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\title{Application of Proper Forecasting Technique in Juice Production: A Case Study}
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             \author[1]{Dalgobind  Mahto}

             \affil[1]{  Green Hills Engineering College, Solan}

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\date{\small \em Received: 14 December 2012 Accepted: 5 January 2013 Published: 15 January 2013}

\maketitle


\begin{abstract}
        


Every organisation that produces product evaluates their performance at certain intervals to keep the pace with the market. Forecasts are evaluated to improve models to achieve better policy and planning outcomes. The purpose of this study is to observe whether the forecast errors are within the reasonable limit of expectations or whether these errors are irrationally large and require an improvement in the statistical models and process of producing these forecasts. Statistical time series modelling techniques like â??" Moving Average, Simple Exponential Smoothing and Least Square methods are used for the study and their performance evaluated in terms of Mean Average Deviation (MAD), Mean Squared Error (MSE).

\end{abstract}


\keywords{moving average method, simple exponential smoothing method, least square method, mean average deviation, mean squared error (MSE).}

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\let\tabcellsep& 	 	 		 
\section[{Introduction}]{Introduction}\par
odern production activities are becoming more complex technologically, the basic inputs are becoming expensive and there are lot of restrictions on them. The planning of the production activities is, therefore, essential to put the resources for best use. Planning is a fundamental activity of management. Forecasting forms the basis of planning and it enables the organisation to respond more quickly and accurately to market changes. It plays a crucial role in the development of plans for the future. It is essential for the organisations to know for what level of activities one is planning before investments in inputs i.e. men, machines and materials. It uses many statistical techniques. Therefore, it is also called as Statistical Analysis. It refers to a systematic analysis of past and present circumstances. It is essentially a technique of anticipation. Before making an investment decision, questions may arise like:\par
? What should be the size of the order and safety stock?\par
? What should be the capital cost required for the work?\par
? What should be the capacity of the plant?\par
? How much labour is required?\par
The answers to the above questions depend upon the forecast for the future level of operations. The success of a business greatly depends upon the efficient forecasting and preparing for future events. It should be no surprise that forecasts are not always accurate -they are essentially about predicting the future with incomplete information. Nevertheless, forecast inaccuracies, particularly consistent underestimation of revenues and budget surpluses generally draws intense criticism. Forecast accuracy has been a matter of concern and subject of review. In general, the reasons for inaccuracies may fall into the following categories:\par
? Technical issues, such as data accuracy, forecasting methodology, process and agency structures.\par
? Effects of fiscal objectives.\par
? The economic cycle. Forecasting agencies generally review and improve data and models on an ongoing basis, and issues identified in major reviews are generally marginal. 
\section[{II.}]{II.} 
\section[{Aims and Objectives}]{Aims and Objectives}\par
The main emphasis of this work is to compare the various forecasting techniques prevalent in the industries based on the data obtained from a juice producing factory. In this manuscript an attempt has been made to forecast juice production by using the Moving Average Method, Simple Exponential Smoothing and Least Square Method. The aim is to evaluate the performances in terms of  
\section[{Methodology}]{Methodology}\par
This study was carried out on the basis of juice production data collected for the period 2000 to 2011 as shown in the table 1. When demand for a product is neither growing nor declining rapidly and if it does not have seasonal characteristics, a moving average can be useful in removing the random fluctuations for forecasting. Although moving averages are frequently centered, it is more convenient to use past data to predict the following period directly. Although it is important to select the best period for the moving average, there are several conflicting effects of different period lengths. The different moving averages produce different forecasts. The greater the number of periods in the moving average, the greater the smoothing effect. If the underlying trend of the past data is thought to be fairly constant with substantial randomness, then a greater number of periods should be chosen. The formula for a simple moving average isF t = ( A t-1 + A t-2 + A t-3 + A t-n ) n\textbf{(1)}\par
Where , F t = Forecast for the coming period, n = Number of period to be averaged n and A t-1 , A t-2 , A t-3 = Actual occurrences in the in the past period, two periods ago, three periods ago and so on respectively.\par
Equal weighting is given to each of the values used in the moving average calculation, whereas it is reasonable to suppose that the most recent data is more relevant to current conditions. An n period moving average requires the storage of (n-1) value to which is added the latest observation. This may not seem much of a limitation when only a few items are considered. The moving average calculation takes no account of data outside the period of average, so full use is not made of all the data available. The use of the unadjusted moving average as a forecast can cause misleading results when there is an underlying seasonal variation. 
\section[{b) Simple Exponential Smoothing Method}]{b) Simple Exponential Smoothing Method}\par
In the previous forecasting method, the major drawback is the need to continually carry a large amount of historical data. As each new piece of data is added in these methods, the oldest observation is dropped, and the new forecast is calculated. The reason this is called exponential smoothing is that each increment in the past is decreased by  {\ref (1-?)}.This method provides short term forecasts. The simplest formula is New forecast = Old forecast + ? (Latest Observation -Old Forecast)\par
Or more mathematically,F t = F t-1 + ? (A t-1 -F t-1 ).\par
(2) Where, Ft = The exponentially smoothed forecast for period t, F t-1 = The exponentially smoothed forecast made for the prior period, A t-1 = The actual demand in the prior period, ? = The desired response rate, or smoothing constant.\par
The value of smoothing constants ? varies from 0 to 1. The higher value of ? (i.e. the nearer to 1), the more sensitive the forecast becomes to current conditions, whereas the lower the value, the more stable the forecast will be, i.e. it will react less sensitively to current conditions. Here the value of alpha is taken as 0.3.Greater weight is given to more recent data. All past data are incorporated there is no cut-off point as with moving averages. Less data needs to be stored than with the longer period moving averages. Like moving averages it is an adaptive forecasting system. That is, it adapts continually as new data becomes available and so it is frequently incorporated as an integral part of stock control and production control systems. To cope with various problems (trend, seasonal factors, etc) the basic model needs to be modified. Whatever form of exponential smoothing is adopted, changes to the model to suit changing conditions can simply be made by altering the value of ?. The selection of the smoothing constant ? is done through trial-error by the researcher/analyst. It is done by testing several values of ? (within the range 0 to 1) and selecting one which gives a forecast with the least error (one can take standard error). It has been found that values in the range 0.1 to 0.3 provide a good starting point. 
\section[{c) Least Squares Method}]{c) Least Squares Method}\par
This is the mathematical method of obtaining the line of best fit between the dependent variable and an independent variable. In this, the sum of the square of the deviations of the various points from the line of best fit is minimum or least. (5)\par
These two equations are called normal equations. It is useful for long-term forecasting of major occurrences and aggregate planning. The major restriction in using linear forecasting is that past data and future projections are assumed to fall about a straight line. Although, this does limits its application. 
\section[{d) Evaluating the Forecast Accuracy}]{d) Evaluating the Forecast Accuracy}\par
There are many ways to measure forecast accuracy. Some of these measures are the mean absolute forecast error, called the MAD (Mean Absolute Deviation), the mean absolute percentage error (MAPE) and the mean square error (MSE). This error estimate helps in monitoring erratic demand observations. In addition, they also help to determine when the forecasting method is no longer tracking actual demand and it need to be reset. For this tracking signals are used to indicate any positive or negative bias in the forecast. The mean absolute deviation (MAD) is also important because of its simplicity and usefulness in obtaining tracking signals. MAD is the average error in the forecasts, using absolute values. It is valuable because MAD, like the standard deviation, measures the dispersion of some observed value from some expected value. The only difference is that like standard deviation, the errors are not squared. Standard error a square root of a function, it is often more convenient to use the function itself. This is called the mean square error (MSE) or variance. The mathematical formulas may be used while evaluating data are   
\section[{result analysis}]{result analysis}\par
In this study, we used the data for juice production for the period 2000-01 to 2010-2011. All the three methods are applied one by one and their performance evaluated in terms of MAD, MAPE and MSE.   
\section[{a) Moving Average Method}]{a) Moving Average Method} 
\section[{Discussion}]{Discussion}\par
Initially time series plot (Figure 1) was created to determine the trends in the juice production from 2003 to 2011, the graph shows an increasing trend in juice production during the study period and hence showed that the series was not stationary. It is very clear from the graph that the trend line of Least Square Average method flow on the actual trend line of juice production. The trend line of Simple exponential method is far away from the actual trend line. And finally the performance of the various methods evaluated on the basis of MAPE, MAD and MSE which is shown in the table 6. By comparing the performance of the methods, it was found that Least Square method have least value of MAPE (15.74\%), MAD (0.25) and MSE (0.09) and hence the results produced by the least square method have less error and more accurate than the other method. 
\section[{VI.}]{VI.} 
\section[{Conclusion}]{Conclusion}\par
Forecasting of juice production done by using statistical methods, (Moving Average method, Simple Exponential Method and Least Square Method). Statistical methods are chosen because for their rich historic data and ease of their use. Finally, their performance evaluated by comparing the MAPE, MAD and MSE obtained from the different methods. The results show that least Square method is more accurate than the other methods.\par
The forecasting technique may be different for different industries. It depends upon the variable factors like place, manpower skill, equipment capacity, raw material availability, inventory characteristics and management policies etc. Hence this work may be extended to other industries.\begin{figure}[htbp]
\noindent\textbf{4}\includegraphics[]{image-2.png}
\caption{\label{fig_0}4 )?}\end{figure}
   \begin{figure}[htbp]
\noindent\textbf{1} \par 
\begin{longtable}{P{0.10461538461538462\textwidth}P{0.2353846153846154\textwidth}P{0.51\textwidth}}
\tabcellsep \tabcellsep company\\
S. No.\tabcellsep Year\tabcellsep Production (in millions)\\
1\tabcellsep 2000-01\tabcellsep 16.6\\
2\tabcellsep 2001-02\tabcellsep 19.3\end{longtable} \par
 
\caption{\label{tab_1}Table 1 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{2} \par 
\begin{longtable}{P{0.18598848368522072\textwidth}P{0.030998080614203453\textwidth}P{0.5432821497120921\textwidth}P{0.07341650671785029\textwidth}P{0.003262955854126679\textwidth}P{0.013051823416506717\textwidth}}
\multicolumn{2}{l}{Technique}\tabcellsep \tabcellsep \multicolumn{2}{l}{Measures}\tabcellsep \\
\multicolumn{2}{l}{Mean Squared}\tabcellsep \multicolumn{4}{l}{The average of squared errors}\\
\multicolumn{2}{l}{Error (MSE)}\tabcellsep \tabcellsep \multicolumn{3}{l}{over the sample period}\\
\multicolumn{2}{l}{Mean Error (ME)}\tabcellsep \multicolumn{4}{l}{The average dollar amount or}\\
\tabcellsep \tabcellsep \multicolumn{4}{l}{percentage points by which}\\
\tabcellsep \tabcellsep \multicolumn{4}{l}{forecasts differ from outcomes}\\
\multicolumn{2}{l}{Mean Percentage}\tabcellsep \multicolumn{4}{l}{The average of percentage errors}\\
\multicolumn{2}{l}{Error (MPE)}\tabcellsep \multicolumn{4}{l}{by which forecasts differ from}\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{outcomes}\tabcellsep \\
Mean\tabcellsep Absolute\tabcellsep \multicolumn{4}{l}{The average of absolute dollar}\\
\multicolumn{2}{l}{Error (MAE)}\tabcellsep \multicolumn{4}{l}{amount or percentage points by}\\
\tabcellsep \tabcellsep \multicolumn{4}{l}{which a forecast differs from an}\\
\tabcellsep \tabcellsep \multicolumn{2}{l}{outcome}\tabcellsep \tabcellsep \\
Mean\tabcellsep Absolute\tabcellsep The\tabcellsep average\tabcellsep of\tabcellsep absolute\\
\multicolumn{2}{l}{Percentage Error}\tabcellsep \multicolumn{4}{l}{percentage amount by which}\\
(MAPE)\tabcellsep \tabcellsep \multicolumn{4}{l}{forecasts differ from outcomes}\\
\tabcellsep IV.\tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_2}Table 2 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{3} \par 
\begin{longtable}{P{0.14725557461406516\textwidth}P{0.12538593481989707\textwidth}P{0.10643224699828473\textwidth}P{0.07144082332761577\textwidth}P{0.055403087478559175\textwidth}P{0.0860205831903945\textwidth}P{0.1137221269296741\textwidth}P{0.14433962264150943\textwidth}}
\multicolumn{7}{l}{Application of Proper Forecasting Technique in Juice Production: A Case Study}\tabcellsep \\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Year 2013\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep XIII Issue v v v IV Version I\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep Volume\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep D D D D ) G\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep (\\
S. No. 1 2 3 4 5\tabcellsep Year 2000-01 2001-02 2002-03 2003-04 2004-05\tabcellsep Production (in millions) P 16.6 19.3 20.8 23.8 26.5\tabcellsep Forecast F 18.9 21.3\tabcellsep Error E 4.9 5.2\tabcellsep Squared Error E 2 24.01 27.04\tabcellsep Absolute Percentage Error (E/P)x 100 20.59 19.62\tabcellsep Global Journal of Researches in Engineering\\
6\tabcellsep 2005-06\tabcellsep 29\tabcellsep 23.7\tabcellsep 5.3\tabcellsep 28.09\tabcellsep 18.28\tabcellsep \\
7\tabcellsep 2006-07\tabcellsep 31.1\tabcellsep 26.43\tabcellsep 4.67\tabcellsep 21.78\tabcellsep 15.01\tabcellsep \\
8\tabcellsep 2007-08\tabcellsep 33.4\tabcellsep 28.87\tabcellsep 4.53\tabcellsep 20.55\tabcellsep 13.57\tabcellsep \\
9\tabcellsep 2008-09\tabcellsep 36.4\tabcellsep 31.17\tabcellsep 5.23\tabcellsep 27.39\tabcellsep 14.38\tabcellsep \\
10\tabcellsep 2009-10\tabcellsep 38.9\tabcellsep 33.63\tabcellsep 5.27\tabcellsep 27.74\tabcellsep 13.54\tabcellsep \\
11\tabcellsep 2010-11\tabcellsep 40.7\tabcellsep 36.23\tabcellsep 4.47\tabcellsep 19.95\tabcellsep 10.97\tabcellsep \end{longtable} \par
 
\caption{\label{tab_3}Table 3 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{4} \par 
\begin{longtable}{P{0.03565121412803532\textwidth}P{0.1519867549668874\textwidth}P{0.12571743929359824\textwidth}P{0.1501103752759382\textwidth}P{0.0956953642384106\textwidth}P{0.13322295805739515\textwidth}P{0.1576158940397351\textwidth}}
S. No.\tabcellsep Year\tabcellsep Production\tabcellsep Forecast\tabcellsep Error\tabcellsep Squared Error\tabcellsep Absolute\\
\tabcellsep \tabcellsep (in millions) P\tabcellsep F\tabcellsep E\tabcellsep E 2\tabcellsep Percentage Error\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep (E/P)x 100\\
1\tabcellsep 2000-01\tabcellsep 16.6\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
2\tabcellsep 2001-02\tabcellsep 19.3\tabcellsep 16.6\tabcellsep 2.7\tabcellsep 7.29\tabcellsep 13.99\\
3\tabcellsep 2002-03\tabcellsep 20.8\tabcellsep 16.87\tabcellsep 3.93\tabcellsep 15.44\tabcellsep 18.89\\
4\tabcellsep 2003-04\tabcellsep 23.8\tabcellsep 17.26\tabcellsep 6.54\tabcellsep 42.73\tabcellsep 27.47\\
5\tabcellsep 2004-05\tabcellsep 26.5\tabcellsep 17.92\tabcellsep 8.58\tabcellsep 73.67\tabcellsep 32.39\\
6\tabcellsep 2005-06\tabcellsep 29\tabcellsep 18.78\tabcellsep 10.22\tabcellsep 104.55\tabcellsep 35.26\\
7\tabcellsep 2006-07\tabcellsep 31.1\tabcellsep 19.80\tabcellsep 11.30\tabcellsep 127.75\tabcellsep 36.34\\
8\tabcellsep 2007-08\tabcellsep 33.4\tabcellsep 20.93\tabcellsep 12.47\tabcellsep 155.56\tabcellsep 37.34\\
9\tabcellsep 2008-09\tabcellsep 36.4\tabcellsep 22.17\tabcellsep 14.23\tabcellsep 202.35\tabcellsep 39.08\\
10\tabcellsep 2009-10\tabcellsep 38.9\tabcellsep 23.60\tabcellsep 15.30\tabcellsep 234.17\tabcellsep 39.34\\
11\tabcellsep 2010-11\tabcellsep 40.7\tabcellsep 25.13\tabcellsep 15.57\tabcellsep 242.50\tabcellsep 38.26\\
\tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{c) Least Square Method}\tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_4}Table 4 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{5} \par 
\begin{longtable}{P{0.070418410041841\textwidth}P{0.43246861924686186\textwidth}P{0.04765690376569038\textwidth}P{0.03414225941422594\textwidth}P{0.02845188284518828\textwidth}P{0.04481171548117154\textwidth}P{0.044100418410041836\textwidth}P{0.03556485355648535\textwidth}P{0.05619246861924686\textwidth}P{0.05619246861924686\textwidth}}
Year 2013\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
46\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
I\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
XIII Issue v v IV Version\tabcellsep X 1 2 3 4\tabcellsep Production (in millions) P 16.6 19.3 20.8 23.8\tabcellsep XP 16.6 38.6 62.4 95.2\tabcellsep X 2 1 4 9 16\tabcellsep P 2 275.56 372.49 432.64 566.44\tabcellsep Forecast F 16.52 18.98 21.43 23.88\tabcellsep Error E 0.08 0.32 0.63 0.08\tabcellsep Squared Error E 2 0.01 0.10 0.40 0.01\tabcellsep Absolute Percentage Error (E/P)x 100 0.48 1.69 2.94 0.34\\
Volume\tabcellsep 5 6 7\tabcellsep 26.5 29 31.1\tabcellsep 132.5 174 217.7\tabcellsep 25 36 49\tabcellsep 702.25 841 967.21\tabcellsep 26.33 28.78 31.23\tabcellsep 0.17 0.22 0.13\tabcellsep 0.03 0.05 0.02\tabcellsep 0.65 0.76 0.42\\
( D D D D ) G\tabcellsep 8 9\tabcellsep 33.4 36.4\tabcellsep 267.2 327.6\tabcellsep 64 81\tabcellsep 1115.56 1324.96\tabcellsep 33.69 36.14\tabcellsep 0.29 0.26\tabcellsep 0.08 0.07\tabcellsep 0.86 0.72\\
Global Journal of Researches in Engineering\tabcellsep \multicolumn{9}{l}{10 11 ?X=66 Mean X = 6 Therefore general equation for forecast is F = 14.07 + 2.45X 38.9 389 100 1513.21 38.59 40.7 447.7 121 1656.49 41.04 ?P=66 ?XP=66 ?X 2 =66 ?P 2 =66 ? F =66 Mean P = 28.77 a= 14.07 b= 2.45 0.31 0.34 ?E=2.83 ?E 2 =0.97 0.10 0.12 Forecast of juice production 23.8 26.5 29 31.1 33.4 36.4 38.9 40.7 18.9 21.3 23.7 26.43 28.87 31.17 33.63 36.23 17.26 17.92 18.78 19.8 20.93 22.17 23.6 25.13 23.88 26.33 28.78 31.23 33.69 36.14 41.04 38.59 actual production 0.80 0.83 ?=10.48 moning average method Production Millions simple exponential method}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Least square method}\\
\tabcellsep \tabcellsep \tabcellsep \tabcellsep \multicolumn{2}{l}{Production Year}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \\
\tabcellsep \multicolumn{2}{l}{© 2013 Global Journals Inc. (US)}\tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \tabcellsep \end{longtable} \par
 
\caption{\label{tab_5}Table 5 :}\end{figure}
 \begin{figure}[htbp]
\noindent\textbf{6} \par 
\begin{longtable}{P{0.3390710382513661\textwidth}P{0.16721311475409836\textwidth}P{0.19508196721311474\textwidth}P{0.14863387978142076\textwidth}}
\multicolumn{4}{l}{best forecasting method for juice production}\\
Measures\tabcellsep Moving\tabcellsep Simple\tabcellsep Least Square\\
of accuracy\tabcellsep Average\tabcellsep Exponential\tabcellsep Method\\
\tabcellsep Method\tabcellsep Method\tabcellsep \\
MAPE\tabcellsep 15.74 \%\tabcellsep 31.83 \%\tabcellsep 0.95\%\\
MAD\tabcellsep 4.95\tabcellsep 10.08\tabcellsep 0.25\\
MSE\tabcellsep 24.57\tabcellsep 120.60\tabcellsep 0.09\end{longtable} \par
 
\caption{\label{tab_6}Table 6 :}\end{figure}
 			\footnote{© 2013 Global Journals Inc. (US)} 		 		\backmatter  			 			 			  				\begin{bibitemlist}{1}
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\end{document}
