 series of 12 months. Gomez 17 analyzed 24 time series classified as strong intermittent (criterion of BOYLAN; SYNTETOS; KARAKOSTAS, 2008), using auto adjustment techniques over the classical forecasting models (Simple Smoothing, Croston s and SBA) and an original model based on Kalman s Filter. For this sample, the model with Kalman s Filter presented smaller Mean Absolute Percentage Error (MAPE) in 21 of the series; while the auto adjusted SBA model was better in 3. Teunter and Duncan 5 compared the following methods: Moving Average, Simple Exponential Smoothing, Croston s, SBA, and bootstrapping. Initially, the inadequacy of the traditional forecasting error measures (MAD, MSE and MAPE) was discussed and the adoption of measures based on the service and inventory level was recommended. The study realized with 5,000 spare parts for British air-force (RAF) proved the superiority of Croston s, SBA and bootstrapping techniques. The authors propose adjustments in the demand forecasting during the lead-time, so that orders are trigged when there is demand, obtaining better results than the original ones. 4. Theoretical Background 4.1 Croston s Method Croston s Method (CR) forecasts separately the time between consecutive transactions Pt and the magnitude of the individual transactions Zt. At the review period if no demand occurs in a review period then the estimates of the demand size and inter-arrival time at the end of time t, Zt and Pt, respectively, remain unchanged. If a demand occurs so that Xt > 0, then the estimates are updated by: Zt+1=α X t + (1-α) Zt-1 Pt+1=α G t + (1-α) Pt-1 Xt actual value of the demand at the instant t; Gt actual value of the time between consecutive transactions at the instant t; α smoothing constant between zero and one. Ft+1= Zt+1/Pt+1 (1) Vol 8 (25) October Indian Journal of Science and Technology 3

4 Enhancement of Intermittent Demands in Forecasting for Spare Parts Industry 4.2 Syntetos Boylan Approximation An error in Croston s mathematical derivation of expected demand size was reported by Syntetos and Boylan 2, who proposed a revision to approximately correct Croston s demand estimates: the SBA or SB method. In an attempt to confirm the good performance of their SB method, Syntetos and Boylan 3 carried out a comparison of forecasting methods including theirs and the original CR method. A simulation exercise was carried out on 3000 products from the automotive industry with fast intermittent demand. It was shown that the modification is the most accurate estimator. In another study, Syntetos et al. 3 Analyzed a wider range of intermittent demand patterns and made a categorisation to guide the selection of forecasting methods. They indicated that there are demand categories that are better used with the CR method and there are others that go well with the SBA method. There are several variation applied at Croston s Method after his introduction in 1972, and SBA is considered one the most performing by several authors. Syntetos and Boylan 2 pointed out that Croston s Method is biased. They showed that in CR the expected value is not 1/p, but: 1 1 E(Ft) = m - In (2) p-1 p 4.3 Moving Average The Moving Average (MA) method is the mean of the previous n data sets. The formula for the moving average is: Xt - 1+ Xt Xt - n Ft = MA(n) = (5) n As it transpires from the formula, this method is really simple and easy to compute, but it is applicable only in case of slow moving demand. In the other cases the demand gravitates with difficult around the average of last n periods. 5. Numerical Comparison of Existing Method and Proposal Method In this section Croston s Method, Syntetos-Boylan approximation is used to forecast spare parts demand for a business in the iron and steel sector. Starting from a list of 20 different spare parts with their consumptions in one year, 2 kinds of spare parts were chosen for the analysis. The year was divided into 53 periods (the weeks) (Table 3.), the first 38 weeks were used as training set, the last 15 as testing set. Where: µ is the mean of historical demand; p is the mean of historical inter- demand intervals Pt; And, in particular, for α = 1: 1 1 E(Ft) = m - In p-1 p (3) Based on and ignoring the term (p-1)/p, Syntetos and Boylan proposed a new estimator given as: a Zt Ft+1 = 1- (4) 2 Pt One can expect this new estimator to perform better as (p-1)/p gets closer to one, i.e., as the probability 1/p of positive demand in a period gets smaller. The effect is that Croston s original method has a smaller (positive) bias if 1/p is large (few demands are zero), and the Syntetos - Boylan modification has a maller bias if 1/p is small (many demands are zero). Figure 3. Comparison of predicted values of (C ) proposal method and original Croston s Method. The following table shows the demand of these spare parts. C refers to a black washer, while C refers to a yellow marker. There are more 4 Vol 8 (25) October Indian Journal of Science and Technology

5 B. Vasumathi and A. Saradha Table 3. Dataset of spare parts Weeks C C Table 4. Compare the CR and BS predicted values for C spare part C CR Method BS CR Method Vol 8 (25) October Indian Journal of Science and Technology 5

6 Enhancement of Intermittent Demands in Forecasting for Spare Parts Industry MSE Table 5. Compare the CR and BS predicted values C spare part C CR Method BS CR Method MSE Table 6. Comparison of MSE values Methods MSE C C CR Method (Original Method) BS Method (Proposed Method) Vol 8 (25) October Indian Journal of Science and Technology

7 B. Vasumathi and A. Saradha consumption materials in spare parts, but demand for the above two spare parts is sporadic (Table 3.) and tied to the casual phenomenon of breakdown during the functioning of the system where they are used. Bisection method of an innovative approach which adapts Croston s 1 method to data with an average of last two demands. The following Table 4 shows the predicted values of Croston s Method and New Method for first spare part (C ). Table 4 shows that the comparison of predicted values of original method and New method. It shows that the MSE values of New Method (BisectionCR Method) are lesser than the Croston s Method (CR Method). So that the New Method produce the better results than the original Method. Figure 3 shows the comparison of predicted values of Croston s Method and New Method. The following Table 5 shows the predicted values of Croston s Method and New Method for Second Spare Part (C ). In Table 5 shows that the comparison of predicted values of Original Method and New Method. It shows that the MSE values of New Method (BisectionCR Method) are lesser than the Croston s Method (CR Method). So that the New Method produce better results than the original Method. Figure 4 shows the comparison of predicted values of Croston s Method and New Method. the squared function. Which mean that MSE with an evaluation of original Croston s Method and New Method may present different results. T MSE = 1/T ( X t - X t ) 2 t=1 (6) Figure 5. Comparison of MSE values of New Method and Original Croston s Method. 7. Conclusion The results of the analysis (MSE) (Table 6.) show that the New Method (Bisection CR Method) produce better results than the existing method (Croston s Method). In this study, the result obtained by comparing the two spare parts by using the MSE Value is appreciable; In C and C spare parts, New Method (Bisection method) (Figure 5.) produces better results. 8. References Figure 4. Comparison of predicted values of (C ) proposal method and original Croston s Method 6. Forecast Accuracy It is the very nature of intermittent demand data and common measures for forecasting errors and its variability are MAD and MSE. Because Mean Square Error (MSE) is related to standard variation of forecast errors Silver et al. 18 recommend the use of MSE. However MSE is more sensitive to outlier and errors smaller than one due to 1. Croston JD. Forecasting and stock control for intermittent demands. Operational Research Quarterly. 1972; 42(3): Syntetos AA, Boylan JE. On the bias of intermittent demand estimates. International Journal of Production Economics. 2001; 71: Syntetos AA, Boylan JE. The accuracy of intermittent demand estimates. International Journal of Forecasting. 2005; 21: Teunter R, Sani B. On the bias of Croston s forecasting method. European Journal of Operational Research. 2009; 194(1): Teunter R, Duncan L. Forecasting intermittent demand: A comparative study. Journal of the Operational Research Society. 2009; 60: Wallstrom P, Segerstedt A. Evaluation of forecasting error measurements and techniques for intermittent demand. Int J Production Economics. 2010; 128: Willemain TR, Smart CN, Shockor PH, DeSautels PA. Forecasting intermittent demand in manufacturing: A Vol 8 (25) October Indian Journal of Science and Technology 7

8 Enhancement of Intermittent Demands in Forecasting for Spare Parts Industry comparative evaluation of Croston s method. Journal of Forecasting. 1994; 10: Silver EA, Pyke DF, Peterson R. Inventory management and production planning. 3rd ed. New York: John Wiley and Sons; Johnston FR, Boylan JE. Forecasting for items with intermitent demand. Journal of the Operational Research Society. 1996; 47: Ghobbar AA, Friend CH. Evaluation of forecasting methods for intermittent parts demand in the field of aviation: A predictive model. Computers and Operations Research. 2003; 30: Regattieri A, et al. Managing lumpy demand for aircraft spare parts. Journal of Air Transportation Management. 2005; 11: Eaves AHC, Kingsman BG. Forecasting for the ordering and stock-holding of spare parts. Journal of the Operational Research Society. 2004; 50: Willemain TR, Smart CN, Schwarz HF. A new approach to forecasting intermittent demand for service parts inventories. International Journal of Forecasting. 2004; 20: Hua ZS, et al. A new approach of forecasting intermittent demand for spare parts inventories in the process industries. Journal of the Operational Research Society. 2007; 58: Gutierrez RS, Solis AO, Mukhopadhyay S. Lumpy demand forecasting using neural networks. International Journal Of Production Economics. 2008; 111: Li SG, Kuo X. The inventory management system for automobile spare parts in a central warehouse. Expert Systems with Applications. 2008; 34: Gomez GCG. Lumpy demand characterization and forecasting performance using self-adaptive forecasting models and kalman filter. Dissertacao (Mestrado em industrial engineering). El Paso: The University of Texas; Silver EA, Pyke DF, Peterson R. Inventory management and production planning and scheduling. 3rd ed. New York: Wiley; Vol 8 (25) October Indian Journal of Science and Technology