THE BUSINESS OF PRACTICE: STRATEGY IN ACTION


Table 1. Savings Provided by Holt-Winters Seasonal Method Over Average-Based Demand Forecasting for a Single Inventory Item During the 2015 Breeding Season


Demand Based on Average Consumption Over Last 4 Years


Demand forecast Quantity per order Purchase cost Holding cost Order cost


Total actual inventory cost PE from actual sales


Savings over average-based forecast EOQ, economic order quantity; PE, percent error.


sales data and therefore a number 1 should be en- tered for any quarter in which the sales data was zero. The spreadsheet will calculate the seasonal index for each quarter of data and will generate the corresponding level, trend and seasonal components based on the Holt-Winters Seasonal formula. Each smoothing equation will utilize a pre-populated ar- bitrary number for its respective smoothing param- eter , , and , which will be corrected during a process of optimization to follow. The resulting forecast for each of the 16 quarters of data will be compared with the actual sales data to determine the mean squared error of the difference between the forecast and the actual sale.


Optimizing the Formulas


The mean squared error (MSE) is a statistics for- mula that measures the average of the squares of the errors in the data and, in this case, presents the difference between the forecast and the actual sales data. The smaller the MSE, the more accurate the calculated forecast for the actual historical demand. Microsoft Excel has a data analysis tool called Solver that can minimize the value of an objective cell by changing the values of variable cells, which are subject to a constraint. The objective cell for our model is the calculated value of the MSE pro- vided by the analysis. The variable cells are the values of , , and  that the smoothing equations use in the calculations. The value of these smooth- ing parameters are constrained to individual values between 0 and 1. Optimization of the smoothing parameters will provide the smallest possible MSE and therefore help improve the accuracy of the forecast. The process of optimization has been enabled in a


macro embedded within the spreadsheet (after en- tering the sales data click the Optimize button) but the process is as follows: in your Excel program, install the Solver analysis tool under File-Options- Add ins and make Solver Add-in an active applica- tion. Find Solver under Data menu. Set Objective as the cell containing the mean squared error value. Set TO to minimize (you want to re- duce the value of the objective cell). Set the vari-


able cells, separated by a comma, as the cells containing the values for , , and . Add two constraints to each variable cell, one as “cell”  0, and another as “cell”  1 (sets each smoothing pa- rameter to be constrained at (0  value  1). Se- lect the Solving Method as “GRG Nonlinear.” Click on Options and then on the GRG Nonlinear Tab and check the Use Multistart box, click OK. Once re- turned to the Solver Parameters window click Solve. Once the optimization is calculated, select Keep Solver Solution in the Solver Results window, and click OK.


3. Results


The values for , , and tell each smoothing equa- tion how much weight to place on the different com- ponents of each equation for the process of exponential smoothing. Given that the forecast is based on the level, trend, and seasonality, optimiza- tion of the smoothing parameters leads to a more accurate forecast as Solver finds the values for , , and  that lead to minimization of the calculated MSE. The end result being a projected forecast for the next four quarters that has been optimized for accuracy through exponential smoothing that took into account the level, trend and seasonality of the previously observed data. Although MSE provides the statistics analysis to


help us improve accuracy in the forecast, the statis- tics of mean absolute percent error (MAPE) can be used as a more easily understandable measure of how well we are doing over time in our forecasting. A statistics measurement that compares the fore- cast to a perfect forecast, MAPE expresses accuracy in terms of percentage so that we can see, on aver- age, how far off the forecast has been. By entering into the spreadsheet the actual sales data for each quarter related to the forecasted period, the calcu- lator will compute the MAPE over time to give an indication of the level of accuracy achieved. This will allow the practitioner to evaluate the forecast in light of the qualitative aspects of the forecasting that statistics cannot foresee and therefore cannot compute.


AAEP PROCEEDINGS  Vol. 61  2015 543


42 cases 42 cases $2,713.94 $237.47 $10.00


$2,961.41 23.53%


Demand Based on Holt-Winters Seasonal Method


36 cases


8 cases (based on EOQ) $2,326.23 $45.12 $45.12


$2,416.47 5.88%


$544.94 (22.55%)


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