Group Project. Forecasting sales of Other Dairy (Lassi, Srikhand) & Ice-creams

Transcription

1 Forecasting Analytics Group Project Forecasting sales of Other Dairy (Lassi, Srikhand) & Ice-creams Group members: PG ID Name Arpita Bhattad Ushhan Gundevia Ridhima Gupta Kapil Dev Tejwani Kaushik Sur

2 Executive Summary Problem Definition: ABC retail is a large format hyper market. It sells food, fashion and electronics. Data led insights and analytics forms the foundation of all decision making and communication. It now wishes to ascertain unique shopping needs to better service customers. In an attempt to do the same, our group chose to study sales of everyday items such as dairy products including lassi, srikhand and ice-creams. These are part of two classes Other Dairy & Ice Creams & Gelato. We analyze the data to determine trends, seasonality or unique patterns and use the same to forecast daily sales of the dairy products (lassi& srikhand) and ice-cream to give a reasonable prediction of future demand to assist the retailer to manage stocks better. We consider both the data series individually as both these series show different seasonal trend. Other Dairy (Lassi& Srikhand) Brief description of the data: The data when plotted did not indicate any upward/ downward trend but showed significant weekly seasonality with sales being highest on Sunday followed by Saturday, and Monday and Tuesday with minimum sales. This was no surprise as we expect more people shopping over the weekends, far less on Monday and Tuesday as they are well stocked and sales again pick up from Wednesday peaking towards the weekend. There are a few outliers; we see higher sales in the middle of the week owing to festivals/ public holidays. High level description of final method and performance: In order to build a forecasting model that would best capture the seasonality we experimented with various techniques. We discovered that today s sales were somewhat related to past two days sales and with this knowledge we built a model to predict sales for next two days given last two day s sales. There is not much correlation between weekly sales. With Moving Average we have developed a model that can reasonably predict sales for next 2 days. We tested the model and this one offered minimum deviation from the actual values indicated by the MAPE % error. Ice-Cream and Gelatos Brief description of the data: We could clearly see that this series is dominated by two subclasses in terms of data available Cups, Cones and Bars and Family Packs. We analyzed each series individually and found two kinds of seasonality (i) Weekly seasonality in terms of weekend and weekday seasonality. Sales were higher on weekends as compared to weekdays. (ii) A half yearly seasonality in terms of summer and winter months. Sales were considerably higher in summer months (Mar-Aug) as compared to winters. Page 1

3 In addition we replaced the holes in the data with the average quantity sold as well as identified the outliers (festival dates), though we did not change the values or removed them considering the fact that there wasn t enough data to justify our assumptions. To understand weekly variation we did a Trellis of sum of quantity sold over day of week. We can clearly see higher demand over the weekend, compared to the weekdays (Fig. 8 in the Appendix) High level description of final method and performance: While building the forecasting model, we performed a Naïve Forecast initially and used the results as our reference. After performing Naïve, we performed a multiple linear regression with a single seasonality (weekly) and a linear trend. Thereafter, we performed a Holt Winter s analysis with a trend and additive seasonality followed by a multiple regression with multiplicative seasonality. Our parameters kept on improving in the order sequence mentioned with Multiple Regression with Dual Seasonality giving the best results. Forecasts: After training the model on training data and validating on validation data we used the model to forecast for the next two days. Here are the forecasts Row Labels Forecast LCI UCI 9/1/ /2/ Managerial Implications: For the dairy line we conclude that the model can be used to predict next two days sales based on previous two days sales and hence the retailer can use the forecasts to decide how much of the lassi and srikhand does he wish to stock on any given day. For the Ice Cream and Gelato class, we can accurately predict data for the next week using a regression model. With further advancement in the IT infrastructure, an ERP/order management system could be used to integrate the supply chain and share this information with the dairy products supplier. This would even let the supplier plan his stock better and the retailer will be spared from the hassle of debating/discussing the requirement every day. Needless to say this would result in financial gains. Our models assume that the current pattern in demand for the products (including the trend, seasonality, level etc.) will remain consistent with historical data on which the forecasts are made (his includes customer preferences and also product attributes). Page 2

4 Technical Summary Details of methods used Data Source: Provided by HansaCEquity Period 13 months of data from Aug 2011 to Aug 2012 The daily transaction data is available for a particular store in Mumbai which contains quantity sold, extended price among other variables Data Availability Assumption: We assume that data will be available in this format on an ongoing basis. Data Partitioning: We partitioned data into training set (Aug 2011 to Jul 2012) and validation set (Aug 2012: 4 weeks) Other Dairy Products Data Exploration & Visualization We used spot fire to aggregate, visualize & explore available data. This exercise generated few time series which are shown in Fig. 1 (a, b, c) in the Appendix. For each series we looked at three daily series Total Quantity Sold, Total Sales &# of Transactions per day. Outlier treatment: We observed few outliers Feb 2012 and May 2012 but we have not removed them as we believe there may be few months which see spikes due to certain reasons and our model should be able to take into account such outliers as well. To understand weekly variation we did a Trellis of sum of quantity sold over day of week. We can clearly see higher demand over the weekend, compared to the weekdays (Fig. 2 in the Appendix) We ran Auto correlation (ACF) on the data and we understood that there is correlation between sales today and the sales yesterday, and 6 & 7 days ago (Fig. 3 in Appendix) Forecasting: We are doing a rollover forecast on a daily basis. The forecast will be used to predict daily sales. Methods: We tried multiple methods starting with Naïve as our benchmark (Fig. 4 in Appendix). The ACF plot indicated correlations which did not make much sense besides the one that indicated weekly correlation. The MAPE was 130%, there was much scope to improve. Then we moved on to Multiple Linear Regression with Weekly dummy variables. Although the MAPE was still high but the ACF indicated that there is correlation between today s and next 2 days sales. This aspect was not being captured by our model. (Fig. 5 (a, b, c) in Appendix). Further need for improvisation. Page 3

5 Output from Moving Average with 7 days (MA7) seasonality was even worse as MAPE increased to 241%. But the plot of Actual vs forcasted on the validation set indicated that the model is doing fine while predicting next 2 day s sales. (Fig. 6 in Appendix) To improvise, then we did holt winter s with additive seasonality with 7 days period which was great improvement as MAPE came down to 80%. (Fig. 7 in Appendix) But it was evident from the earlier experiments that there is connection with last 2 days sales, so we went ahead with 2 days period with holt winter s with even improved MAPE to 56%. Finally after this we did MA (2) which gave the best results in terms of MAPE 48%. Results are provided below Note: The main limitation of this method despite giving good results is that it has to be used on rolling forward basis and it can predict accurately for only the next two days. Ice-Cream and Gelatos Data Exploration & Visualization We used spot fire to aggregate, visualize & explore available data. To understand weekly variation we did a Trellis of sum of quantity sold over day of week. We can clearly see higher demand over the weekend, compared to the weekdays (Fig. 8 in the Appendix) Forecasts: We are doing a rollover forecast on a daily basis. The forecast will be used to predict daily sales. Methods used We tried multiple methods starting with Naïve as our benchmark Then we moved on to Multiple Linear Regression with Weekly dummy variables. Page 4

6 After learning from this model we used Moving Average with 7 days (MA7) seasonality which did not make much sense. Then we did Holt Winter s with additive seasonality with 7 days period (Fig. 9 in Appendix) Finally after this we did Multiple Linear Regression with Weekly and Half Yearly dummy variables and Polynomial trend (t and t^2). We obtained the best MAPE in this case. Page 5

7 Appendix Fig. 1(a) Total Daily Quantity Sold Fig. 1(b) Total Daily Sales (Rs.) Page 6

8 Fig. 1(c) No. of Daily Transactions Fig. 2 Trellis for Daily Quantity Sold Page 7

9 Fig. 3 ACF for Total Daily Sales Fig. 4 Naïve Forecast Data Data source Time variable Selected variables CategoryVar1!$D$11:$O$367 Row Labels Sum of QuantitNaïve Residual Day of w eek Weekday_Fri Weekday_MonWeekday_Sat Weekday_SunWeekday_ThuWeekday_TueWeekday_Wed Partitioning Method Sequential # training row s 329 # validation row s 28 Fig. 5 (a) Dummy Variables for Day of Week Page 8

10 Fig. 5 (b) Linear Regression with Dummy Variables Fig. 5 (b) ACF /PACF from Regression Page 9

11 Fig. 6 Moving Average MA (7) Page 10

12 Error Measures (Validation) MAPE MAD MSE Fig. 7 Holt Winter s Additive Seasonality Model Sum of Quantity_Sold Time Plot of Actual Vs Forecast (Validation Data) Row Labels Actual Forecast Error Measures (Validation) MAPE MAD MSE Fig. 10 Holt Winter s Additive Seasonality Model Page 11

13 Fig. 8 Trellis for Daily Quantity Sold Fig. 9 Methods used to predict Ice-Cream Sales Page 12

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