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MSCI 432 (10)
Lecture

Assignment #1 - Solution Winter 2010

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Department
Management Sciences
Course
MSCI 432
Professor
Binyamin Mantin
Semester
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
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