Question

The actual demand for the patients at Omaha Emergency Medical Clinic for the first six weeks of this       year are as follows:

Week                   Actual # of Patients

65

66

70

58

63

54

Compute a simple exponential smoothing forecast for week 7 with ?=.5.   Assume the forecast for week 1 is 65.

b)Compute MAPE.

c)What is the interpretation of your answer in part b)?

Answer 1

alpha for forecast (a) = 0.5

week 1 forecast = 65

week 1 actual demand = 65

week 2 exponential smoothin forecast = 65*0.5 + 65*(1-0.5)

= 32.5 + 32.5

=65

week 2 forecast = 65

Week 3 forecast = 65*0.5 + 66*(1-0.5)

= 32.5 + 33

= 65.5

similarly we calculate the forecast for all the weeks. The result is shown below in table:

Week	Actual patients	Forecast
1	65	65
2	66	65
3	70	65.5
4	58	67.75
5	63	62.88
6	54	62.94
7		58.47

Week 7 forecast = 62.94*0.5 + 54*(1-0.5)

= 58.47

b) MAPE = mean abbsolute percentage error

1st we take the difference of actual demand with forecast :

week 1 = actual demand - forecast

= 65 - 65

=0

week 2 = 66 - 65 = 1

week 3 = 70 - 65.5 = 4.5

week 4= 58 - 67.75 = -9.75

week 5 = 63 - 62.88 = 0.12

week 6 = 54 - 62.94 = -8.94

now, we ignore the -negative sign since we want absolute error.

Then we divide each difference by actual demand:

week 1 = 0/65 = 0

week 2 = 1/66 = 0.015

week 3 = 4.5/70 = 0.064

week 4 = 9.75/58 = 0.168

week 5 = 0.12/63 = 0.002

week 6 = 8.94/54 = 0.166

adding all: 0 + 0.015 + 0.064 + 0.168 + 0.002 + 0.166 = 0.414

diving the sum by total no. of weeks = 6

0.414/6 = 0.069

this is the mean absolute error percentage, we multiply it by 100 to represent it in terms of percentage = 0.069*100 = 6.9%

MAPE = 6.9%

c) the MAPE is 6.9% which means the mean error between the forecast and actual demand for 6 weeks is 6.9%.