### State a normal probability distribution

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1. For many waiting line situations, the arrivals occur randomly and independently of other arrivals and it has been found that a good description of the arrival pattern is provided by

A. A normal probability distribution.

B. An exponential probability distribution.

C. A uniform probability distribution.

D. A Poisson probability distribution.

2. Transportation, assignment, and transshipment problems have wide applications and belong to a class of linear programming problems called

A. distance problems.

B. network flow problems.

C. distribution design problems.

D. minimum cost problems.

3. The problem which deals with the distribution of goods from several sources to several destinations is the

A. maximal flow problem.

B. transportation problem.

C. assignment problem.

D. shortest-route problem.

4. The parts of a network that represent the origins are

A. the capacities.

B. the flows.

C. the nodes.

D. the arcs.

5. Activities with zero slack

A. can be delayed.

B. must be completed first.

C. lie on a critical path.

D. have no predecessors.

SECTION II: MATCHING

Please match the numbered terms with their definitions by placing the letter that identifies the best definition in the blank space next to the term.

1. Arcs

2. Crashing

3. Critical Path

4. Network

5. Nodes

6. Poisson Probability Distribution

7. Queueing Theory

8. Relevant Cost

9. Slack

10. Sunk Cost

A. A cost that depends upon the decision made.

B. A cost that is not affected by the decision made.

C. The intersection or junction points of a network.

D. The lines connecting the nodes in a network.

E. A graphical representation of a problem consisting of numbered circles (nodes) interconnected by a series of lines (arcs); arrowheads on the arcs show the direction of the flow.

F. The longest path in a project network.

G. The length of time an activity can be delayed without affecting the project completion.

H. The shortening of activity times by adding resources and hence usually increasing cost.

I. The body of knowledge dealing with waiting lines.

J. A probability distribution used to describe the arrival pattern for some waiting line models.

1. SENSITIVITY ANALYSIS

How is sensitivity analysis used in linear programming? Give an example of types of questions that can be answered using sensitivity analysis.

2. TRANSPORTATION, ASSIGNMENT, TRANSSHIPMENT

Give a brief description of each of the following problems: transportation, assignment, and transshipment. Your examples should clearly distinguish among the types.

3. CRITICAL PATH

Once the earliest and latest times are calculated, how is the critical path determined

4. WAITING LINE MODELS

A. What are two possible ways to improve the service rate of a waiting line operation? B. Briefly describe a real life example where this might be applied.

5. BONUS

What do you think you will take from this course that may be useful in your present and/or future career?

SECTION IV: PROBLEMS

PROBLEM 1: TRANSPORTATION PROBLEM

Canning Transport is to move goods from three factories to three distribution centers. Information about the move is as follows:

 Factory Units Supplied Distribution Center Units Demanded A 200 X 100 B 100 Y 150 C ISO Z 200

Costs per unit to ship from each factory to each distribution center are:

 Distribution Center Factory X Y Z A S3 \$2 \$5 B \$9 \$10 S7 C \$5 \$6 \$4

REQUIRED:

1. Develop a Network representative of this problem.

2. Formulate the problem as a linear program showing the objective function and the constraints.

PROBLEM 2: WAITING LINE MODELS

The Grand Movie Theater has one box office clerk. For the theater's normal offerings, customers arrive at the average rate of 3 per minute. On the average, each customer who comes to see a movie can be sold a ticket at the rate of 6 per minute. Assume arrivals follow the Poisson probability distribution and service times follow exponential probability distribution.

REQUIRED:

1. What is the probability that no customers are in the system?

2. What is the average number of customers waiting in line?

3. What is the average time a customer spends in the waiting line?

4. Do the operating characteristics indicate that the one-clerk system provides an acceptable level of service? Explain.

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