Among other services and products that Karl\'s Copiers provides, it sells and re

Question

Among other services and products that Karl's Copiers provides, it sells and repairs photocopy machines. It is now the end of December, 2014 and the manager needs to plan his service staffing for January, 2015. The manager first needs to forecast the number of service calls for January, 2015. Following are the record of service calls for the past 12 months. Month Number of Service Calls Month Number of Service Calls January 30 July 31 February 24 August 38 March 27 September 37 April 31 October 36 May 37 November 32 June 34 December 29 You have been asked by the manager to help with the forecast for January, 2015. He has asked you to provide forecasts for January using the following three methods: Moving Average Weighted Moving Average Exponential Smoothing He has also asked you to determine which of these three forecasts he should select. To make this assessment, he has asked that you compare the actual number of service calls to what the forecasts would have been for September through December, 2014 using each of the three methods. i) For the moving average, use a three month moving average. ii) For the weighted moving average, use a two-period weighted average with a weight of 0.70 for the most recent month and the remaining weight(s) consistent with this forecasting method as we applied it. iii) For exponential smoothing, use an ? = 0.25, and using a starting forecast for July, 2014 of 33. a) Prepare a forecast for January, 2015 using each of the three methods. b) Recommend which of these three methods the manager should use for January, 2015 based on the results of evaluation of the forecasts for September through December. Your selection criteria must be based on one of the numerical evaluation methods we have learned and used this semester. Only saying it is the easier method is not acceptable.

Explanation / Answer

(i) 3 month moving average = total of last 3 months service calls/3. forecast for september = sum of calls of (june+july+august)/3

(ii) 2 period moving average. Weight for the most recent month = 0.70. weigh for the period before it will be: 1-0.70 = 0.30

Forecast for september = (0.70*august service calls + 0.30*july service calls) = 0.7*28+0.3*31 = 28.9

(iii) alpha = 0.25. forecast for July = 33. Forecast for august = forecast for July+alpha*(actual value of July - forecast for July) = 33+0.25*(31-33) = 32.5

a. Forecast for Januray 2015 under 3 month moving average = sum of calls of (october+november+december)/3 = 36+32+29/3 = 97/3 = 32.33

Forecast for January 2015 under 2 period weighted moving average = 0.7*calls of december + 0.30*calls of november = 0.7*29+0.3*32 = 29.90

Forecast for January 2015 under exponential smoothing = forecast for december+0.25*(actual value of december - forecast for december) = 33.19+0.25*(29 - 33.19) = 32.14

b. To determine which method is best (based on september to december forecasts) i will use mean square error or MSE. MSE = sum of (actual value - forecast value)^2

The technique with the lowest MSE should be selected.

MSE is the lowest for exponential smoothing forecast and hence this method should be used for January 2015 forecast.

Month Service calls 3 month moving total 3 month moving average January 30 February 24 March 27 April 31 May 37 June 34 July 31 August 28 September 37 93 31.00 October 36 96 32.00 November 32 101 33.67 December 29 105 35.00

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