Question

In: Operations Management

The actual demand for the patients at Omaha Emergency Medical Clinic for the first six weeks...

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)?

Expert Solution

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%.

keosha answered 8 months ago

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