Karl\'s Copiers sells and repairs photocopy machines in Seattle. The manager nee

ID: 468136 • Letter: K

Question

Karl's Copiers sells and repairs photocopy machines in Seattle. The manager needs weekly forecasts of service calls so that he can schedule service personnel. Use the actual demand in the first period for the forecast for the first week so error measurement begins in the second week. The manager uses exponential smoothing with =0.3. Forecast the number of calls for week 6, which is next week.

The forecast for week 6 is ____ service calls. (Enter your response rounded to two decimal places.)

Week Actual Service Calls 1 28 2 32 3 36 4 25 5 30

Explanation / Answer

Exponential smoothing method

In exponential smoothing method, the new forecast is based on the previous forecast, plus a percentage of the difference between that forecast and the actual forecast of the series at that point.

Next forecast = Previous forecast + (Actual Previous forecast)

The equation is:

Ft = Ft-1 + (At-1 Ft-1)

Ft = Ft-1 + At-1 Ft-1

Ft = At-1 + (1 – )Ft-1

Where,

Ft = Forecast for time period t

Ft1 = Forecast for time period t1

At1 = Actual value in period (t1)

= Smoothing constant (percentage)

Let the forecast of first period be equal to actual service calls of same week 1.

Forecast for the period t by exponential smoothing method ( = 0.3)

Ft = 0.3At-1 + (1 – 0.3)Ft-1 = 0.3At-1 + 0.7Ft-1

Week

Actual Service Calls

Forecast

( = 0.3)

Ft = 0.3At-1 + 0.7Ft-1

28.00

29.20

31.24

29.37

29.56

For week 6,

= 0.3, 1 = 0.7

A5 = 30 and F5 = 29.37

F6 = 0.3A5 + 0.7F5 = 0.3 × 30 + 0.7 × 29.37 = 29.56

F6 = 29.56

The forecast for week 6 is 29.56 service calls