false

Class Notes
(835,507)

Canada
(509,212)

University of Waterloo
(18,569)

Management Sciences
(148)

MSCI 432
(10)

Binyamin Mantin
(10)

Lecture

Unlock Document

Management Sciences

MSCI 432

Binyamin Mantin

Fall

Description

MSCI 432: Production and Service Operations Management, Winter 2010
Assignment # 1 – solutions to qualitative questions
3. [3 marks] A major oil company is consideri ng 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 co sts 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
a) Find the value of k and a assuming a relationship of the form f(y) = ky . 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) 2 a = 1.68 => a ln(2) = ln(1.68) => a = .7485.
.7485
To find k substitute 6 = k(10,000) => 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 2.72.475ears
4. [20 marks] Shouldice Hospital Case Analysis
Question 1:
Pre-surgery
Patient examinations, Surgery Recovery Healthy
orientation, etc individual
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 Question 3 (Actual throughput rate):
Assume that there are no weekend (Saturday and Sunday) operations. Suppose the hospital admits
patients 30 patients per day on Sunday, Monday, Tuesday, Wednesday, and Thursday.
a) What is the weekly throughput rate of the hospital?
b) Draw a Gantt chart for the beds usage. What is the average bed utilization?
c) Use Little’s Law to calculate the average bed utilization.
Weekly throughput rate = 30 patients/day * 5 day/week = 150 patients / week
Gantt chart
Sun Mon Tue Wed Thu Fri Sat
Bed # 1-30
Bed #31-60
Bed #61-90
Bed utilization = 71.4%
By Little’s Law:
Throughput rate R = 150 patients/week
Flow time T = 3 days
By Little’s Law:
Average inventory I = R x T = (150 patients/week) * (3 / 7 week) = 450/7 patients
Bed utilization = (450 / 7) / 90 = 71.4%
Question 4 (Increasing throughput rate):
The vice-president of the hospital wants to increase the throughput rate of the hospital. He has a target
of increasing the throughput rate by 20% (as compared to the throughput rate of Q3). One option to
increase throughput is to add Saturday operations (i.e., admit 30 patients on Friday).
a) Draw a Gantt chart for the beds usage. What is the average bed utilization?
b) Use Little’s Law to calculate the average bed utilization.
c) Do any surgeons have to work 6 days per week or can all surgeons still work 5 days per week?
Please develop a Gantt chart for surgeons.
Gantt Chart
Sun Mon Tue Wed Thu Fri Sat
Bed # 1-30

More
Less
Related notes for MSCI 432

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

Continue

Continue
OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.