Question

Problem 3

Hospitality Hotels forecasts monthly labor needs.

(a) Given the following monthly labor figures, make a forecast for June using a three-period moving average and a five-period moving average. (Round answers to 2 decimal places, e.g. 15.25.)

Month		Actual Values
January		33
February		45
March		44
April		41
May		44

3-Period Moving Average
5-Period Moving Average

(b) What would be the forecast for June using the naïve method? (Round answers to 2 decimal places, e.g. 15.25.)

Forecast for June

(c) If the actual labor figure for June turns out to be 45, what would be the forecast for July using each of these models? (Round answers to 2 decimal places, e.g. 15.25.)

3-Period Moving Average
5-Period Moving Average
Naïve method

(d) Compare the accuracy of these models using the mean absolute deviation (MAD). (Round answers to 2 decimal places, e.g. 15.25.)

MAD (3-period)
MAD (5-period)
MAD (naïve)

(e) Compare the accuracy of these models using the mean squared error (MSE). (Round answers to 2 decimal places, e.g. 15.25.)

MSE (3-period)
MSE (5-period)
MSE (naïve)

Answer 1

a)

Three year moving Average

period	demand
t	Dt
1	33
2	45
3	44
4	41
5	44

3-Period Moving Average =(44+41+44)/3 = 43.00   
5-Period Moving Average=(33+45+44+41+44)/5 = 41.40

b)

Forecast for June using Naive method = 44

c)

3-Period Moving Average = 43.33
5-Period Moving Average = 43.80
Naïve method = 45

d)

MAD (3-period) = Σ |et|/n = 1.00
MAD(5-period) = 3.60

MAD (naïve) = Σ |et|/n = 4.00

e)

MSE (3-period) = Σ(et)²/n = 1.52
  
MSE (5-period) = 12.96   
MSE (naïve)= Σ(et)²/n = 32.80