Question

Forecasting: Measuring Forecast Accuracy

Tires for You, Inc. (TFY), founded in 1987, is an automotive repair shop specializing in replacement tires. Located in Altoona, Pennsylvania, TFY has grown successfully over the past few years because of the addition of a new general manager, Ian Overbaugh. Since tire replacement is a major portion of TFY’s business (it also performs oil changes, small mechanical repairs, etc.), Ian was surprised at the lack of forecasts for tire consumption for the company. His senior mechanic, Skip Grenoble, told him that they usually stocked for this year what they sold last year. He readily admitted that several times throughout the season, stockouts occurred and customers had to go elsewhere for tires. Although many tire replacements were for defective of destroyed tires, most tires were installed on cars whose original tires had worn out. Most often, four tires were installed at the same time. Ian was determined to get a better idea of how many tires to hold in stock during the various months of the year. Listed below is a summary of individual tire sales by month.

Period 2010 October November December 2011 January February March April May June July August September October November December Tires Used 9,800 11,000 11,000 9,700 8,800 9,300 10,700 9,300 8,700 10,200 10,800 9,700 10,200 11,600 11,100

Ian has hired you to determine the best technique for forecasting TFY demand based on given data.

1. Calculate forecasts for August, 2011 through December 2011 using a simple four-month moving average. Round your answers to the whole number.

Period 2011 August September October November December Forecasts

2. Calculate forecasts for August, 2011 through December 2011 using the exponential smoothing method with α = 0.4. Assume the forecast for August, 2011 is 11,000. Round your answers to the whole number.

Period 2011 August September October November December Forecasts 11,000

3. Calculate the forecast errors, the MAD, the MSE, and the MAPE for the forecasts you made in Question 1. Use the actual sales data for 2011. Round your answers to the whole number.

Period August September October Actual Sales 10,800 9,700 10,200 Forecasts Errors Absolute Error Error2 Absolute % Error November 11,600 December 11,100 MAD= MSE= MAPE= 2

4. Calculate the forecast errors, MAD, MSE, and MAPE for the forecasts you made in Question 2. Use the actual sales data for 2011 given below. Round your answers to the whole number.

Period August September October Actual Sales Forecasts 10,800 11,000 9,700 Errors Absolute Error Error2 Absolute % Error 10,200 November 11,600 December 11,100 MAD= MSE= MAPE=

5. Based on the two methods used to calculate forecasts for TFY, which method produced the best forecast? The moving average method or the exponential smoothing method?

Answer 1

Four-month moving average

Data			Forecasts and Error Analysis
Period	Demand		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	9800
Period 2	11000
Period 3	11000
Period 4	9700
Period 5	8800		10375	-1575	1575	2480625	17.90%
Period 6	9300		10125	-825	825	680625	08.87%
Period 7	10700		9700	1000	1000	1000000	09.35%
Period 8	9300		9625	-325	325	105625	03.49%
Period 9	8700		9525	-825	825	680625	09.48%
Period 10	10200		9500	700	700	490000	06.86%
Period 11	10800		9725	1075	1075	1155625	09.95%
Period 12	9700		9750	-50	50	2500	00.52%
Period 13	10200		9850	350	350	122500	03.43%
Period 14	11600		10225	1375	1375	1890625	11.85%
Period 15	11100		10575	525	525	275625	04.73%
			Total	1425	8625	8884375	86.44%
			Average	130	784	807670	08%
				Bias	MAD	MSE	MAPE
					SE	993.55562
Next period	10650

Exponential smoothing method with α = 0.4

Data			Forecasts and Error Analysis
Period	Demand		Forecast	Error	Absolute	Squared	Abs Pct Err
Period 1	9800		9800	0	0	0	00.00%
Period 2	11000		9800	1200	1200	1440000	10.91%
Period 3	11000		10280	720	720	518400	06.55%
Period 4	9700		10568	-868	868	753424	08.95%
Period 5	8800		10220.8	-1420.8	1420.8	2018672.6	16.15%
Period 6	9300		9652.48	-352.48	352.48	124242.15	03.79%
Period 7	10700		9511.488	1188.512	1188.512	1412560.8	11.11%
Period 8	9300		9986.893	-686.893	686.8928	471821.72	07.39%
Period 9	8700		9712.136	-1012.14	1012.136	1024418.6	11.63%
Period 10	10200		9307.281	892.7186	892.7186	796946.48	08.75%
Period 11	10800		9664.369	1135.631	1135.631	1289658.1	10.52%
Period 12	9700		10118.62	-418.621	418.6213	175243.8	04.32%
Period 13	10200		9951.173	248.8272	248.8272	61914.983	02.44%
Period 14	11600		10050.7	1549.296	1549.296	2400319.1	13.36%
Period 15	11100		10670.42	429.5778	429.5778	184537.08	0.0387007
			Total	2605.633	12123.49	12672160	119.71%
			Average	174	808	844811	08%
				Bias	MAD	MSE	MAPE
					SE	987.31024
Next period	10842