# STAT201-QUANTITATIVE METHODS ASSIGNMENT-4

August 30, 2017

Question
Section-I

State whether the following statements are True or False. ( Marks)

PERT and CPM are quantitative analysis tools designed to schedule and control large projects.
2. Through the use of PERT/CPM, astute managers can derive flexibility by identifying noncritical activities and replanning, rescheduling, and reallocating resources such as personnel and finances.

3. Gantt charts and PERT diagrams provide the same information, just in different formats.

4. Simulation models are designed to generate optimal solutions, which can then be applied to real-world situations.

5. Simulation models are useful for economic order quantity problems with probabilistic demand and lead time.

Section-II

1. Slack time in a network is the

A) amount of time that an activity would take assuming very unfavorable conditions.

B) shortest amount of time that could be required to complete the activity.

C) difference between the expected completion time of the project using pessimistic times and the expected completion time of the project using optimistic times.

D) amount of time that an activity can be delayed without delaying the entire project.

2. Your company is considering submitting a bid on a major project. You determine that the expected completion time is 100 weeks and the standard deviation is 10 weeks. It is assumed that the normal distribution applies. You wish to set the due date for the project such that there is an 85 percent chance that the project will be finished by this time. What due date should be set? (The probability of 0.85 associated with Z value 1.04)

A) 108.0

B) 110.4

C) 89.6

D) 85.0

3. Which of the following scenarios would require simulation for a queuing model?

A) Poisson arrival process

B) exponential service time

C) deterministic arrival process

D) None of the above

4. Which of the following isnotconsidered one of the 5 steps of Monte Carlo Simulation?

A) establishing probability distributions for important input variables

B) generating random number

C) building a cumulative probability distribution for each input variable

D) establishing an objective function

5. The logic in a simulation model is presented graphically through which of the following?

A) scatterplot

B) flowchart

C) blueprint

D) decision tree

Section-III

Answer the following Essay Type Questions (3X5 )

1. Development of a new deluxe version of a particular software product is being considered. This deluxe version has seven major activities. The times are estimated and provided in the table below:

Activity

Immediate

Predecessor

Optimistic

Most

Likely

Pessimistic

A

3

4

5

B

6

7

14

C

A

6

9

12

D

B

0.5

1

1.5

E

B

2

3

10

F

D,C

4

5

12

G

E

1

3

11

Constract a network for this problem

Determine the expected time and variance for each activity

Find the earliest, latest and slack time for each activity.

Find the critical path. What is the expected completion time for this project?

What variance would be used in finding probabilities of finishing by a certain time?

2. The number of cars arriving at a self-service gasoline station during the last 50 hours of operation are as follows:

Number of Cars Arriving

Frequency

6

10

7

14

8

18

9

8

Set up a probability and cumulative probability distribution for the variable of car arrivals.

Establish random number intervals for the variable.

The following random numbers have been generated: 99, 98, 26, 09, 49, 52, 33, 89, 21, 37. Simulate 10 hours of arrivals at this gas station. What is the average number of arrivals during this period?

3. Dumoor Appliance Center sells and services several brands of major appliances. Past sales for a particular model of refrigerator have resulted in the following probability distribution for demand:

DEMAND PER WEEK

0

1

2

3

4

Probability

0.20

0.40

0.20

0.15

0.05

The lead time, in weeks, is described by the following distribution:

1

2

3

Probability

0.15

0.35

0.50

Based on cost considerations as well as storage space, the company has decided to order 10 of these each time an order is placed. The holding cost is

\$1 per week for each unit that is left in inventory at the end of the week. The stockout cost has been set at \$40 per stock out. The company has decided to place an order whenever there are only two refrigerators left at the end of the week. Simulate 10 weeks of operation for Dumoor Appliance assuming there are currently 5 units in inventory. Determine what the weekly stockout cost and weekly holding cost would be for the problem. (Use the following random number 52, 37, 82, 69, 98, 96, 33, 50, 88, 90 when simulating demand and 06, 63, 57, 02, 94, 52, 69, 33, 32, 30 when simulating lead time).

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