PERT/CPM - Markov Process.

PERT/CPM

1. Arcs in a project network indicate

a. completion times.

b. precedence relationships.

c. activities.

d. the critical path.

2. The critical path

a. is any path that goes from the starting node to the completion node.

b. is a combination of all paths.

c. is the shortest path.

d. is the longest path.

3. Activities following a node

a. can begin as soon as any activity preceding the node has been
completed.

b. have an earliest start time equal to the largest of the earliest
finish times for all activities entering the node.

c. have a latest start time equal to the largest of the earliest finish
times for all activities entering the node.

d. None of the alternatives is correct.

4. Slack equals

a. LF – EF.

b. EF – LF.

c. EF – LS.

d. LF – ES.

5. Activities with zero slack

a. can be delayed.

b. must be completed first.

c. lie on a critical path.

d. have no predecessors.

6. Which of the following is always true about a critical activity:

LS = EF.

b. LF = LS.

c. ES = LS.

d. EF = ES.

PART two - 20 pts.

A project network is shown below. Use a forward and a backward pass to
determine the critical path, and then fill out the table below.



Activity Precedence Activities Activity

Time (weeks)

ES

LS

EF

LF

Slack

A







B







C







D







E







F







G







H







I







Finish

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Markov Processes

 

1.         In Markov analysis, we are concerned with the
probability that the

            a.         state is part of a system.

            b.         system is in a particular
state at a given time.

            c.         time has reached a steady
state.

            d.         transition will occur.

2.         For a situation with weekly dining at either an
Italian or Mexican restaurant,

            a.         the weekly visit is the trial
and the restaurant is the state.

            b.         the weekly visit is the state
and the restaurant is the trial.

            c.         the weekly visit is the trend
and the restaurant is the transition.

            d.         the weekly visit is the
transition and the restaurant is the trend.

3.         A transition probability describes

            a.         the probability of a success
in repeated, independent trials.

            b.         the probability a system in a
particular state now will be in a specific state next period.

            c.         the probability of reaching an
absorbing state.

            d.         None of the alternatives is
correct.

4.         The probability of going from state 1 in period 2 to
state 4 in period 3 is

            a.         p12

            b.         p23

            c.         p14

            d.         p43

5.         The probability a system is in a particular state
after a large number of periods is

            a.         independent of the beginning
state of the system.

            b.         dependent on the beginning
state of the system.

            c.         equal to one half.

            d.         the same for every ending
system.

The daily price of a farm commodity is up, down, or unchanged from the
day before.  Analysts predict that if the last price was down, there is
a .5 probability the next will be down, and a .4 probability the price
will be unchanged.  If the last price was unchanged, there is a .35
probability it will be down and a .35 probability it will be up.  For
prices whose last movement was up, the probabilities of down, unchanged,
and up are .1, .3, and .6.

           

a Construct the matrix of transition probabilities.

 b.  Provide a system of equations for calculating the steady state
probabilities.

Start

A

5

B

4

C

8

D

4

E

12

F

10

G

3

H

0

I

5

Finish