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**preview**shows page 1. to view the full**4 pages of the document.**MSCI 432: Production and Service Operations Management, Winter 2010

Assignment # 1 – solutions to qualitative questions

3. [3 marks] A major oil company is considering the optimal timing for the construction of new

refineries. From the past experience, each doubling of the size of a refinery at a single location results in

an increase in the construction costs of about 68%. Furthermore, a plant size of 10,000 barrels per day

costs $6 million. Assume that the demand for the oil is increasing at a rate of 2 million barrels yearly

and the discount rate for the future costs is 15 percent.

a) Find the value of k and a assuming a relationship of the form f(y) = kya. Assume that y is in units of

barrels per day.

b) Determine the optimal timing of the plant additions and the optimal size of each plant.

c) Suppose that the largest single refinery that can be built with current technology is 15000 barrels per

day. Determine the optimal timing of plant additions and the optimal size of each plant in this case. (

Year = 365 days)

1. a) 2a = 1.68 => a ln(2) = ln(1.68) => a = .7485.

To find k substitute 6 = k(10,000).7485 => k = .0061

b) Locating a = .7485 on Figure 1.14 gives a value of u of approximately 0.67. Solving: x =

u/r = .67/.15 = 4.47 years.

The optimal size of each new addition is (4.47)(2) = 8.94 million barrels (per year).

c) [(15,000)/day][365 days/year] = 5,475,000. The optimal plant size = min [5.475 million,

8.94 million] = 5.475 million barrels per year.

In this case, plants need to be added every 2.7375 years

4. [20 marks] Shouldice Hospital Case Analysis

Question 1:

What are the resources needed for each of the above task?

Stage1: bed, examination rooms, nurses, dining rooms

Stage2: surgeon, operating room

Stage3: bed, recovery room, dining room, recreation facilities

Question 2 (Bottleneck analysis):

What is the bottleneck of the Shouldice Hospital, and what is the weekly capacity rate of the hospital?

Surgeons’ capacity: 12 x 4 = 48 patients / day

Operating rooms (OR)’ capacity: 8 x 5 = 40 patients / day

Beds’ capacity: 90 / 3 = 30 patients / day

Beds are the bottleneck.

Hospital Capacity = 30 patients / day or 210 patients / week

5.475

2

Pre-surgery

examinations,

orientation, etc

Surgery

Recovery

Patient Healthy

individual

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