Problem 1
The product development group at SJJC Corporation has been working on a new bio-plastic product that has the potential to capture a large market share. Through outside sources, SJJC’s management learned that a competitor is working to introduce a similar product. As a result, SJJC’s
top management increased it pressure on the product development group. The group’s leader turned to PERT/CPM as an aid to scheduling the activities remaining before the new product can be brought to the market. The relationship between activities and the activity time estimates (in
weeks) are given as follows:
Activity Immediate Predecessor Activities Optimistic Time Most Likely Time Pessimistic Time
A -- 4 5 6
B -- 4 4.5 8
C B 3 5 7
D A,C 3 4 8
E B,C 5 5 14
F B,D 5 6 7
G E 4.5 6.5 8.5
H D,G 5 6 13
I D,G 3 5 8.5
J H 2 5 8
a. Compute the expected time and variance for each activity. (5 points)
b. Draw the PERT/CPM network for this project and determine the critical path and the
expected duration of the project. (12 points)
c. What is the probability that the project will be completed so that the SJJC Corporation may
introduce the new product within 32 weeks? Within 37 weeks? (5 points)
d. Top management would like to complete certain set of a tasks earlier to be able to test the
quality and begin advertising for the product few weeks prior to releasing in the market. Compare
the risk of overrunning a new deadline of 22 weeks for paths B-E-G-I and A-D-H-J? (8 points)
Problem 2
MATWORKS manufactures computer software. They developed a prototype of a new object-
oriented programming language. According to their preliminary marketing and financial analysis,
following parameters are determined with certainty:
Selling price= $2000 /license
Administrative cost= $ 500,000
Advertising cost= $700,000
The cost of software engineer follows a normal distribution with the mean $45 per hour and the
standard deviation $5.2 per hour. The large-scale production cost follows a uniform distribution
with the smallest value $80 per hour and the largest value of $167 per hour. They are expecting a
limited market for the first-year demand. Thus, the first-year demand follows a discrete distribution
as follows:
Demand Probability
500 0.1
600 0.2
800 0.5
1200 0.1
1250 0.1
a) Develop a simulation model in the template for 250 trials. (25 points)
b) Fill the summary of statistics in your file. (5 points)
c) Plot the histogram for the specified ranges of profit. (5 points)
Problem 3
Wayne International Airport primarily serves domestic air traffic. Whenever an international plane arrives at the airport the two customs inspectors on duty set up operations to process the passengers. The inter-arrival time of the passengers follow a uniform distribution with the smallest value 0 minutes and the largest value 10 minutes.
Incoming passengers must first have their passports and visas checked. This is handled by two inspectors. The inspectors work at the same pace. The time required to check a passenger's passports and visas can be described by the probability distribution as follows:
Time Required to Check a Passenger’s Passport and Visa Probability
5 0.2
8 0.4
10 0.3
12 0.1
a) Develop a simulation model in the template for 100 incoming passengers. (25 points)
b) Fill the summary of statistics in your file. (5 points)
c) Plot the histogram for the specified ranges of waiting times. (5 points)