Global Supply Chains-Problem Set Time Series Forecasting

Problem Set #1: Time Series Forecasting

Penguin Images Services is a US-based healthcare service provider, specializing in state-of-the-art medical imaging. The imaging services they offer include MRI, MR Angiography (MRA), CT Scan, 3D Imaging, X-ray and Ultrasound. Their business model is based on low cost but responsive service. They attempt to achieve this goal by maintaining a group of radiologists who are paid to evaluate images and to be available during various periods when services are expected. That is, when on duty, each radiologist is paid a minimum amount even when service is not required. Labor costs are minimized by hiring radiologists located in certain high quality but lower cost locations, mainly India.

The effectiveness of Penguin’s service is affected a great deal by their ability to forecast demand. Penguin does not require that patients make an appointment, because most patients were referred by their physician. These patients necessitated service on short notice.

Penguin’s location in Bainston, Rhode Island, is opened for customers Monday through Friday (0800-1700) and Saturday (0800-1200). At this location, a short-term increase in demand for MRI image evaluation has occurred. This growth was caused by the closing of the other major imaging service provider in Bainston. The increase in demand is expected to continue over the next several weeks. Historical demand (number of images by day) is shown below and included on the accompanying Excel file:

Create an Excel spreadsheet that fits a time series model (with level, linear trend, and seasonal components) for purposes of forecasting daily demand at Penguin. Include calculations necessary to determine forecast margin of uncertainty. Assume that forecast errors are normally distributed.

Use your time series model to forecast future daily demand for the next three weeks (April 9-28), including a margin of uncertainty for each day’s forecast. Include a graph that shows information regarding the forecast.

The assessment of your work will include the accuracy as well as the clarity of the spreadsheet and graph (e.g., clear labels, good alignment, easy to understand, etc.).

Attach one Excel file, using a file name Lastname_PS1.

Date Day Images

5-Mar Monday 29

6-Mar Tuesday 36

7-Mar Wednesday 46

8-Mar Thursday 39

9-Mar Friday 32

10-Mar Saturday 27

12-Mar Monday 35

13-Mar Tuesday 40

14-Mar Wednesday 56

15-Mar Thursday 47

16-Mar Friday 41

17-Mar Saturday 34

19-Mar Monday 44

20-Mar Tuesday 53

21-Mar Wednesday 73

22-Mar Thursday 61

23-Mar Friday 59

24-Mar Saturday 46

26-Mar Monday 61

27-Mar Tuesday 73

28-Mar Wednesday 96

29-Mar Thursday 84

30-Mar Friday 79

31-Mar Saturday 61

2-Apr Monday 80

3-Apr Tuesday 96

4-Apr Wednesday 129

5-Apr Thursday 111

6-Apr Friday 102

7-Apr Saturday 81

0

20

40

60

80

100

120

140

M o

n 0

3 /0

5

T u

e 0

3 /0

6

W ed

0 3

/0 7

T h

u 0

3 /0

8

Fr i 0

3/ 09

Sa t

0 3

/1 0

M o

n 0

3 /1

2

T u

e 0

3 /1

3

W ed

0 3

/1 4

T h

u 0

3 /1

5

Fr i 0

3/ 16

Sa t

0 3

/1 7

M o

n 0

3 /1

9

T u

e 0

3 /2

0

W ed

0 3

/2 1

T h

u 0

3 /2

2

Fr i 0

3/ 23

Sa t

0 3

/2 4

M o

n 0

3 /2

6

T u

e 0

3 /2

7

W ed

0 3

/2 8

T h

u 0

3 /2

9

Fr i 0

3/ 30

Sa t

0 3

/3 1

M o

n 0

4 /0

2

T u

e 0

4 /0

3

W ed

0 4

/0 4

T h

u 0

4 /0

5

Fr i 0

4/ 06

Sa t

0 4

/0 7

N um

b er

Demand for Images (March 5 through April 7)