CHAPTER 1
INTRODUCTION TO MANAGEMENT SCIENCE MODELS
TRUE/FALSE QUESTIONS
1. Other than for the military, the application of management
science is inappropriate for non-profit organizations.
2. Management science replaces common sense with scientific
3. Constrained mathematical models contain variable constraints
4. Heuristic solution procedures always yield an optimal solution
5. Constrained mathematical models are sometimes used to find
merely “good” or “better” solutions, not always “optimal” ones.
6. In defining decision variables, it is important to specify the
7. In management science problems, algorithms are rarely used
8. Both management and operating personnel should be involved
throughout the management science process, even before the
9. The linear constraints in a management science model need not
10. Frederick Taylor applied the scientific approach to improving
operations in a production setting more than 100 years ago.
11. Mathematical modeling is a process that translates observed or
12. Once a mathematical model is complete, you cannot change the
13. The management science team should make certain that
management is sure of its objective before developing and solving a
14. Computer programs exist for all standard management science
MULTIPLE CHOICE QUESTIONS
1. Management science does not:
a. use the scientific approach
b. provide a tool to aid in executive decision making.
c. involve mathematical modeling
d. guarantee improvement
2. The developer of the simplex method in linear programming is
generally regarded to be:
a. Gene Woolsey.
b. N. Karmarkar.
c. A. A. Markov.
d. George Dantzig
3. If “necessity is the mother of invention,” management
science’s mother was probably:
a. World War II.
b. the electronic computer.
c. the Great Depression
d. linear programming
4. Constrained mathematical models do not contain:
a. functional constraints.
b. non-negativity requirements.
c. management preferences.
d. boundary restrictions.
5. Constrained mathematical models may be characterized as:
a. optimization vs. prediction.
b. linear vs. quadratic.
c. probabilistic vs. stochastic.
d. heuristic vs. deterministic.
6. Profit maximization will yield the same result as cost
minimization when:
a. costs and revenues are both variable.
b. costs are constant.
c. per unit profits are constant.
d. revenues are constant.
7. In management science problems, algorithms are:
a. very complex, thus rarely used.
b. used in optimization but not in heuristics.
c. employed in heuristics as well as optimization.
d. substitutes for computer-based solution techniques.
8. Variable constraints may not include:
a. non-negativity constraints.
b. boundary (upper or lower) constraints.
c. integer constraints.
d. resource constraints.
9. A “model shell” contains:
a. actual data.
b. generic symbols.
c. both actual data and generic symbols.
d. neither actual data nor generic symbols.
10. Decision variable definition need not include:
a. specific units of measure.
b. the time frame involved.
c. variable names.
d. integer requirements, if any.
11. In a business organization, the “80/20” rule relates to:
a. work accomplished vs. people who perform it.
b. the average input/output ratio of production processes.
c. the value of a “good” problem solution vs. its cost.
d. “key” products vs. product line “fillers.”
12. At what state in the management science process should the
operating personnel, who are responsible for solution
implementation, first be consulted?
a. Problem definition.
b. Mathematical modeling.
c. Solution of the model.
d. Communication/marketing of results.
13. The worst mistake a management science analyst can make in
addressing the organization’s problem is probably:
a. giving the wrong answer to the right question.
b. giving the right answer to the wrong question.
c. including extraneous data in the model.
d. failing to anticipate “what if” questions.
14. Management science applications do not include:
a. simulation.
b. queuing.
c. decision analysis.
d. internet programming.
15. Constraints in the mathematical model do not include:
a. amount of resources (decision variables) required.
b. relational operators.
c. availability of resources.
d. shadow prices.
16. Which name is most commonly associated with Game Theory?
a. Andrey A. Markov
b. E. K. Erlang
c. Jon von Neuman
d. N. Karmarkar
17. Which step is not part of the mathematical modeling process?
a. Problem definition.
b. Data gathering.
c. Constructing a model shell.
d. Quantifying the objective and constraints.
18. Which executive reaction to your management science solution
would suggest the model is invalid?
a. “We never tried this before.”
b. “This doesn’t make sense to me.”
c. “We may not have as much money for this as we thought.”
d. “We’re profitable and have always done things our way.”
19. Which Excel function finds the value X such that 55% of the
probability lies below X from a normal distribution with mean
= 20 and standard deviation = 3?
a. NORMDIST(.55,20,3,TRUE)
b. NORMSDIST(.55,20,3)
c. NORMINV(.55,20,3)
d. NORMSINV(.55,20,3)
20. Which Excel data analysis tool returns the p-value for the F–
test?
a. Descriptive Statistics.
b. Regression.
c. Exponential Smoothing.
d. ANOVA.
SHORT ANSWER QUESTIONS
1. Erlang’s pioneering work in queuing theory emerged shortly
after the start of the twentieth century. The next truly
significant work in the field (by Little, et al) came roughly fifty
years later. Why the long delay?
2. How should a management science analyst proceed when it is
obvious that the “front line” people and their immediate management
do not agree as to the definition of the problem to be addressed?
3. What is the purpose of model shells in the management science
process?
4. “Let X = the number of 750 ml bottles of Federini Chablis to
be produced and shipped next calendar month.” Critically evaluate
this as the definition of a decision variable in a management
science problem.
5. Why should the management science analyst anticipate
resistance from operating personnel responsible for implementation
of the study’s results, most especially when the study’s
recommendations are substantially different from current practices?
What should be done to eliminate or reduce such resistance?
6. Globe Spanners, a local travel agency, is facing a financial
“crunch.” In September, 1997, most airlines reduced the commissions
they pay travel agencies to book airline tickets from ten percent to
eight percent. Having initially capped commissions at $25 for a one
way ticket and $50 for a round trip in February of 1995, the
combination of both changes had reduced Globe Spanners’ compensation
to less than six percent, below their operating costs for booking
air travel. Is this a problem amenable to management science
analysis?
7. What is the difference between “deterministic” and
“stochastic”?
8. What are three time and cost considerations for data
gathering?
9. Name one thing you should do if the results of your model
validation are unacceptable to management.
10. What does a dollar sign (“$”) in an Excel address signify?
FORMULATION/SOLUTION/ANALYSIS QUESTIONS
1. Dr. Zuck wants to study the effectiveness of a particular type
of back brace on patients suffering from scoliosis (curvature of the
spine). He wants to locate and test the largest possible number of
patients. He has obtained a grant for one million dollars and
estimates the cost of locating and recruiting a patient to be
$5,000. Half of the patients drop out of the study. There are two
types of patients. Type A must constitute at least 50% of the
study.
2. The Deepsea Sponge Company wishes to maximize profit. Real
sponges cost C1 dollars and sell for P1. Synthetic sponges cost C2
and sell for P2. Deepsea wants at least M% of their sales to be real
sponges. Create a mathematical model shell (objective function and
constraints).
3. Harold Shein, the accordion teacher, charges $A per hour
lesson for a novice and $B (greater than $A) for an advanced
student. P percent of novice students become advanced, and R
percent of advanced students cease taking lessons. Shein has H
hours available each week and prefers that at least half his
students are advanced. Create a mathematical model shell (objective
function and constraints) of his business.
4. The Dennis Advertising Company wants you to model their
business. Create a model shell for the following. For each client,
Dennis estimates per person costs for each type of media:
5. Boragon Middle School wishes to minimize the cost of audio–
visual equipment. The school has R classrooms, each of which must
have at least one piece of AV equipment. The school as a whole must
have at least one TV/VCR combination, one computer projector, one
laptop, and one overhead slide projector. Create a model shell.