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Demand Forecasting for Lean Supply Chain

Faculty Contributor: Janat Shah, Professor
Student Contributors: Pawan Aseri, Kartik Varadpande

Correct estimation of future sales is an important challenge for a company. Better forecasting not only reduces the inventory and holding cost of the firm but also helps in maintaining a lean and efficient supply chain. Employing Grid Search technique to calculate the smoothing parameters in the forecast model used by a leading Paints company in India shows an improvement in the seasonal sales forecast by 18%. Companies can further modify this model and use it in a variety of demand forecasting situations.
<p>Forecasting is the art and science of estimating business parameters in an unknown scenario. It is used in many business applications, ranging from capacity planning at emergency medical treatment in intensive care units, to tracking enemy moves in military command and control systems. Managers use forecasting tools extensively to arrive at the most likely future scenarios. The objective of this article is to discuss ways developed by the authors to reduce the forecasting error for a leading paint manufacturing company in India. The company was earlier using its own forecasting tool to arrive at a sales forecast of its SKUs (Stock Keeping Units).</p> <h2> Description of the Earlier Model</h2> <h3> Need for Forecasting</h3> <p>A paints company derives its competitive advantage from a lean and responsive supply chain. It is essential for the company to maintain high service levels, while maintaining inventory as low as possible. The finished goods inventory acts as a buffer against unpredictable variations in demand faced by the company s dealers and the end-consumers. The company regularly forecasts the demand expected in the coming months. These forecasts are used for planning its sales and distribution.</p> <h3> Winter s Model</h3> <p>Since the demand for paints varies in yearly cycles, the company used Winter s model<sup>1</sup> (also called as Holt-Winter s model) of forecasting, which is a decomposition model. The forecast is  decomposed into level, trend and seasonality components, and then smoothened individually. The model uses three parameters ,  and  for smoothing the three components. Further, the seasonality component can be built in two ways  additive or multiplicative<sup>2</sup>.</p> <p>The forecasting tool arrives at the values of ,  and  parameters for a given combination of SKUs and depots in order to minimize the observed error, assuming that the same set of parameters can give reasonably accurate forecasts for the future. As the forecast depends on these parameters, it is important to calculate suitable values for them and the sensitivity of the forecast to these values. On a given data set, values of these parameters are varied on an incremental basis, thus producing a different forecast for each set of values. The best forecast chosen is the one which gives the minimum error when compared with reference data points.</p> <h3> Error Measurement</h3> <p>Error can be calculated in various ways<sup>3</sup>: Mean Absolute Deviation (MAD), Mean Absolute Percentage Error (MAPE) and Mean Square Error (MSE) are some of the more commonly used measures<sup>3</sup>. The choice of this measurement depends on the objective of the analysis. In the case of the Paints company, since different SKUs have different sales volumes, percentage error (MAPE) was chosen to keep all SKUs at par. MAPE also needed to be smoothened as it could then consider all the data points, while giving more weightage to the recent ones.</p> <img width="540" src="images/11-01.gif"/> <span class="caption"> <em>Exhibit 1.</em> Relative weightage given in smoothening MAPE with different coefficients ('s = 0.05, 0.10 and 0.1538) </span> <p>Exhibit 1 shows the importance given to MAPEs for 24 months before a given month during the calculation of smoothened MAPE (which is to be minimised). Given the background of the problem, it is important to understand how the error (measured as smoothened MAPE) can be reduced.</p> <h2> Reducing Error in Forecast</h2> <h3> Grid Search</h3> <p>Modern statistical packages like SPSS give an option of varying the parameters (,  and ) in an incremental fashion in a given range (known as the grid search technique) to obtain the forecast with minimum error.</p> <p>The company was using a statistical demand planner tool for obtaining the forecast through Winter s model. The main drawback of the configuration was that instead of using a grid search technique for calculating the values of variable parameters to arrive at the forecast, it was using fixed values of these parameters in a limited range with  and  being a function of . These sets of fixed values are shown in Exhibit 2.</p> <table cellpadding="0" cellspacing="0" class="center-columns"> <tr> <th width="80">Model no.</th> <th width="190">Type of seasonality</th> <th width="90"></th> <th width="90"></th> <th width="90"></th> </tr> <tr><td>1</td><td>Additive</td><td>0.10</td><td>0.050</td><td>0.30</td></tr> <tr><td>2</td><td>Additive</td><td>0.15</td><td>0.075</td><td>0.35</td></tr> <tr><td>3</td><td>Additive</td><td>0.20</td><td>0.100</td><td>0.40</td></tr> <tr><td>4</td><td>Additive</td><td>0.25</td><td>0.125</td><td>0.45</td></tr> <tr><td>5</td><td>Additive</td><td>0.30</td><td>0.150</td><td>0.50</td></tr> <tr><td>6</td><td>Multiplicative</td><td>0.10</td><td>0.050</td><td>0.30</td></tr> <tr><td>7</td><td>Multiplicative</td><td>0.15</td><td>0.075</td><td>0.35</td></tr> <tr><td>8</td><td>Multiplicative</td><td>0.20</td><td>0.100</td><td>0.40</td></tr> <tr><td>9</td><td>Multiplicative</td><td>0.25</td><td>0.125</td><td>0.45</td></tr> <tr><td>10</td><td>Multiplicative</td><td>0.30</td><td>0.150</td><td>0.50</td></tr> </table> <span class="caption"> <em>Exhibit 2.</em> Set of parameters in Winter s model used by the company </span> <p>When the grid search technique was applied i.e. the parameters ,  and  were varied from 0 to 1 with suitable increment, the sample data set of 25 data points showed an improvement in forecast error by 18.5 percentage points. The underlying logic was to remove the interdependence of the parameters (,  and ) and to provide a wider range of variation. In the authors view, these limitations put on the basic model were uncalled for. The results are shown in Exhibit 3.</p> <table cellpadding="0" cellspacing="0" class="center-columns"> <tr> <td class="th" width="195"> &nbsp; </td> <td class="th" width="115"> Forecast error from Company s tool (1) </td> <td class="th" width="115"> Forecast error from Grid Search (2) </td> <td class="th" width="115"> Improvement (1)-(2) </td> </tr> <tr><td class="th" colspan="4"> All 25 datasets used</td></tr> <tr><td> Average MAPE (%) </td><td> 50.8 </td><td> 32.3 </td><td> 18.5</td></tr> <tr><td> Std. dev. of % MAPE </td><td> 37.0 </td><td> 22.4 </td><td> 18.6</td></tr> <tr><td class="th" colspan="4"> After eliminating top and bottom 3 deviations</td></tr> <tr><td> Average MAPE (%) </td><td> 44.1 </td><td> 28.2 </td><td> 15.9</td></tr> <tr><td> Std. dev. of % MAPE </td><td> 22.0 </td><td> 14.5 </td><td> 13.0</td></tr> <tr><td colspan="4"> <em>Note: Period Of MAPE Calculation was 24 months</em></td></tr> </table> <span class="caption"> <em>Exhibit 3.</em> Improvement in Forecast Error using Grid Search </span> <p>In grid search, as increments for variation in the parameters were reduced, the forecast became refined at the cost of increase in calculation steps. It was interesting to note that the sensitivity of error to each of the parameters was different. By far the forecasts were most sensitive to change in level (), then seasonality () and least to trend (). This sensitivity analysis helped in identifying the minimum amount of increment in each parameter to be used for obtaining forecast through the grid search technique.</p> <p>The sales pattern often showed sudden unexplained deviation from the regular pattern. Incorporating such unexplained data points could corrupt the future forecasts so it was necessary to eliminate such errors. The filtering of such data points helped us to eliminate the errors in the forecast due to these unexplained sales. Exhibit 4 shows one such instance where sudden peaks in sales were noticeable and were filtered out (adjusted actual sales).</p> <img width="540" src="images/11-02.gif"/> <span class="caption"> <em>Exhibit 4.</em> Limiting unexplained variation </span> <h3> Further Forecast Improvements</h3> <p>While grid search is the most prominent way of reducing the forecast error, the model could be improved further in different ways such as limiting unexplained variation, removing festival effect and removing the effect of one-time promotions, etc.</p> <p>There was variation in sales of certain SKUs because of the festival season. It was observed that the sales increased two months prior to the Diwali festival. The seasonality component of the model is supposed to capture this behaviour. However, the Hindu calendar does not remain the same across years hence the forecast has to be adjusted for incorporating the effect of festival seasons. Although an attempt was made to adjust the forecast for festival effects, since the effect kept on changing for different SKUs across geographies it was unsuitable for application on every SKU sales data.</p> <p>Many times national and local marketing promotions are run. One can either ignore them saying that they will be averaged out over time or use the data on promotions and sales figures to arrive at an unbiased forecast demand. For the purpose of capturing the promotional effects on the sales it was necessary to decompose the input sales into two components: <em>sales under normal condition</em> and <em>incremental sales under promotion</em> and find the corresponding forecast. Data sets for at least 6-7 years were required to study the effect of promotion on sales. These were unavailable. Hence it was suggested that the company maintain longer period of data in their forecasting tool.</p> <p>Another factor which needs to be considered for accurate forecast is capturing the effect of unusual occurrences. For e.g. due to fear of rise in oil prices in 2008, the demand for the product spiked in the period May-July 2008 (with the acknowledgement that these sales were coming at the cost of future sales). So, when these occurrences happen, it is useful to filter out the deviations from the data points in the forecast and also adjust the future forecast in accordance with their effect on future sales.</p> <p>All these seemingly unconnected yet simple additions have a single common thread: use of relevant data in the mathematical model of forecasting to arrive at an unbiased estimate of future demand. A further step in mathematical analysis can be mining useful patterns out of transactions data of sales and distribution.</p> <h2> Conclusion</h2> <p>The article shows a strong need to periodically review the relevance of analytical tools used by any organization. For an executive, forecasting tools are like a black box, where the focus is more on obtaining the final forecast values rather than analyzing how the forecast is calculated. But, focusing on the methodology of the forecasting tool is as important as the forecast itself. For a paints company using made-to-stock configurations, better forecasting techniques can provide a competitive advantage vis a vis its peers. In our case, implementing grid-search technique in Winter s model improved the forecasting accuracy by 18%, which in turn can enhance the bottom line for the firm. The article elaborates how a tool based on outdated methods and assumptions, used without sufficient understanding of the underlying forecasting model, can cause competitive disadvantage to the firm, and how a periodic review, and up to date methodology can help regain the advantage.</p> <h4> Authors</h4> <p><strong>Janat Shah </strong> is the Head of Supply Chain Management Centre and a faculty in the Production and Operations Management Area at IIM Bangalore. He is a Fellow of IIM Ahmedabad and holds a B. Tech. in Mechanical Engineering from IIT Bombay. He can be reached at <a href="mailto:jjanat@iimb.ernet">inanat@iimb.ernet.in</a> </p> <p><strong>Kartik Varadpande </strong> is a second year PGP student at IIM Bangalore. He holds a B. Tech. in Industrial Engineering from IIT Kharagpur. He can be reached at <a href="mailto:kartikv07@iimb.ernet.in">kartikv07@iimb.ernet.in</a></p> <p><strong>Pawan Aseri </strong> is a second year PGP student at IIM Bangalore. He holds a B. E. in Electrical Engineering from MNIT Jaipur. He can be reached at <a href="mailto:pawana07@iimb.ernet.in">pawana07@iimb.ernet.in</a></p> <h4>Keywords</h4> <p> Operations, Demand Forecasting, Lean Supply Chain, Paints, Grid Search, Winter's Model </p> <h4> References</h4> <ol> <li> Hanke, John E. and Reitsch, Arthur G., 1991, 'Time Series and Their Components', <i> Business Forecasting (4th ed.) </i>, Allyn &amp; Bacen publication, pp 143-192</li> <li> ibid.</li> <li> Makridakis, Spyros G. and Hyndman, Rob J., 1980,  Exponential Smoothing Methods in <i> Forecasting: Methods &amp; Application (3rd ed.) </i>, John Wiley &amp; Sons publication, pp 135-184</li> </ol>
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