Proceedings of the Asia Pacific Industrial Engineering & Management Systems Conference 2012 V. Kachitvichyanukul, H.T. Luong, and R. Pitakaso Eds.
The Application of Forecasting Techniques: A Case Study of Chemical Fertilizer Store
Chompoonoot Kasemset† and Watcharapat Chatchayangkul Department of Industrial Engineering, Faculty of Engineering Chiang Mai University, Chiang Mai, Thailand Tel: (+66) 53- 944125-6 Fax: (+66) 5353-944185 Email: [email protected]
Abstract. This research work aims to propose sales forecasting models for a case study of chemical fertilizer store. The first step is to group products based on ABC classification concept while considering ordering lead time as an additional criterion. In this case study, there are 2 types of chemical fertilizer, 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah), classified as group A. The historical sales of both products are analyzed to obtain practical forecasting models. The results are (1) using liner trend line with seasonal adjustment forecasting model for 16-20-0 (Kra-tai) and (2) using exponential smoothing technique for 46-0-0 (Chor-fah). These two methods give minimum value of mean absolute percentage error (MAPE) for both products comparing with other methods. Keywords: Forecasting, ABC Analysis, Case Study
1. INTRODUCTION
Presently, a chemical fertilizer product is in maturity stage of their product life cycle in which market saturation is reached. Particularly in Thailand, the use of chemical fertilizers trend to decrease due to uncertain economic conditions and natural disaster affected on Thai’s agricultures. Chemical fertilizer stores have to decrease prices in order to compete in the market. Improving inventory management policy in order to reduce inventory costs is one possible way that can help in gaining more profit when reducing price is applied to compete with other shops. The starting step of inventory management is to estimate the future sales as input data in setting optimal lot sizing policy. In this study, one chemical fertilizer store in Thailand is selected to be a case study. This store sells chemical fertilizers to general customers. Currently, the store has collected historical sales but there is no procedure to utilize this data. The objective of this study is to develop forecasting models for this shop. The starting step is product classification based on ABC concept. Then, products in class A are selected to be analyzed and assigned practical forecasting models. The paper organization starts with preliminaries in
section 2, research methodology in section 3, case study and results in section 4, conclusion and discussion in section 5 and recommendation and further study in section 6.
2. PRELIMINARIES 2.1 ABC Classification
The objective of ABC classification is to classify products in to different classes based on values of products turnover. The advantage of this concept is to set up appropriate policy for each product group depended on its important level in company’s investment. Class A is the most important group of product classified from 15-20 % of total products quantity and 6080% of total product value. Class B is the group of product with 20-30 % of total product quantity and 15-25% of total product value. Class C is the least important with 50-60 % of total products quantity and 5-10% of total product value. The concept of ABC classification mentioned above is the common policy widely used in normal case. In many research works, modified ABC classification by considering multi-criteria were proposed, for example; Lei et al. (2005), Zhou and Fan (2007), Hadi-Vencheh (2010),
† : Corresponding Author 739
Kasemset and Chatchayangkul
Bošnjakovic (2010), , and most of them proposed mathematical models for ABC classification based on linear and non-linear models. When products are classified as different groups, group each group will be controlled by different policies as shown in Table 1. Table 1: ABC Inventory Management Policy
Class Degree of Control Tight Type of Records Accurate and complete good Simple Lot Sizes Low Frequency of Review Continuous Size of Safety Stocks Small
forecasting demand. Linear trend tr line is used to formulate a linear equation that presents the relationship between demand as s a dependent variable and time (shown in Figure 1). The error occurring between actual values value and forecast values from this technique will be minimized because the concept of least square error is used when formulating linear trend equation. The disadvantage of this technique is all future forecasts will follow a straight line and this technique will good-perform performed when the trend of data is unchanged.
A
B C
Moderate Loose
Medium Large
Occasional Infrequent
Moderate Large
Source: Tersine (1994)
For this case study, the problem is not complicated and it is practical with simple technique as basic ABC classification. The detail is addressed in section 3 and 4. 4
Figure 1: Linear Trend Line
Source: Russell & Taylor (2011)
2.2 Forecasting
Forecasting is a technique for predicting redicting the future that always wrong. In supply chain management, forecasting is still needed because having partial artial knowledge from forecasting is better than having no knowledge. Thus, the better management is able to estimate the future, the better it should be able to prepare for it. Forecasting techniques can be classified as two main groups. The first group is qualitative ualitative methods using management judgment, expertise, and opinion to predict future demand. The second group is quantitative uantitative methods based on mathematical formulas, i.e. time ime series methods, regression methods, and so on, attempting to develop a mathematical relationship between demand and factors that cause its behavior. Time series methods are statistical tatistical techniques technique that use historical demand and data to predict future demand. demand The well known techniques, i.e. simple moving average (MA), weighted moving average, , exponential smoothing and adjusted exponential smoothing, are examples of this group. The advantage of time series methods is that this technique is simple to be implemented due to uncomplicated calculation. In contrast, the forecasting value from this method will not present variations due to season, cycle and trend. Thus, this method will be practical with a short-time forecasting that contains less variation. Regression model is used to develop a mathematical relationship between demand and factors that cause its behavior. When demand displays obvious trend overtime, linear trend line that relates demand to time can be used for The decision on selecting the right forecasting method is to determine forecasting accuracy that depended on forecasting error or the he difference between forecast vales and actual values. . The well known methods are mean absolute deviation (MAD), mean absolute a percent deviation (MAPD), mean absolute percent error (MAPE), cumulative error, , average error or bias, etc. Accurate forecasts of future demand can help in effective operations improvement in retail supply chain because retail sales s always present seasonal variation. Chu and Zhang (2003) presented a comparative study among linear and non-linear models in aggregate retail sales forecasting. In conclusion of this work, non-linear non model was recommended to be used for retail forecasting especially neural network based models. In this study, forecasting models are developed based on simple techniques (explain in section 3) due to not much number of historical data and simple pattern of sales. Thus, forecasting model based on simple techniques are practical in real working situation and easy to be handle by the shop owner.
3. METHODOLOGY
The research methodology is addressed as follows.
3.1 Data Collection
Data ata of fertilizer types, types their ordering lead times and historical sales s of the year 2009 to 2011, 2011 were collected.
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Kasemset and Chatchayangkul
These data were used in ABC classification and forecasting model development in following steps.
3.2 ABC Classification
In this step, fertilizer types and their lead times were used in modified ABC classification while considering product values, sales volume and ordering lead time. Based on ABC classification concept, A is the group of high significant product, B is the group of medium significant product and C is the group of low significant product. After the product classification, product group A is selected to find the optimal forecasting model.
to be transformed to quarterly value by multiplying with seasonal index. After optimal forecasting model for products in class A are obtained, these models are used to develop the decision support tool for the fertilizer store as the further work.
4. CASE STUDY AND RESULTS 4.1 Case Study
Data collections of fertilizer types and monthly sales during 2009-2011 are analyzed. There are 18 fertilizer types presented in Figure 2.
3.3 Forecasting Model Development
In this step, the collected data, historical sales, of product group A are used to design forecasting models for each product. In this study, three basic techniques are used to calculate F(t) as forecasting value for time t; 1) Linear Trend Line (modified from detail in Figure 1) F(t) = a + bt (1)
2) Exponential Smoothing based on equation (2) F(t) = ?Dt-1 + (1-?)Ft-1 (2) Figure 2: 18 Fertilizers Demand Ordering lead time is one factor applied in product classification. In this case, there are two supply sources that are manufacturer and wholesaler. Products delivered by manufacturer take seven days while products from wholesaler take only two days for transportation.
when ? is a smoothing constant, Dt-1 is real sales for period t-1 and Ft-1 is sales forecasting value for period t-1. 3) Adjusted Exponential Smoothing From forecasting value based on exponential smoothing method, trend adjustment is added following equation (3) to (4); AF(t) = Ft + Tt (3)
4.2 Product Classification
Appling the concept of ABC classification, Pareto chart of sales values for all fertilizers can be presented as Figure 3. There are two fertilizer types, 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah), that can be considered as group A due to their high sales volumes. Then, lead time is considered as additional criterion for product classification. The detail is shown in Table 1. Table 1 shows that when lead time is considered the same types of fertilizers are still classified as group A because of their longest lead time, seven days, that the store have to wait for the transportation from fertilizer manufacturers to the shop.
where T is exponentially smoothed trend factor that can be calculated as equation (4); T(t) = ß(Ft - Ft-1)+ (1- ß)Tt-1 (4)
when ß is a smoothing trend factor that is 0 < ß < 1. To obtain optimal forecasting models, mean absolute percent error (MAPE) of each model are compared (as equation 5). The smallest value of MAPE identifies the optimal forecasting model for each product in group A. (5) The optimal forecasting model will give yearly sales forecasting values. In practical, this yearly sales value has
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while monthly sales show seasonal effects that cause the difference among sales of each month. From monthly data, there are four periods classified following the effect of seasonal as; 1th-3rd month (January-March), 4th-6th (AprilMay), 7th-9th (July-September) and 10th-12th (OctoberDecember).
Figure 3: Pareto Chart of Fertilizers From this step, there are two types, 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah), of fertilizer that can be considered as group A. The following step is to find the practical forecasting models for both of them. Table 1: Fertilizer Classification
Fertilizer Type 16-20-0 (Rabbit) 46-0-0 (Chor Fah) 15-15-15 (A) 13-13-22 8-24-24 (B) 16-20-0 25-7-7 15-15-15 (B) 8-24-24 (A) 25-0-0 0-0-60 15-0-0 46-0-0 (B) 14-14-22 27-6-6 21-0-0 16-16-8 46-0-0 (A) % Sale 31.17 30.69 8.10 5.72 3.91 3.34 3.25 3.14 2.22 2.06 1.75 1.14 0.94 0.82 0.81 0.47 0.27 0.20 Cumulative % Sale 31.17 61.86 69.96 75.68 79.59 82.93 86.18 89.32 91.54 93.6 95.35 96.49 97.43 98.25 99.06 99.53 99.8 100 Lead Time (Day) 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Supplier Manufacturer Manufacturer Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Class A A B B B B B B C C C C C C C C C C
Figure 4a: Monthly Sales of 16-20-0 (Kra-tai)
Figure 4b: Yearly Sales of 16-20-0 (Kra-tai) The finding of optimal forecasting model can be presented as in Table 2. When considering % MAPE, linear trend model is the best model among other methods with 1.11% MAPE as the minimum value. The linear trend line forecasting model of 16-20-0 (Kra-tai) can be represented as equation (6). F(t) = 1806 + 631t (6)
4.3 Proposed Forecasting Model
For each type of fertilizer in group A, three basic techniques are evaluated using sales historical data from the year 2009 to 2011; 1) Linear Trend Line 2) Exponential Smoothing 3) Adjusted Exponential Smoothing To obtain optimal forecasting models, mean absolute percent error (MAPE) is used to identify the optimal forecasting model for each product in group A.
4.3.1 Forecasting Model for 16-20-0 (Kra-tai)
Sales data for 16-20-0 (Kra-tai) during 2009 to 2011 are presented in Figure 4a and 4b. From Figure 4a and 4b, sales data show that the yearly sales of 16-20-0 (Kra-tai) trend to increase continuously
when F(t) is a forecasting value for year t. Then, this equation is used to calculate the forecasting value for year 2012 as 4,330 bags. In practical, the store interest in quarterly sales forecast so the yearly sales forecast is multiplied by each period seasonal index to derive quarterly forecasting value as shown in Table 3.
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Table 2: Forecasting Model Fitting for 16-20-0 (Kra-tai)
Table 3: Forecasting Model Fitting for 16-20-0 (Kra-tai)
4.3.2 Forecasting Model for 46-0-0 (Chor-fah)
Sales data for 16-20-0 (Kra-tai) during 2009 to 2011 are presented in Figure 5a and 5b.
From Figure 5a and 5b, sales data show that the yearly sales of 46-0-0 (Chor-fah) seem stable while monthly sales show some variation among different periods. The finding of optimal forecasting model can be presented as in Table 4. When considering % MAPE, exponential smoothing with ? = 0.7 is the best model with minimum value of MAPE. The forecasting model of 46-0-0 (Chor-fah) can be represented as equation (7). F(t) = 0.7 Dt-1 + 0.3Ft-1 (7)
Figure 5a: Monthly Sales of 46-0-0 (Chor-fah)
when F(t) is a forecasting value for year t, Dt-1 is real sales for period t-1 and Ft-1 is sales forecasting value for period t1. Then, this equation is used to calculate the forecasting value for year 2012 as 3,265 bags. In practical, the store uses quarterly sales forecast so the yearly sales forecast is multiplied by seasonal index of each quarter to derive quarterly forecasting values as shown in Table 5.
5. CONCLUSION AND DISCUSSION
In this study, the forecasting models of chemical fertilizer store are proposed. The starting step is to classify group of fertilizer products based on ABC classification considering sales value and ordering lead time. There are two fertilizer types classified in group A that are 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah). Both products are totally 62% of total sales and ordering lead times are the longest as 7 days. Then, the sales of group A is used to derive the practical forecasting model.
Figure 5b: Yearly Sales of 46-0-0 (Chor-fah)
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Table 4: Forecasting Model Fitting for 46-0-0 (Chor-fah)
Table 5: Forecasting Model Fitting for 46-0-0 (Chor-fah)
In conclusion, 16-20-0 (Kra-tai) sales is fitted with forecasting model based on linear trend line adjusted by seasonal index and 46-0-0 (Chor-fah) sales is fitted with exponential smoothing based model. The sales pattern of 16-20-0 (Kra-tai) is fitted with linear trend line because the sales contain the effect of increasing trend. When the data have trend pattern, linear trend line is good for predicting future values. For 46-0-0 (Chor-fah) sales, exponential smoothing is fitted for forecasting future sales when the historical data have no-trend pattern.
ACKNOWLEDGMENT
The author would like to thank the Department of Industrial Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand, for the financial support.
REFERENCES
Chu, C.W. and Zhang, G.P. (2003) A comparative study of linear and nonlinear models for aggregate retail sales forecasting, Int. J. Production Economics, 86, 217231. Hadi-Vencheh, A. (2010) An improvement to multiple criteria ABC inventory classification, European Journal of Operational Research, 201, 962-965. Bošnjakovic, M. (2010) Multi-criteria Inventory Model for Spare Parts, Tehnicki Vjesnik, 17(4), 499-504. Lei, Q., Chen, J. and Zhou, Q. (2005) Multiple Criteria Inventory Classification Based on Principal Components Analysis and Neural Network, School of Economics and Management, Tsinghua University, Beijing, China. Russell & Taylor (2011) Operations Management 7th Edition, John Wiley & Sons Limited. Tersine, R. T. (1994) Principles of Inventory and Materials Management, Prentice-Hall, Englewood Cliff, NJ.
6. RECOMMENDATION STUDY
AND
FURTHER
From this study, the forecasting models of chemical fertilizer store are developed for fertilizer types classified in group A that are 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah). The developed models from this study are used again in decision supporting tool development for this store to help in real working situation. The used models are not long-lasting correct. The model validation is needed. One measurement used in measure model validation called “Tracking Signal (TS)” used to identify how model correctly perform under current situation. If the tracking signal is out of control, the model need to be adjusted to maintain the ability if forecasting. Normally, TS control chart is set as 2-5 MADs (Mean Absolute Deviation). The detail of TS can also be found in Russell & Taylor (2011), as well.
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AUTHOR BIOGRAPHIES Chompoonoot Kasemset is a lecturer in Department of Industrial Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand. Her research interests include operation management, applied operations research and simulation in production and operation management. Her area of specialization is Theory of Constraint (TOC). Her email address is Watcharapat Chatchayangkul is a Master student of Industrial Management, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand. He received a B.Eng from Electrical Engineering, King Mongkut’s Institute of Technology Lardkrabang, Thailand in 1998. His email address is
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doc_649767260.pdf
The Application of Forecasting Techniques: A Case Study of Chemical Fertilizer Store
Chompoonoot Kasemset† and Watcharapat Chatchayangkul Department of Industrial Engineering, Faculty of Engineering Chiang Mai University, Chiang Mai, Thailand Tel: (+66) 53- 944125-6 Fax: (+66) 5353-944185 Email: [email protected]
Abstract. This research work aims to propose sales forecasting models for a case study of chemical fertilizer store. The first step is to group products based on ABC classification concept while considering ordering lead time as an additional criterion. In this case study, there are 2 types of chemical fertilizer, 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah), classified as group A. The historical sales of both products are analyzed to obtain practical forecasting models. The results are (1) using liner trend line with seasonal adjustment forecasting model for 16-20-0 (Kra-tai) and (2) using exponential smoothing technique for 46-0-0 (Chor-fah). These two methods give minimum value of mean absolute percentage error (MAPE) for both products comparing with other methods. Keywords: Forecasting, ABC Analysis, Case Study
1. INTRODUCTION
Presently, a chemical fertilizer product is in maturity stage of their product life cycle in which market saturation is reached. Particularly in Thailand, the use of chemical fertilizers trend to decrease due to uncertain economic conditions and natural disaster affected on Thai’s agricultures. Chemical fertilizer stores have to decrease prices in order to compete in the market. Improving inventory management policy in order to reduce inventory costs is one possible way that can help in gaining more profit when reducing price is applied to compete with other shops. The starting step of inventory management is to estimate the future sales as input data in setting optimal lot sizing policy. In this study, one chemical fertilizer store in Thailand is selected to be a case study. This store sells chemical fertilizers to general customers. Currently, the store has collected historical sales but there is no procedure to utilize this data. The objective of this study is to develop forecasting models for this shop. The starting step is product classification based on ABC concept. Then, products in class A are selected to be analyzed and assigned practical forecasting models. The paper organization starts with preliminaries in
section 2, research methodology in section 3, case study and results in section 4, conclusion and discussion in section 5 and recommendation and further study in section 6.
2. PRELIMINARIES 2.1 ABC Classification
The objective of ABC classification is to classify products in to different classes based on values of products turnover. The advantage of this concept is to set up appropriate policy for each product group depended on its important level in company’s investment. Class A is the most important group of product classified from 15-20 % of total products quantity and 6080% of total product value. Class B is the group of product with 20-30 % of total product quantity and 15-25% of total product value. Class C is the least important with 50-60 % of total products quantity and 5-10% of total product value. The concept of ABC classification mentioned above is the common policy widely used in normal case. In many research works, modified ABC classification by considering multi-criteria were proposed, for example; Lei et al. (2005), Zhou and Fan (2007), Hadi-Vencheh (2010),
† : Corresponding Author 739
Kasemset and Chatchayangkul
Bošnjakovic (2010), , and most of them proposed mathematical models for ABC classification based on linear and non-linear models. When products are classified as different groups, group each group will be controlled by different policies as shown in Table 1. Table 1: ABC Inventory Management Policy
Class Degree of Control Tight Type of Records Accurate and complete good Simple Lot Sizes Low Frequency of Review Continuous Size of Safety Stocks Small
forecasting demand. Linear trend tr line is used to formulate a linear equation that presents the relationship between demand as s a dependent variable and time (shown in Figure 1). The error occurring between actual values value and forecast values from this technique will be minimized because the concept of least square error is used when formulating linear trend equation. The disadvantage of this technique is all future forecasts will follow a straight line and this technique will good-perform performed when the trend of data is unchanged.
A
B C
Moderate Loose
Medium Large
Occasional Infrequent
Moderate Large
Source: Tersine (1994)
For this case study, the problem is not complicated and it is practical with simple technique as basic ABC classification. The detail is addressed in section 3 and 4. 4
Figure 1: Linear Trend Line
Source: Russell & Taylor (2011)
2.2 Forecasting
Forecasting is a technique for predicting redicting the future that always wrong. In supply chain management, forecasting is still needed because having partial artial knowledge from forecasting is better than having no knowledge. Thus, the better management is able to estimate the future, the better it should be able to prepare for it. Forecasting techniques can be classified as two main groups. The first group is qualitative ualitative methods using management judgment, expertise, and opinion to predict future demand. The second group is quantitative uantitative methods based on mathematical formulas, i.e. time ime series methods, regression methods, and so on, attempting to develop a mathematical relationship between demand and factors that cause its behavior. Time series methods are statistical tatistical techniques technique that use historical demand and data to predict future demand. demand The well known techniques, i.e. simple moving average (MA), weighted moving average, , exponential smoothing and adjusted exponential smoothing, are examples of this group. The advantage of time series methods is that this technique is simple to be implemented due to uncomplicated calculation. In contrast, the forecasting value from this method will not present variations due to season, cycle and trend. Thus, this method will be practical with a short-time forecasting that contains less variation. Regression model is used to develop a mathematical relationship between demand and factors that cause its behavior. When demand displays obvious trend overtime, linear trend line that relates demand to time can be used for The decision on selecting the right forecasting method is to determine forecasting accuracy that depended on forecasting error or the he difference between forecast vales and actual values. . The well known methods are mean absolute deviation (MAD), mean absolute a percent deviation (MAPD), mean absolute percent error (MAPE), cumulative error, , average error or bias, etc. Accurate forecasts of future demand can help in effective operations improvement in retail supply chain because retail sales s always present seasonal variation. Chu and Zhang (2003) presented a comparative study among linear and non-linear models in aggregate retail sales forecasting. In conclusion of this work, non-linear non model was recommended to be used for retail forecasting especially neural network based models. In this study, forecasting models are developed based on simple techniques (explain in section 3) due to not much number of historical data and simple pattern of sales. Thus, forecasting model based on simple techniques are practical in real working situation and easy to be handle by the shop owner.
3. METHODOLOGY
The research methodology is addressed as follows.
3.1 Data Collection
Data ata of fertilizer types, types their ordering lead times and historical sales s of the year 2009 to 2011, 2011 were collected.
740
Kasemset and Chatchayangkul
These data were used in ABC classification and forecasting model development in following steps.
3.2 ABC Classification
In this step, fertilizer types and their lead times were used in modified ABC classification while considering product values, sales volume and ordering lead time. Based on ABC classification concept, A is the group of high significant product, B is the group of medium significant product and C is the group of low significant product. After the product classification, product group A is selected to find the optimal forecasting model.
to be transformed to quarterly value by multiplying with seasonal index. After optimal forecasting model for products in class A are obtained, these models are used to develop the decision support tool for the fertilizer store as the further work.
4. CASE STUDY AND RESULTS 4.1 Case Study
Data collections of fertilizer types and monthly sales during 2009-2011 are analyzed. There are 18 fertilizer types presented in Figure 2.
3.3 Forecasting Model Development
In this step, the collected data, historical sales, of product group A are used to design forecasting models for each product. In this study, three basic techniques are used to calculate F(t) as forecasting value for time t; 1) Linear Trend Line (modified from detail in Figure 1) F(t) = a + bt (1)
2) Exponential Smoothing based on equation (2) F(t) = ?Dt-1 + (1-?)Ft-1 (2) Figure 2: 18 Fertilizers Demand Ordering lead time is one factor applied in product classification. In this case, there are two supply sources that are manufacturer and wholesaler. Products delivered by manufacturer take seven days while products from wholesaler take only two days for transportation.
when ? is a smoothing constant, Dt-1 is real sales for period t-1 and Ft-1 is sales forecasting value for period t-1. 3) Adjusted Exponential Smoothing From forecasting value based on exponential smoothing method, trend adjustment is added following equation (3) to (4); AF(t) = Ft + Tt (3)
4.2 Product Classification
Appling the concept of ABC classification, Pareto chart of sales values for all fertilizers can be presented as Figure 3. There are two fertilizer types, 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah), that can be considered as group A due to their high sales volumes. Then, lead time is considered as additional criterion for product classification. The detail is shown in Table 1. Table 1 shows that when lead time is considered the same types of fertilizers are still classified as group A because of their longest lead time, seven days, that the store have to wait for the transportation from fertilizer manufacturers to the shop.
where T is exponentially smoothed trend factor that can be calculated as equation (4); T(t) = ß(Ft - Ft-1)+ (1- ß)Tt-1 (4)
when ß is a smoothing trend factor that is 0 < ß < 1. To obtain optimal forecasting models, mean absolute percent error (MAPE) of each model are compared (as equation 5). The smallest value of MAPE identifies the optimal forecasting model for each product in group A. (5) The optimal forecasting model will give yearly sales forecasting values. In practical, this yearly sales value has
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while monthly sales show seasonal effects that cause the difference among sales of each month. From monthly data, there are four periods classified following the effect of seasonal as; 1th-3rd month (January-March), 4th-6th (AprilMay), 7th-9th (July-September) and 10th-12th (OctoberDecember).
Figure 3: Pareto Chart of Fertilizers From this step, there are two types, 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah), of fertilizer that can be considered as group A. The following step is to find the practical forecasting models for both of them. Table 1: Fertilizer Classification
Fertilizer Type 16-20-0 (Rabbit) 46-0-0 (Chor Fah) 15-15-15 (A) 13-13-22 8-24-24 (B) 16-20-0 25-7-7 15-15-15 (B) 8-24-24 (A) 25-0-0 0-0-60 15-0-0 46-0-0 (B) 14-14-22 27-6-6 21-0-0 16-16-8 46-0-0 (A) % Sale 31.17 30.69 8.10 5.72 3.91 3.34 3.25 3.14 2.22 2.06 1.75 1.14 0.94 0.82 0.81 0.47 0.27 0.20 Cumulative % Sale 31.17 61.86 69.96 75.68 79.59 82.93 86.18 89.32 91.54 93.6 95.35 96.49 97.43 98.25 99.06 99.53 99.8 100 Lead Time (Day) 7 7 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Supplier Manufacturer Manufacturer Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Wholesaler Class A A B B B B B B C C C C C C C C C C
Figure 4a: Monthly Sales of 16-20-0 (Kra-tai)
Figure 4b: Yearly Sales of 16-20-0 (Kra-tai) The finding of optimal forecasting model can be presented as in Table 2. When considering % MAPE, linear trend model is the best model among other methods with 1.11% MAPE as the minimum value. The linear trend line forecasting model of 16-20-0 (Kra-tai) can be represented as equation (6). F(t) = 1806 + 631t (6)
4.3 Proposed Forecasting Model
For each type of fertilizer in group A, three basic techniques are evaluated using sales historical data from the year 2009 to 2011; 1) Linear Trend Line 2) Exponential Smoothing 3) Adjusted Exponential Smoothing To obtain optimal forecasting models, mean absolute percent error (MAPE) is used to identify the optimal forecasting model for each product in group A.
4.3.1 Forecasting Model for 16-20-0 (Kra-tai)
Sales data for 16-20-0 (Kra-tai) during 2009 to 2011 are presented in Figure 4a and 4b. From Figure 4a and 4b, sales data show that the yearly sales of 16-20-0 (Kra-tai) trend to increase continuously
when F(t) is a forecasting value for year t. Then, this equation is used to calculate the forecasting value for year 2012 as 4,330 bags. In practical, the store interest in quarterly sales forecast so the yearly sales forecast is multiplied by each period seasonal index to derive quarterly forecasting value as shown in Table 3.
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Table 2: Forecasting Model Fitting for 16-20-0 (Kra-tai)
Table 3: Forecasting Model Fitting for 16-20-0 (Kra-tai)
4.3.2 Forecasting Model for 46-0-0 (Chor-fah)
Sales data for 16-20-0 (Kra-tai) during 2009 to 2011 are presented in Figure 5a and 5b.
From Figure 5a and 5b, sales data show that the yearly sales of 46-0-0 (Chor-fah) seem stable while monthly sales show some variation among different periods. The finding of optimal forecasting model can be presented as in Table 4. When considering % MAPE, exponential smoothing with ? = 0.7 is the best model with minimum value of MAPE. The forecasting model of 46-0-0 (Chor-fah) can be represented as equation (7). F(t) = 0.7 Dt-1 + 0.3Ft-1 (7)
Figure 5a: Monthly Sales of 46-0-0 (Chor-fah)
when F(t) is a forecasting value for year t, Dt-1 is real sales for period t-1 and Ft-1 is sales forecasting value for period t1. Then, this equation is used to calculate the forecasting value for year 2012 as 3,265 bags. In practical, the store uses quarterly sales forecast so the yearly sales forecast is multiplied by seasonal index of each quarter to derive quarterly forecasting values as shown in Table 5.
5. CONCLUSION AND DISCUSSION
In this study, the forecasting models of chemical fertilizer store are proposed. The starting step is to classify group of fertilizer products based on ABC classification considering sales value and ordering lead time. There are two fertilizer types classified in group A that are 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah). Both products are totally 62% of total sales and ordering lead times are the longest as 7 days. Then, the sales of group A is used to derive the practical forecasting model.
Figure 5b: Yearly Sales of 46-0-0 (Chor-fah)
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Table 4: Forecasting Model Fitting for 46-0-0 (Chor-fah)
Table 5: Forecasting Model Fitting for 46-0-0 (Chor-fah)
In conclusion, 16-20-0 (Kra-tai) sales is fitted with forecasting model based on linear trend line adjusted by seasonal index and 46-0-0 (Chor-fah) sales is fitted with exponential smoothing based model. The sales pattern of 16-20-0 (Kra-tai) is fitted with linear trend line because the sales contain the effect of increasing trend. When the data have trend pattern, linear trend line is good for predicting future values. For 46-0-0 (Chor-fah) sales, exponential smoothing is fitted for forecasting future sales when the historical data have no-trend pattern.
ACKNOWLEDGMENT
The author would like to thank the Department of Industrial Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand, for the financial support.
REFERENCES
Chu, C.W. and Zhang, G.P. (2003) A comparative study of linear and nonlinear models for aggregate retail sales forecasting, Int. J. Production Economics, 86, 217231. Hadi-Vencheh, A. (2010) An improvement to multiple criteria ABC inventory classification, European Journal of Operational Research, 201, 962-965. Bošnjakovic, M. (2010) Multi-criteria Inventory Model for Spare Parts, Tehnicki Vjesnik, 17(4), 499-504. Lei, Q., Chen, J. and Zhou, Q. (2005) Multiple Criteria Inventory Classification Based on Principal Components Analysis and Neural Network, School of Economics and Management, Tsinghua University, Beijing, China. Russell & Taylor (2011) Operations Management 7th Edition, John Wiley & Sons Limited. Tersine, R. T. (1994) Principles of Inventory and Materials Management, Prentice-Hall, Englewood Cliff, NJ.
6. RECOMMENDATION STUDY
AND
FURTHER
From this study, the forecasting models of chemical fertilizer store are developed for fertilizer types classified in group A that are 16-20-0 (Kra-tai) and 46-0-0 (Chor-fah). The developed models from this study are used again in decision supporting tool development for this store to help in real working situation. The used models are not long-lasting correct. The model validation is needed. One measurement used in measure model validation called “Tracking Signal (TS)” used to identify how model correctly perform under current situation. If the tracking signal is out of control, the model need to be adjusted to maintain the ability if forecasting. Normally, TS control chart is set as 2-5 MADs (Mean Absolute Deviation). The detail of TS can also be found in Russell & Taylor (2011), as well.
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AUTHOR BIOGRAPHIES Chompoonoot Kasemset is a lecturer in Department of Industrial Engineering, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand. Her research interests include operation management, applied operations research and simulation in production and operation management. Her area of specialization is Theory of Constraint (TOC). Her email address is Watcharapat Chatchayangkul is a Master student of Industrial Management, Faculty of Engineering, Chiang Mai University, Chiang Mai, Thailand. He received a B.Eng from Electrical Engineering, King Mongkut’s Institute of Technology Lardkrabang, Thailand in 1998. His email address is
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