Sales Forecast for Bhushan Steel Limited
December 17, 2016 | Author: Omkar Hande | Category: N/A
Short Description
This is a project report on sales forecasts for Bhushan Steel Ltd. for its 3rd quarter FY 2012. For the Matlab code ref...
Description
BITS Pilani-Goa Campus
Sales Forecasting of BSL 3rd quarter FY 12, Bhushan Steel Ltd. Omkar Sayaji Hande ID:2010C6PS650G
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PREFACE
Jan/12
Jun/11
Nov/10
Apr/10
Sep/09
Feb/09
Jul/08
Dec/07
May/07
Oct/06
Mar/06
Aug/05
Jan/05
Jun/04
Nov/03
Apr/03
Sep/02
Based on data, it's been noted that Bhushan steel has been growing leaps and bounds in past few years – as compare to its customers (automobiles). BSL growth and comparitives Demand forecasting and 12 planning is a very important aspect for capital incentive 10 industry such as Bhushan 8 Steel. Absentia of doing this 6 costs organization with lack of potential growth. 4 This report discusses forecasting methods like 2 Time-Series and Regression 0 analysis which forecast sales based on past data and can -2 eventually be used to predict BSL growth AL Growth M&M Growth Voltas growth sales of Bhushan Steel Ltd. for 3rd quarter of FY 2012. Metal Growth M Growth TM Growth Currently, the assessment is done in an adHoc manner and based on gut-feel, but not based on projections. Having said that, BSL has been able to grow at the rate of its customers and more! This possibly by expanding its product lines and customer base. Following graph of growth gives a picture. In view of capital intensive nature of steel industry, forecasts related sales, volume, market demand are essential for assessing market trends, planning productions and providing growth projections to investors of the company. Forecasting methodologies, which are data-driven, based on past data, exist in literature of economics and statistics. They are regularly used for various scenarios where there is ‘randomness’. There are various techniques such as regression, time series that are used to ‘fit’ a model and use it for projections. It is to be noted that, ‘fitment’ of a model can differ – as its subjective assessment based on data. Though major firms such as ones in steel sector ought to forecast sales, the methods or models used for forecasting differ from one firm to another. For instance, for a company such as Bhushan Steel which has had full utilization of its capacity for past 20 quarters, future sales ‘volume’ would be same as its capacity to produce in future which is very well the forecasting technique used by Bhushan Steel Ltd.
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ACKWOLEDGEMENT I would like to extend my heartfelt gratitude to our instructor Dr. Akhlad Iqbal and our mentor Mr. Deepak Aggarwal for their guidance. I would also like to thank Mr. Sunil Aggarwal of Accounts Dept. and Mr. Pankaj Tiwari of Sales Dept. who have been valuable sources of information for providing insights into Bhushan Steel's cash budgeting process.
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Contents 1.
INTRODUCTION...................................................................................................................... 5 1.1
2.
SALES FORECASTING – Why Needed? ............................................................................... 5 SALES FORECASTING TECHNIQUES ...................................................................................... 6
2.1
QUALITATIVE ANALYSIS .................................................................................................... 7
Jury of executive opinion........................................................................................................... 7 Customer expectations ............................................................................................................. 7 Sales force composite ............................................................................................................... 7 2.2
QUANTITATIVE APPROACH ............................................................................................... 7
2.3
FORECASTING PROCEDURE AT BHUSHAN STEEL LTD. .................................................... 8
3.
FORECASTING SALES FOR BHUSHAN STEEL ........................................................................ 9 3.1
PROCESS OVERVIEW .......................................................................................................... 9
3.2
SOFTWARE TOOLS USED ................................................................................................... 9
3.3
FORECASTING METHODOLOGIES & RESULTS ................................................................ 10
3.3.1
Time Series Analysis................................................................................................... 10
3.3.2
Regression Analysis.................................................................................................... 14
3.3.3 Time Series and Regression Analysis............................................................................... 16 4.
CONCLUSION ....................................................................................................................... 18
APPENDIX-I .................................................................................................................................... 19 MATLAB CODE USED FOR FORECASTING ................................................................................ 19 Appendix-II Forecasting Techniques - Details ................................................................................. 25 Regression Analysis .................................................................................................................... 25 Time Series Analysis ................................................................................................................... 26 Appendix-III Software Tools- Details............................................................................................... 27 IBM SPSS .................................................................................................................................... 27 SAP ERP ..................................................................................................................................... 27 APPENDIX-IV ................................................................................................................................. 28 Data used in section 3.4.1............................................................................................................ 28 Data used in section 3.4.2 & 3.4.3 ................................................................................................ 29 REFERENCES ................................................................................................................................. 31
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1.
INTRODUCTION
Managing a business has its own challenges.. Entrepreneurs constantly need to evaluate future market circumstances (eg: market size, market share, growth, pricing) to reduce the degree of risk in operations. The best way to do this is by analyzing trends of the past. This is especially true when predicting sales of a product or service. Sales forecasting uses past figures to predict short-term or long-term performance. Tough this has strong statistical and economics foundation; there are many unknowns and randomness of nature. This is because a number of factors can affect future sales: economic downturns, employee turnover, changing trends, needs and fashions, increased competition, manufacturer recalls and other factors. However, there are several standard methods that can, with help of your domain expertise, past data, produce consistently accurate sales forecasts from year to year. All said – results would be as good as input data and expertise applied using domain knowledge. It is a tool that lets user ‘quantify’ the assessments based on past data. 1.1
SALES FORECASTING – Why Needed?
Primary parameters that appear in balance sheet are Sales, among others, such as expenses
and profits. Sales numbers are the sources of money to pay employees, cover operating expenses, buy more inventory, market new products, raise investments and attract more investors. Hence, Sales forecasting is a crucial part of the financial planning of a business. It's a selfassessment tool that uses past and current sales statistics to intelligently predict future performance. Among others – following are a few key usage of ‘sales’ forecasts. 1. Production and Pricing: With an accurate sales forecast in hand, you can plan for the future – production, inventory management, management of excess production, better pricing, among others. One simple sales forecast can inform every other aspect of a business. 2. Investments and Expansions- business viability: One needs to show them numbers that prove a business is viable. In other words, we need a business plan. A central part of that business plan is the sales forecast. New businesses need investments / loans / startup capital to get off the ground. In case, there is no past data, ‘similar’ representative data can be used. Of course, research needs to be done about related businesses that operate in the same geographical market with a similar customer base. 3. Pulse to Stakeholders: As a business grows, sales forecasts continue to be an important measurement of a company's health. Investors measures the success of a company by how well it meets its quarterly sales forecasts. For instance, If a company predicts robust sales in the fourth quarter but only earns half that amount, it's a sign to stockholders that not only is the company performing poorly, but management is clueless. When attracting new investors to a private company, sales forecasts can be used to predict the potential return on investment. The overall effect of accurate sales forecasting is a business that runs more efficiently, saving money on excess inventory, increasing profit and serving its customers better. 5
Lets look at growth of BSL in comparison with competition and its customers. Following are sales numbers or index1. We have used ‘growth’ (= [current-base]/base), to see comparative data. Base being Dec 2002.
As it’s very clear, over the years, customers (and their demands), metal industry as grown many fold. BSL too grew. However, the growth is beyond all the comparative #s. For example, between Dec 2002 and 2011, BSL has and M&M has grown 10 times, Maruti and Tata Motors have grown 5-6 times. Needless to say, growth demand of steel products is possibly captured by BSL from competition and beyond automobile industry!! What could be reason for this? Is it Capacity planning alone? Given the fact that capacity needs higher capital inflow and BSL develops only it see visible demand. This paper proposes possible alternative techniques to look at possible future demands to polish its forecasts and planning further.
2.
SALES FORECASTING TECHNIQUES
In this section we discuss techniques and concepts behind these techniques. Forecasting of sales is done using a diverse range of techniques depending on the nature of the industry, accuracy of the forecast and time period of the forecast. The forecast technique should be appropriately chosen to help manager make better decisions in planning the business strategy. Forecasting techniques can be largely categorized as: 1. Qualitative Analysis – views of experts 2. Quantitative Analysis – views of experts and further quantification using data Businesses are run on the basis of views of experts, gut feel, intuition among others. This forms the foundation. This is called ‘qualitative’. Qualitative analysis relies on expert opinions or jury of expert opinion, sales force estimation, Delphi method etc. Whereas, quantitative analysis is a more objective approach which relies on sophisticated statistical tools like regression, time series, moving average etc. In real life, forecasting models are neither purely qualitative nor quantitative. Often, qualitative analysis is used to overcome the shortcomings of quantitative model that tends to ignore certain real life variables like changes in economy or tastes of the customers. Also, creation of a ‘prediction model’ is based 1
TM= Tata Motors, M = Maruti, M&M= Mahindra and Mahindra, AL = Ashok Leyland, BSL = Bhushan Steel
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on ‘qualitative’ – which are possible dependant variables that would help predicting ‘independent’ variable. In summary, most forecasting analysis uses both methods. Start with ‘qualitative’ methods to define model, hypothesis and data and then use ‘quantitative’ to quantify. In following sections we provide a brief on these techniques. Details can be found in Appendix. 2.1
QUALITATIVE ANALYSIS
Qualitative forecasting techniques are sometimes referred to as judgmental of subjective techniques. They rely more upon opinion and less upon mathematics in their formulations. The absence of past sales means that you have to be more creative in coming up with prediction in the future. Sales forecast for new products are often based on executive judgments, sales force projection, surveys and user’s expectation. These can be summarized as following: Jury of executive opinion consists of combining top executives’ views concerning future sales. This type of forecasting technique is term a ‘top down’ technique whereby a forecast is produced for the industry. Customer expectations use customer’s expectations of their needs and requirements as the basis for the forecast. The data are typically gathered by a survey of customers or by the sales force Sales force composite combines the individual forecasts of salespeople. This technique involves salesperson making a product-by-product forecast for their particular sales territory. Such a method is a bottom-up approach. Others are further advanced techniques, such as Delphi and Bayesian, mixture of subjective and objectives techniques. These are beyond scope of this document. These techniques are often utilized when markets have been disturbed by strikes, wars, natural disasters, recessions, inflation or absence of representative data. Under these conditions historical data are useless and judgmental procedures that account for the factors causing market stocks are usually more accurate. 2.2
QUANTITATIVE APPROACH
Quantitative techniques are sometimes termed objective or mathematical techniques as they rely more upon mathematics and less upon judgment in their computation. The results of these techniques are backed by strong and fundamental statistical theories. Most quantitative techniques make use of past data or trends of the variable to be predicted. These techniques have become popular as they can be implemented and executed easing using computers. Time series and Regression are some popular techniques. Further details of techniques are discussed in Appendix-II.
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2.3
FORECASTING PROCEDURE AT BHUSHAN STEEL LTD.
Bhushan steel has been operating at its full capacity for past 4-5 years (20 quarters). In other words, the quantity sold has been same as the capacity to produce. Hence dynamics of the turnover is decided by pricing only. Bhushan steel has been steadily increasing its capacity Since its establishment in 1987 and surprisingly sales have matched the increased capacity most of the times. Thus the forecasting technique used by Bhushan Steel Ltd is simply self-evaluation of its production capacity. This seems interesting and curious, as one would aim at increasing the capacity by first evaluating market demand for the product rather than just focusing on supply side of the equation. Despite the fact, Bhushan Steel vehemently uses this method to forecast its sales. Please note a sales target and a sales forecast are distinct from each other. Sales targets are given to the sales team to encourage them in achieving higher sales. Sales targets are always higher than sales forecasts. Whereas, sales forecasts are more realistic numbers that are arrived at after certain analysis on past data etc. Sales forecasts are of more importance at higher levels of management rather than managers working at operational levels. Various software tools exist and are used, such as SAS, SPSS, SAP among others. They are discussed in details in Appendix-II
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3.
FORECASTING SALES FOR BHUSHAN STEEL
As mentioned before, Bhushan Steel Ltd follows heuristic and qualitative techniques in forecasting sales. It is based on the assumption that all produced would get sold and hence sales equals production capacity. In this paper we suggest quantifying techniques to establish a process that would help to judge market conditions or quantitatively estimate market's demand. Clearly, it needs an overhaul. Perhaps, Time-Series and Regression analysis are the most standard and suitable techniques which Bhushan Steel can bring into practice. This section will illustrate how Time Series and Regression analysis can be utilized to predict sales. By the end of this section we will have a sales prediction for 3rd quarter of FY 2012 for Bhushan Steel Ltd. 3.1
PROCESS OVERVIEW
Read data in Get Data (in
software (from Excel to Matlab)
Estimate key parameters
Save output data
using Time Series and Regression in software (Matlab)
Analyse and validate output. Repeat steps with changes if needed.
Excel)
3.2
SOFTWARE TOOLS USED
We will be making use of Microsoft® Excel2 and MathWorks MATLAB®3 to arrive at the final prediction.
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Microsoft Excel is a commercial spreadsheet platforms with calculations, graphics, pivot tables, etc. Matlab is a widely accepted numerical computing tool used by scientists / engineers that allows users to do matrix manipulations, etc
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Following are the process steps 1. The 1st step was Data Preparation, this includes: data ordering, computing quarterly figures, and ensuring readability in to Matlab. 2. Model Fitment and creation: Implementation of the prediction model(s) is done in Matlab (see Appendix-I for Matlab Code). The Matlab code is executed and the final forecasts are displayed on the Matlab terminal. 3. Model Validation and Visualization: The results obtained from Matlab are fed back to Excel where final processing of the data like computing standard errors, comparing results and graphing of modeled sales is done.
3.3
FORECASTING METHODOLOGIES & RESULTS
This section describes in detail the process followed for predicting sales. To build predictive model for ‘sales’ of BSL, we make use of three methodologies 1. Time Series analysis 2. Regression analysis 3. a combination of both Time Series and Regression analysis. Results of each model are then graphed and compared with the original sales data. These models were described in detail in Appendix II. Please note the data series is available for quarterly intervals. While finalizing a model, ‘independent’ and ‘dependant’ variables are selected. Then, model is built. Finally, model is validated for fitment. For example, ‘errors’ need to be independently and identically distributed. Data Used: We are going to use time series data of – Sales of BSL, Tata Motors, Maruti, Ashok Leyland, Voltas, Eicher; Mahindra & Mahindra and International Metal Index, Primary dependent4 variable is Sales of BSL. For Regression model, past values of others variables would be independent variable. Whereas for Time Series, past Sales of BSL would be independent variables. 3.3.1 Time Series Analysis In this model we try to investigate sales of the current quarter with sales of the past three quarters. Hence the model can be represented as, This is solved by minimizing the sum of errors, , called the least squares method 5as mentioned in previous text. Here , is sales of BSL at ‘quarter’ t.
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In Statistics, ‘dependant’ variable is a variable of interest that one would like to predict using ‘independent’ variables – that are known at that point of time. 5 For details of estimating parameters using ‘Least Square Methods’, please see Appendix II
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Using least squares method we obtain,
Model 1: Hence, the sales prediction for 3rd quarter (Jun-12) can be calculated by feeding values of past 3 quarters (Sep-11 , Dec-11 and Mar-12).
This value comes out to be ` 3076.38 Cr. Model fitment and Validation: For fitment of the ‘model’ it is essential to see that errors are IID. Meaning they don’t demonstrated any pattern when plotted against time etc. The error6 for each observation is plotted in Figure 2.
Error Plot 300 200 100 0 -100Jun-99 -200 -300 -400 -500 -600
Jun-01
Jun-03
Jun-05
Jun-07
Jun-09
Jun-11
Error
From the plot it is visible that the errors are magnifying with time. This is indicating a time series amongst errors themselves. We need to suppress these errors to have a consistent model. To do this, we rework the data again by taking a logarithmic transformation. This means the variable we are dealing with now is (refered as ) instead of . The same process is carried out again to solve the recursive relation and a drastic improvement in the results is observed.
Model 2
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‘Errors’ are supposed to be IID – independent and identically distributed.
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Again, the sales prediction for 3rd quarter (Jun-12) can be calculated by feeding values of past 3 quarters (Sep-11 , Dec-11 and Mar-12). log ( For model 2, the forecasted value for June quarter of 2012 comes out to be `2833.769. Model fitment and Validation: The errors seem more randomly distributed now, unlike before. Please see following error plot after logarithmic transformation.
Error Plot 0.4 0.2 Sep-11
Feb-11
Jul-10
Dec-09
May-09
Oct-08
Mar-08
Aug-07
Jan-07
Jun-06
Nov-05
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May-02
Oct-01
Mar-01
Aug-00
-0.4
Jan-00
-0.2
Jun-99
0
-0.6 Error
The forecasted sales for both models are plotted along with the actual sales . Errors are calculated for each entry and standard error is computer (root mean square or RMS error). RMS error is calculated using the following formula:
Model 1
Forecast for Jun'12 quarter ` 3076.38 Cr.
125.24
2
`2833.769
128.64
Error distribution Magnifying with time Independent and Identically Distributed
Recursive relation
After taking an inverse logarithm operation on forecasted sales, it is plotted along with the original sales data. A standard error of ` 128.64 is observed, which is slightly higher than previous version of the 12
model but fits the distribution required by the model, hence is more acceptable. Following is the plot of forecasted and actual sales .
Time Series Model 1 3000 2500 2000 1500 1000 500
Jun-08
Dec-08
Jun-09
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Jun-11
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Dec-07
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Actual
Jun-06
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0
Forecast
Time Series Model 2 3000 2500 2000
1500 1000 500
Actual
Dec-07
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Forecast
Using Time Series techniques, Model 2 should be used for forecast. 13
3.3.2 Regression Analysis Regression analysis is an approach to study relationship between a dependent variable and other independent variables. In our case, the dependent variable is sales of Bhushan Steel Ltd and independent variables are the factors that can affect sales. Choice of independent variables is subjective. One needs to qualitatively analyze and choose appropriate variables that have causal effect on the sales. In this model, we have identified 7 such independent variables. These variables are mostly the sales turnovers (of last quarter) of Bhushan Steel's customers. It is only logical to choose such variables as sales of Bhushan Steel will increase only when their customers which use steel as raw material will perform well. The variables are Sales turnover of Ashok Leyland, Mahindra & Mahindra, Voltas, Maruti-Suzuki, Eicher, Tata Motors and International metal price index. Please note, Tata Motors is not a customer of Bhushan Steel. This variable is strategically chosen to demonstrate a negative trend. Hence our model is:
To estimate the parameters we will use least squares method. The regression model is solved in Matlab. The following relation is obtained between Sales of Bhushan Steel and other independent variables.
Where, Table 1
Variable Sales of Ashok Leyland Sales of Mahindra & Mahindra Sales of Voltas International Metal Price index Sales of Maruti-Suzuki Sales of Eicher Sales of Tata Motors The regressed sales are plotted along with actual sales and standard error is computed.
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Regression Model: Sales 3000 2500 2000
1500 1000 500
Actual
Nov-11
Jun-11
Jan-11
Aug-10
Mar-10
Oct-09
May-09
Dec-08
Jul-08
Feb-08
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Apr-07
Nov-06
Jun-06
Jan-06
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Mar-05
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Dec-03
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Feb-03
Sep-02
0
Forecast
Figure 1
Regression Model: Error 300 200 100 0 Sep-02 -100
Sep-04
Sep-06
Sep-08
Sep-10
-200 -300 -400 Error Figure 2
The error plot as seen from Figure 5 seems random and thus fulfills the requirement of regression model. For regression model, . Thus for this model, on an average sales of the forecast, deviate roughly `111.72 Cr from the actual sales. The forecasted value for June-2012 is `3076.327.
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3.3.3 Time Series and Regression Analysis In this model we will do a time series analysis on both dependent as well as independent variables. We then find a relation between current sales and current values of other variables using regression. Now we use the predicted values for each of the independent variables to find the predicted value of sales. This model is very similar to the above model, except for the fact that here we try to study the relation of current sales and current values of other independent variables. The model is solved in Matlab using least squares estimate. The following relation is obtained:
Where are same as mentioned in Table 1. Please note that at future “t” all are unknown above. Here, on right side, one uses projections of those time series and then use above equation. Plot of actual vs. forecasted sales is shown in Figure 7 and RMS error is estimated.
Regression with usage of predictions using TS 3000 2500 2000 1500 1000 500
Actual
Jan-12
Aug-11
Mar-11
Oct-10
May-10
Dec-09
Jul-09
Feb-09
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Apr-08
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Forecast
Figure 3
The errors for this model are plotted in Figure 8.
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Error Plot 600 500 400 300 200 100 0 -100Jun-02
Jun-04
Jun-06
Jun-08
Jun-10
-200 -300 Error Figure 4
For the above model This means forecasted sales deviate approximately ` 121.25 Cr. From actual data.
The forecasted value for June-2012 using this model is `2948.918.
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4.
CONCLUSION Following are basic findings.
Model Linear Regression
Model Description Here dependant variable is sales of BSL; independent variables are sales of its customers, among others.
Parameters Estimated
Estimated Sales for June-2012 is `3076.327.
Time Series – Model 1
Here dependant variable is sales of BSL; independent variables are past three quarters sales of BSL
Time Series – Model 2
Same as above – all variables transferred to ‘log’
Combined Model: Time Series +Regression
1. Time Series model is fitted for all independent and dependant variables. 2. Regrgession Model is fitted between dependant and independent for each quarter 3. Future quarters estimates of dependant are created using step 1 and then fitted in step 2
Estimated Sales for June-2012 is ` 2939.92 Cr. Issue: Errors show ‘skew’ over time Estimated Sales for June-2012 is ` 2833.77 Cr.
Estimated Sales for June-2012 is ` 2949. 92 Cr.
1. It should be noted that, in regression BSL sales have zero or negative co-relation to that of Tata Motors and to that of Maruti. Please note that Maurti is a customer of BSL – hence, the model indicates that there is substantial improvement possible with sales to Maruti. Or the model tells, Maruti’s growth is possibly captured by BSLs competition. 2. Same reasoning can be used for Tata Motors, which is one of the largest players and the market representative of India market. On the other hand, it may be on growth path, however, its not contributing to BSLs growth. 3. The estimates for sale stand between 2833 to 3076 with error of margin of 121.
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APPENDIX-I MATLAB CODE USED FOR FORECASTING %% SALES FORECASTING MODEL % Following code is am implementation of forecasting models discussed in % section 4.3 %% INITIALIZATION % Data is read from excel sheets and stored in form of arrays. The sizes of % each array are stored in separate variables. Other matrices which will be % used in future are intialized as well. B=ones(39,7); E=ones(40,8); bsl=xlsread('bsl.xlsx'); ash=xlsread('ashley.xlsx'); mnm=xlsread('MnM.xlsx'); voltas=xlsread('voltas.xlsx'); metal=xlsread('metal.xlsx'); maruti=xlsread('maruti.xlsx'); eicher=xlsread('eicher.xlsx'); tata=xlsread('tata.xlsx'); [bsl_m bsl_n]=size(bsl); [ash_m ash_n]=size(ash); [mnm_m mnm_n]=size(mnm); [voltas_m voltas_n]=size(voltas); [metal_m metal_n]=size(metal); [maruti_m maruti_n]=size(maruti); [eicher_m eicher_n]=size(eicher); [tata_m tata_n]=size(tata); initial_m=[bsl_m ash_m mnm_m
voltas_m metal_m maruti_m eicher_m];
%% REGRESSION ANALYSIS MODEL % The regression model discussed in 4.3.2 is implemented in this section. % The results obtained are written to an excel file as output. C=bsl(1:39); B(:,1)=1; B(:,2)=ash(2:40); B(:,3)=mnm(2:40); B(:,4)=voltas(2:40); B(:,5)=metal(2:40); B(:,6)=maruti(2:40); B(:,7)=eicher(2:40); B(:,8)=tata(2:40); theta_bsl_2=(inv((transpose(B))*B))*((transpose(B))*C); xlswrite('forecast.xlsx',C,'Reg', 'A1'); xlswrite('forecast.xlsx',B,'Reg', 'B1'); xlswrite('forecast.xlsx',B*theta_bsl_2,'Reg','J1');
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%% TIME SERIES AND REGRESSION ANALYSIS MODEL % The time series and regression model discussed in section 4.3.3 is % implemented in this section. The output is written into an excel file. D=bsl(1:40); E(:,1)=1; E(:,2)=ash(1:40); E(:,3)=mnm(1:40); E(:,4)=voltas(1:40); E(:,5)=metal(1:40); E(:,6)=maruti(1:40); E(:,7)=eicher(1:40); E(:,8)=tata(1:40); theta_bsl_3=(inv((transpose(E))*E))*((transpose(E))*D); xlswrite('forecast.xlsx',D,'TS&Reg', 'A1'); xlswrite('forecast.xlsx',E,'TS&Reg', 'B1'); xlswrite('forecast.xlsx',E*theta_bsl_3,'TS&Reg','J1'); %% TIME SERIES ANALYSIS ON BHUSHAN STEEL'S SALES % Time series analysis discussed in section 4.3.1 is implemented here. The % results are stored in an excel file. j=2; clear A; bsl_m=bsl_m - 3; for i=1:bsl_m temp=j; A(i,2)=bsl(j,1); j=j+1; A(i,3)=bsl(j,1); j=j+1; A(i,4)=bsl(j,1); j=temp+1; end A(:,1)=1; bsl=bsl(1:bsl_m); theta_bsl=(inv((transpose(A))*A))*((transpose(A))*bsl); xlswrite('forecast.xlsx',bsl,'TS', 'A1'); xlswrite('forecast.xlsx',A,'TS', 'B1'); xlswrite('forecast.xlsx',A*theta_bsl,'TS','F1'); f_bsl=[1 bsl(1) A(1,2) A(1,3)]*theta_bsl; %% TIME SERIES ANALYSIS ON SALES OF ASHOK LEYLAND % Time series analysis on sales of ashok leyland is performed here. This is % required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; ash_m=ash_m - 3;
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for i=1:ash_m temp=j; A(i,2)=ash(j,1); j=j+1; A(i,3)=ash(j,1); j=j+1; A(i,4)=ash(j,1); j=temp+1; end A(:,1)=1; ash=ash(1:ash_m); theta_ash=(inv((transpose(A))*A))*((transpose(A))*ash); f_ash=[1 ash(1) A(1,2) A(1,3)]*theta_ash; %% TIME SERIES ANALYSIS ON SALES OF MAHINDRA & MAHINDRA % Time series analysis on sales of Mahindra and Mahindra is performed here. % This is required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; mnm_m=mnm_m - 3; for i=1:mnm_m temp=j; A(i,2)=mnm(j,1); j=j+1; A(i,3)=mnm(j,1); j=j+1; A(i,4)=mnm(j,1); j=temp+1; end A(:,1)=1; mnm=mnm(1:mnm_m); theta_mnm=(inv((transpose(A))*A))*((transpose(A))*mnm); f_mnm=[1 mnm(1) A(1,2) A(1,3)]*theta_mnm; %% TIME SERIES ANALYSIS ON SALES OF VOLTAS % Time series analysis on sales of voltas is performed here. This is % required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; voltas_m=voltas_m - 3; for i=1:voltas_m temp=j; A(i,2)=voltas(j,1); j=j+1; A(i,3)=voltas(j,1); j=j+1; A(i,4)=voltas(j,1); j=temp+1; end
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A(:,1)=1; voltas=voltas(1:voltas_m); theta_voltas=(inv((transpose(A))*A))*((transpose(A))*voltas); f_voltas=[1 voltas(1) A(1,2) A(1,3)]*theta_voltas; %% TIME SERIES ANALYSIS ON INTERNATIONAL METAL INDEX % Time series analysis on international metal index is performed here. This % is required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; metal_m=metal_m - 3; for i=1:metal_m temp=j; A(i,2)=metal(j,1); j=j+1; A(i,3)=metal(j,1); j=j+1; A(i,4)=metal(j,1); j=temp+1; end A(:,1)=1; metal=metal(1:metal_m); theta_metal=(inv((transpose(A))*A))*((transpose(A))*metal); f_metal=[1 metal(1) A(1,2) A(1,3)]*theta_metal; %% TIME SERIES ANALYSIS ON SALES OF MARUTI SUZUKI % Time series analysis on sales of maruti suzuki is performed here. This is % required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; maruti_m=maruti_m - 3; for i=1:maruti_m temp=j; A(i,2)=maruti(j,1); j=j+1; A(i,3)=maruti(j,1); j=j+1; A(i,4)=maruti(j,1); j=temp+1; end A(:,1)=1; maruti=maruti(1:maruti_m); theta_maruti=(inv((transpose(A))*A))*((transpose(A))*maruti); f_maruti=[1 maruti(1) A(1,2) A(1,3)]*theta_maruti; %% TIME SERIES ANALYSIS ON SALES OF EICHER % Time series analysis on sales of eicher is performed here. This is
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% required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; eicher_m=eicher_m - 3; for i=1:eicher_m temp=j; A(i,2)=eicher(j,1); j=j+1; A(i,3)=eicher(j,1); j=j+1; A(i,4)=eicher(j,1); j=temp+1; end A(:,1)=1; eicher=eicher(1:eicher_m); theta_eicher=(inv((transpose(A))*A))*((transpose(A))*eicher); f_eicher=[1 eicher(1) A(1,2) A(1,3)]*theta_eicher; %% TIME SERIES ANALYSIS ON SALES OF TATA MOTORS % Time series analysis on sales of tata motors is performed here. This is % required for forecasting method discussed in section 4.3.3. clear A j temp; j=2; tata_m=tata_m - 3; for i=1:tata_m temp=j; A(i,2)=tata(j,1); j=j+1; A(i,3)=tata(j,1); j=j+1; A(i,4)=tata(j,1); j=temp+1; end A(:,1)=1; tata=tata(1:tata_m); theta_tata=(inv((transpose(A))*A))*((transpose(A))*tata); %% DISPLAY OF FINAL OUTPUT f_tata=[1 tata(1) A(1,2) A(1,3)]*theta_tata; f_sales=[1 ash(1,1) mnm(1,1) voltas(1,1) metal(1,1) maruti(1,1) eicher(1,1) tata(1,1)]*theta_bsl_2; f_sales_2=[1 f_ash f_mnm f_voltas f_metal f_maruti f_eicher f_tata]*theta_bsl_3; clc
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fprintf('\n\nSales prediction by Regression Analysis %d\n\n', f_sales); fprintf('\n\nSales prediction by Time Series and Regression Analysis %d\n\n', f_sales_2); fprintf('\n\nSales prediction by Time Series Analysis %d\n\n', f_bsl); %% CORRECTION IN TIME SERIES MODEL OF 4.3.1 % Due to appearence of a time series like pattern amongst the errors of thw % forecasted sales, we take a log transformation and rework the data by % following the same process again. clear; j=2; bsl=xlsread('bsl.xlsx'); [bsl_m bsl_n]=size(bsl);
bsl_m=bsl_m - 3; bsl=log(bsl); for i=1:bsl_m temp=j; A(i,2)=bsl(j,1); j=j+1; A(i,3)=bsl(j,1); j=j+1; A(i,4)=bsl(j,1); j=temp+1; end A(:,1)=1; bsl=bsl(1:bsl_m); theta_bsl=(inv((transpose(A))*A))*((transpose(A))*bsl); xlswrite('forecast.xlsx',bsl,'TS_Log', 'A1'); xlswrite('forecast.xlsx',A,'TS_Log', 'B1'); xlswrite('forecast.xlsx',A*theta_bsl,'TS_Log','F1'); f_bsl_2=[1 bsl(1) A(1,2) A(1,3)]*theta_bsl; fprintf('\n\nSales prediction by Time Series Analysis after taking log %d\n\n', exp(f_bsl_2));
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Appendix-II Forecasting Techniques - Details
Regression Analysis Regression analysis is a statistical tool for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal effect of one variable upon another - the effect of a price increase upon demand, for example, or the effect of changes in the money supply upon the inflation rate. In case of sales forecasting we try to study correlation of sales with external factors that can affect it. In language of statistics, the variable to be predicted (for us sales) is called the dependent variable. The variables which determine the value of this dependent variable are called Independent variables. For example, in sales forecasting, sales is the dependent variable and market demand, production capacity and the rest would be independent variables. By independent we mean that these variables must not be correlated between themselves, i.e., market demand has to independent of our production capacity and so on. Let be the dependent variable and be the independent variables. Let c, be the unknown parameters connecting these variables such that,
As forecasters, our job is to estimate the parameters c, . For this we have with us past data of both the dependent and independent variables. is the error term. For regression model to be accurate, the distribution of should be such that E( )=0. is the constant term. Clearly if you have 4 independent variables, you can actually solve the relation with just 6 observation. But If you have more than 6 observations, which 6 observations do you pick up? The aim of regression is not to solve this relation perfectly. Rather, in statistics, where we deal with much larger data, we make use of generalized least square method to estimate the unknown parameters. We will briefly discuss this method. From equation 2.1, Supposing k observations, we will now find the sum of squares of these errors (SSE).
Now we will choose c, , such that they minimize SSE. This can be done by taking partial derivatives of SSE for each of c, and thereby solving each equation to estimate them. The same model can be represented using matrices, Where,
25
By this method an estimate for β would be,
Once we have β in place, we get the relation between the dependent and independent variables. Time Series Analysis Time series analysis tries to identify relation between current value of a variable with its past values. For example to predict sales for the next year, we might like to investigate its relationship with sales of past 36 quarters or so. Time series model can be obtained from regression model by substituting independent variables by past values of the variable. For example, for predicting , we will investigate how is related to , , and so on. Hence our model becomes Again, the method for estimating the parameters here is the least squares method.
k here is the number of observations. To estimate the parameters will minimize SSE by taking partial derivatives with each of the above parameters.
we
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Appendix-III Software Tools- Details
IBM SPSS IBM SPSS Statistics is an integrated family of products that addresses the entire analytical process, from planning to data collection to analysis, reporting and deployment. With more than a dozen fully integrated modules to choose from, you can find the specialized capabilities you need to increase revenue, outperform competitors, conduct research and make better decisions. IBM SPSS Modeler is a data mining workbench that helps you build predictive models quickly and intuitively, without programming. SAP ERP SAP is a German company that develops business software. ERP stands for Enterprise Resource Planning, and is the term used to describe an integrated software solution that incorporates the key business functions of an organization. SAP today is the most popular ERP system across the globe. Sales forecasting forms an important tool which comes integrated with SAP ERP package. It is a highly customizable module. Users have various prediction models to choose from.
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APPENDIX-IV
Data used in section 3.4.1 Quarter
Actual sales of BSL
Forecasted Sales of BSL - method 1
Forecasted Sales of BSL - method2
Error in method 1
Error in method 2
Jun-99
189.250
188.980
198.692
0.270
-9.442
Sep-99
190.630
198.058
209.089
-7.428
-18.459
Dec-99 Mar-00 Jun-00 Sep-00 Dec-00 Mar-01 Jun-01 Sep-01 Dec-01 Mar-02 Jun-02 Sep-02 Dec-02 Mar-03 Jun-03 Sep-03 Dec-03 Mar-04 Jun-04 Sep-04 Dec-04 Mar-05 Jun-05 Sep-05 Dec-05 Mar-06 Jun-06 Sep-06 Dec-06 Mar-07 Jun-07
252.000 181.790 273.160 221.830 242.210 157.230 256.170 208.090 242.600 279.910 256.010 253.400 281.820 342.870 312.170 340.700 400.750 523.740 577.980 609.390 749.950 744.510 742.540 640.950 668.730 740.520 787.550 994.710 1000.810 1054.660 938.030
201.821 236.602 211.551 261.868 239.298 259.286 201.556 242.595 220.528 251.703 272.103 276.194 276.982 287.642 331.489 336.544 359.845 396.418 493.578 574.186 637.262 743.269 785.994 816.858 753.975 742.372 768.881 823.433 977.926 1049.554 1133.011
204.985 232.993 232.350 238.152 264.636 250.767 214.308 214.278 247.417 242.224 277.760 288.854 275.906 287.056 331.308 352.828 352.057 395.129 486.585 587.785 639.538 724.485 805.593 807.459 754.269 712.370 758.636 823.605 948.379 1075.662 1114.043
50.179 -54.812 61.609 -40.038 2.912 -102.056 54.614 -34.505 22.072 28.207 -16.093 -22.794 4.838 55.228 -19.319 4.156 40.905 127.322 84.402 35.204 112.688 1.241 -43.454 -175.908 -85.245 -1.852 18.669 171.277 22.884 5.106 -194.981
47.015 -51.203 40.810 -16.322 -22.426 -93.537 41.862 -6.188 -4.817 37.686 -21.750 -35.454 5.914 55.814 -19.138 -12.128 48.693 128.611 91.395 21.605 110.412 20.025 -63.053 -166.509 -85.539 28.150 28.914 171.105 52.431 -21.002 -176.013 28
Sep-07 Dec-07 Mar-08 Jun-08 Sep-08 Dec-08 Mar-09 Jun-09 Sep-09 Dec-09 Mar-10 Jun-10 Sep-10 Dec-10 Mar-11 Jun-11 Sep-11 Dec-11 Mar-12
1068.120 982.730 1215.870 1319.790 1516.960 1003.690 1119.950 1304.700 1298.480 1429.000 1608.740 1372.650 1718.910 1942.740 1966.160 2231.780 2465.360 2407.060 2836.760
1079.133 1138.208 1094.701 1242.446 1348.374 1550.945 1321.321 1297.642 1318.035 1392.640 1513.447 1655.719 1594.225 1780.514 1953.523 2111.520 2330.952 2549.651 2641.973
1085.875 1085.686 1113.747 1179.812 1363.184 1526.142 1364.850 1163.523 1300.542 1410.002 1476.651 1636.902 1625.491 1664.334 1965.532 2122.317 2271.189 2538.035 2655.410
-11.013 -155.478 121.169 77.344 168.586 -547.255 -201.371 7.058 -19.555 36.360 95.293 -283.069 124.685 162.226 12.637 120.260 134.408 -142.591 194.787
-17.755 -102.956 102.123 139.978 153.776 -522.452 -244.900 141.177 -2.062 18.998 132.089 -264.252 93.419 278.406 0.628 109.463 194.171 -130.975 181.350
Data used in section 3.4.2 & 3.4.3
Quarter
Actual Ashok Mahindra & Voltas Metal Sales of BSL Leyland Mahindra Sales Index Sales Sales Sep-02 253.400 635.260 820.640 269.710 52.910
Maruti Eicher Tata Forecasted Suzuki Sales Motors Sales of Sales Sales BSL 1722.950 164.390 2159.160 323.150
Dec-02
281.820
573.320
960.000
251.240
57.020
1792.400 154.610
2194.130
295.846
Mar-03
342.870
932.360
1123.050
358.240
55.530
2167.290 183.840
2993.480
350.847
Jun-03
312.170
584.290
992.890
361.560
59.740
2033.100 149.920
2500.920
373.424
Sep-03
340.700
823.890
1118.530
288.690
64.320
2164.200 279.010
3176.600
341.145
Dec-03
400.750
845.920
1327.650
244.980
75.890
2269.980 200.170
3398.260
396.123
Mar-04
523.740
1118.650
1787.110
385.580
81.330
2898.200 464.430
4143.440
454.020
Jun-04
577.980
821.190
1423.170
324.120
81.930
2514.980 345.890
3574.080
708.227
Sep-04
609.390
914.770
1554.410
286.350
85.940
2711.650 445.950
4147.050
545.751
Dec-04
749.950
987.130
1772.280
288.420
93.140
2888.960 533.710
4364.940
593.171
Mar-05
744.510
1459.290
1910.680
487.770
97.710
3045.180 657.010
5338.870
716.031
Jun-05
742.540
1063.230
1811.870
441.690
96.280
2627.130 387.530
3878.090
765.424
29
Sep-05
640.950
1250.090
1914.810
467.260
102.870
3039.930 352.950
4781.310
741.546
Dec-05
668.730
1202.430
2207.170
435.250
124.330
3114.170 389.970
5074.550
705.169
Mar-06
740.520
1734.810
2288.830
513.920
148.400
3277.010 514.440
6882.750
849.231
Jun-06
787.550
1423.870
2236.250
580.400
163.130
3125.470 383.130
5783.410
824.726
Sep-06
994.710
1675.720
2490.500
529.880
173.730
3419.190 456.470
6571.790
877.460
Dec-06
1000.810
1777.590
2576.060
568.920
170.780
3679.470 493.820
6956.840
967.792
Mar-07
1054.660
2290.990
2747.450
721.350
201.950
4429.760 619.080
8267.000
981.716
Jun-07
938.030
1621.140
2612.780
824.930
196.530
3930.820 464.350
6056.820
1069.150
Sep-07
1068.120
1745.890
2802.400
712.740
179.860
4547.370 536.940
6672.650
1130.825
Dec-07
982.730
1800.080
2940.150
664.760
178.400
4674.130 547.750
7251.830
1151.928
Mar-08
1215.870
2562.010
3148.160
842.110
198.950
4762.910 653.350
8749.520
1152.750
Jun-08
1319.790
1883.860
3293.450 1006.730
187.960
4753.580 537.980
6928.440
1218.508
Sep-08
1516.960
1866.400
3137.960
928.490
131.480
4993.620
71.990
7078.850
1366.249
Dec-08
1003.690
1000.850
2519.250
866.010
109.660
4625.810
79.450
4758.620
994.882
Mar-09
1119.950
1218.120
3654.450 1262.620
112.360
6432.900
89.840
6894.880
878.600
Jun-09
1304.700
912.450
4242.590 1178.930
140.020
6493.000
90.990
6404.630
1178.986
Sep-09
1298.480
1577.690
4557.770 1004.250
157.470
7202.610
99.190
7978.820
1510.508
Dec-09
1429.000
1815.530
4497.120
913.530
191.180
7502.850
97.990
8979.900
1560.377
Mar-10
1608.740
2939.040
5304.630 1460.270
220.780
8424.550 100.480 12229.700
1509.862
Jun-10
1372.650
2347.980
5160.100 1375.160
179.370
8231.530 107.970 10416.260
1660.358
Sep-10
1718.910
2713.960
5434.360 1070.780
216.280
9147.270 111.120 11504.070
1671.295
Dec-10
1942.740
2227.250
6121.090
993.050
245.480
9494.450 123.100 11519.550
1770.114
Mar-11
1966.160
3828.530
6778.170 1709.410
250.080
10092.180 150.890 14325.520
2086.214
Jun-11
2231.780
2495.510
6733.540 1381.570
242.230
8529.300 167.830 11897.890
2216.667
Sep-11
2465.360
3094.570
7360.620 1055.610
200.900
7831.620 181.160 12953.800
2332.686
Dec-11
2407.060
2879.800
8386.810 1134.620
202.040
7882.400 171.070 13337.900
2434.210
Mar-12
2836.760
4311.000
9387.200 1621.000
203.490
11727.000 221.360 16391.000
2810.260
30
REFERENCES 1. 2. 3. 4. 5. 6.
www.moneycontrol.com www.fem.uniag.sk managementinnovations.wordpress.com www.businesslink.gov.uk money.howstuffworks.com www.wikipedia.org
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