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Management science modeling techniques focus on model construction and problem
solution.
In solving the facility location problem, the objective is to locate a centralized facility
that serves customers or other facilities such that the distance traveled between the
facility and customers or other facilities is minimized.
Objective functions in linear programs always minimize costs.
Service level is positively correlated with the size of the buffer stock.
Markov analysis is not a descriptive technique that results in probabilistic information.
In goal programming, terms are summed in the objective function in order to make
consistent decisions.
The values assigned to branches typically represent distance, time, or cost.
The divisibility assumption is violated by integer programming.
Monte Carlo is a technique for selecting numbers randomly from a probability
distribution.
Fractional relationships among variables are considered standard form in a blending
problem.
In a balanced transportation model where supply equals demand, all constraints are
equalities.
The area under the normal curve represents probability.
Data are pieces of information from the problem environment.
The basic single-server model assumes that customers who arrive first are served first.
In a total integer model, all decision variables have integer solution values.
A model is a mathematical representation of a problem situation including variables,
parameters, and equations.
The best strategy for each player is his or her optimal strategy.
Diet problems usually maximize nutritional value.
Classical optimization is the use of calculus to determine the optimal value of a
variable.
When using Excel to simulate a system, it is necessary to compute only the probability
(relative frequency) distribution.
The early start for a non-critical activity is always equal to the earliest finish of the
preceding activity.
Markov Analysis always results in a steady state.
The goal of the maximal flow problem is to maximize the amount of flow of items from
an origin to a destination.
In using the simplex method, the number of basic variables is equal to the number of
constraints.
Slack is the amount of time an activity can be delayed without delaying the project.
In a transportation problem, items are allocated from sources to destinations at a
minimum cost.
The first step of the management science process is to define the problem.
An element of project planning is to compare the project schedule objectives.
Markov analysis is an optimization technique.
The maximax criterion results in the maximum of the maximum payoffs.
A work breakdown structure is a useful tool because it addresses the timing of
individual work elements.
The EOQ model with shortages does not allow backorders.
The constraint x + y = z is written in standard form.
The branch and bound method is a solution approach that partitions the infeasible
solution space into smaller subsets of solutions.
The term 'sensitivity analysis" refers to testing how a problem solution reacts to
changes in one or more of the model parameters.
A bakery is considering hiring another clerk to better serve customers. To help with this
decision, records were kept to determine how many customers arrived in 10-minute
intervals. Based on 100 10-minute intervals, the following probability distribution and
random number assignments developed.
Suppose the next three random numbers were .08, .50 and .69. How many customers
would have arrived during this 30-minute period?
A) 22
B) 23
C) 24
D) 25
A professor needs help from three student helpers to complete four tasks. The first task
is grading; the second is scanning; the third is copying, and the fourth is organizing
student portfolios. The estimated time for each student to do each task is given in the
matrix below.
Which of the following constraints represents the assignment for student A?
A) XA1 + XA2 + XA3 + XA4 = 0
B) XA1 + XA2 + XA3 + XA4 = 1
C) XA1 + XA2 + XA3 + XA4 ≤ 1
D) XA1 + XA2 + XA3 + XA4 ≥ 0
A(n) ________ game occurs when each player selects an optimal strategy that does not
result in an equilibrium point when the minimax criterion is used.
A) optimal strategy
B) pure strategy
C) mixed strategy
D) best strategy
A retired operations management professor moves to New Orleans, joins the Krewe of
Orpheus and convinces krewe leadership to buy their own swizzle stick production
equipment. They invest in a medium-scale machine called the Swizzo 2025, which is
capable of producing swizzle sticks at the rate of 1800 per day. They run through the
calculations and realize that with the space taken up by the machine, they can't possibly
produce an optimal batch, so they cut the batch size down to a manageable 60,000
units. If a swizzle stick takes up 0.5 cubic inches, how much warehouse space will they
save at peak inventory levels compared to producing the optimal batch size?
A) 2.11 cubic feet
B) 4.31 cubic feet
C) 6.57 cubic feet
D) 9.34 cubic feet
A Markov assumption is that the probabilities ________ over time.
A) become smaller
B) become larger
C) change
D) are constant
In the substitution method, the constraint equation is solved for one variable ________
and then substituted into the objective function.
A) only
B) after another
C) at a time
D) in terms of another
Jolt - Exp
The soda machine outside the lecture hall sees a steady stream of customers throughout
the day. While the machine takes 4 seconds to deliver a can of carbonated sugar water
once the button is pressed, the student customers introduce variation into the delivery
process by pondering their selection for a while. Thus, we can safely say that the
service time is governed by a negative exponential probability distribution that averages
10 seconds. Over the course of a twelve hour lecture day, students arrive at the rate of
240 per hour, Poisson distributed of course.
When the soda machine is not dispensing product, its CPU participates in the SETI
project. It takes one second to examine an interstellar signal for signs of intelligence.
Over the course of an entire 24 hour period, how many signals can the soda machine
examine?
A) 57,600
B) 43,200
C) 28,800
D) 14,400
The owner of a seafood market determined that the average weight for a crab is 1.6
pounds with a standard deviation of 0.4 pound. What weight is exceeded by 2% of all of
the crabs? (Assume the weights are normally distributed.)
A) 0.78 pounds
B) 1.82 pounds
C) 2.42 pounds
D) 4.36 pounds
Adding 1.5 standard deviations of safety stock to the average demand during lead time
will result in a service level of approximately:
A) 68.4%.
B) 84.1%.
C) 93.3%.
D) 97.7%.
How should the entry for the Newspaper decision variable be interpreted?
A) The director should lower the newspaper advertising expense by $1,000 to reach the
objective of 5,000 customers contacted.
B) If the director were forced to purchase a newspaper advertisement, he would reach
1000 fewer customers than would be reached using the optimal advertising campaign.
C) If the director increased newspaper advertisement by 1,000, he would spend $1000
less than with the current campaign.
D) It is possible to reach an almost infinite fewer number (10 to the 30th power) of
customers by newspaper than by any other method.
A tabular presentation that shows the outcome for each decision alternative under the
various possible states of nature is called a:
A) decision tree.
B) payoff table.
C) feasible region.
D) payback matrix.
Cold & Calculating
The cold, calculating father did exactly that when examining the 27 year old failure to
launch man child that had turned his walk in closet into a bedroom. As he saw it, there
were five alternatives; each had its advantages and disadvantages, and under different
circumstances, each had a different financial incentive. He laid it all out neatly in a
table, but as not to arouse suspicion, he left the table's labels very generic, so the
alternatives were simply labeled A through E while the different circumstances were
simply numbered one through three. He flicked the gray ash off of his favorite purple
smoking jacket and pondered the best course of action under each possible future. It
was good to be devious, he decided.
He set the analysis aside for a few days and when he noticed it on his drawing table he
studied it. He vaguely remembered the potential courses of action but couldn't for the
life of himself remember what the different states of nature were. "This is certainly
embarrassing," he muttered. Perhaps it didn't really matter as long as he treated each
state of nature as equally likely. They certainly were in his own mind now that he
couldn't remember what they were. "If that's not the definition of equally likely, I don't
know what is," he commented to his faithful manservant Jeeves. Which alternative
would be the best choice given this predicament?
A) A
B) B
C) C
D) D
A professor's son, having made the wise decision to drop out of college, has been
finding his way in life taking one job or another, leaving when his creativity is overly
stifled or the employer tires of his creativity. The professor dutifully logs the duration of
his son's last few careers and has determined that the average duration is normally
distributed with a mean of sixty six weeks and a standard deviation of ten weeks. The
next career begins on Monday; what is the likelihood that it endures for less than a year
and a half?
A) 82%
B) 85%
C) 88%
D) 91%
The following table represents the cost to ship from Distribution Center 1, 2, or 3 to
Customer A, B, or C.
In a transshipment problem, items may be transported:
A) from destination to destination.
B) from one transshipment point to another.
C) directly from sources to destinations.
D) all of the above
In a single-server queuing model, L represents the:
A) length of time a customer waits.
B) size of the queue.
C) average number of customers waiting and being served.
D) length of the line.
Jolt - Exp
The soda machine outside the lecture hall sees a steady stream of customers throughout
the day. While the machine takes 4 seconds to deliver a can of carbonated sugar water
once the button is pressed, the student customers introduce variation into the delivery
process by pondering their selection for a while. Thus, we can safely say that the
service time is governed by a negative exponential probability distribution that averages
10 seconds. Over the course of a twelve hour lecture day, students arrive at the rate of
240 per hour, Poisson distributed of course.
Nathan is cutting it close today. At 10:00:00 AM, the professor will close the door to the
classroom and ignore any requests to enter the room once his scintillating lecture has
begun. What is the probability that he finds only one person at the machine buying a
soda?
A) 0.1
B) 0.15
C) 0.22
D) 0.33
Mondo's Runway Show
Mondo Guerra is matching his models with his latest collection for Fashion Week. He
has five models, ranging from 5'10" to 5'10.5" and size 0 to size 1. His five latest
designs run the gamut from prêt-à-porter to an evening gown and he'd like to make sure
each outfit looks as good as possible by having it worn on the runway by the right
model. After an anxious month of sewing, he has each model try on each outfit and he
assigns a fabulosity score to each combination as indicated in the table.
Which term does not belong in an objective function for this scenario?
A) 9WP
B) 4XG
C) 6XC
D) 9ZG
The College Coffee Cafe buys tea from three suppliers. The price per pound is $15.00
from supplier A, $17.50 from supplier B, and $21.00 from supplier C. They have
budgeted $175 to purchase the tea. The cafe needs at least 12 pounds of tea, and
supplier C can supply no more than 4 pounds. Develop constraints for these conditions.
Figure 2
Consider the optimization problem represented by this graph. Which of the following
statements is best?
A) This is a maximization problem with a feasible solution.
B) This is a maximization problem with no feasible solution.
C) This is a minimization problem with a feasible solution.
D) This is a minimization problem with no feasible solution.
Once a project is underway, the project manager is responsible for the:
A) people.
B) cost.
C) time.
D) all of the above
In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of
stocks 1, 2, and 3, which have selling prices of $15, $47.25, and $110, respectively. The
investor has up to $50,000 to invest.
The expected returns on investment of the three stocks are 6%, 8%, and 11%. An
appropriate objective function is:
A) MAX .06X1 +.08X2 +.11X3.
B) MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3.
C) MAX 15X1 + 47.25X2 +.110X3.
D) MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3.
________ involves determining the functional relationship between variables,
parameters, and equations.
A) Problem observation
B) Problem definition
C) Model construction
D) Model solution
If a slack variable has a positive value (is basic) in the optimal solution to a linear
programming problem, then the shadow price of the associated constraint:
A) is always zero.
B) is always greater than zero.
C) is always less than zero.
D) could be any value (i.e., zero greater than zero or less than zero).
Goal constraints can include ________ deviational variables.
A) no
B) some
C) all
D) multiple
Let xij= gallons of component i used in gasoline j. Assume that we have two
components and two types of gasoline. There are 8000 gallons of component 1
available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons,
respectively. Write the constraint stating that the component 1 cannot account for more
than 35% of the gasoline type 1.
A) x11 + x12 (.35)(x11 + x21)
B) x11 + .35(x11 + x12)
C) -.65x11 + .35x21 ≤ 0
D) .65x11 - .35x21 ≤ 0
The gentleman farmer kept chickens for the eggs, the splash of color in the yard, and
because he found their gentle clucking to relax him as he worked on his laptop on his
deck. Their movements around his yard gave meaning to the term random walk you
literally could not predict their location from one minute to the next. His collection of
birds is neatly summarized in this table.
What is the probability that the next chicken that joins him up on the deck is a rooster?
A) .05
B) .10
C) .33
D) .66
What is not considered a measure of system performance in a queuing analysis?
A) average number in the system
B) system utilization
C) average number waiting in line
D) service time
The Vacation
Final exams are almost here and once they are done, it will be time to reward myself
with a well-deserved vacation. As a state employee, I haven't seen a raise since... well,
ever. Thus an important criterion, in fact the most important criterion is to find an exotic
region that can be visited inexpensively. There are three states of nature that could
impact costs in these five areas of interest, and they correspond to the relative strength
of the US Dollar against that region's dominant currency. Rather than squander my time
doing any actual publishable research, instead I have determined the average cost per
day to visit each region under each of the possible states of nature. This table, which
should not be construed as actual vacation advice, appears below.
An pessimistic vacationer would opt for:
A) Scandinavia.
B) Galapagos Islands.
C) Australia.
D) Eastern Europe.
A retired operations management professor moves to New Orleans, joins the Krewe of
Orpheus and convinces krewe leadership to buy their own swizzle stick production
equipment. They invest in a medium-scale machine called the Swizzo 2025, which is
capable of producing swizzle sticks at the rate of 1800 per day. How many days per
year will the Swizzo 2025 be running if they produce the optimal batch size?
A) 340
B) 325
C) 310
D) 295
Which of the following special cases does not require reformulation of the problem in
order to obtain a solution?
A) unboundedness
B) infeasibility
C) alternate optimality
D) Each one of these cases requires reformulation.
________ demand items are used internally to produce a final product.
A) Independent
B) Dependent
C) Assumed
D) Internal
Markov analysis is a ________ technique that results in ________ information.
A) descriptive, descriptive
B) probabilistic, descriptive
C) descriptive, probabilistic
D) probabilistic, probabilistic
Donuts Please
The number of donuts needed for department meetings at the start of the semester can
be modeled by the continuous probability distribution , which we can integrate
from 0 to some value x, which is the number of days before the actual beginning of the
semester.
What is the value for x when random number r is equal to six?
A) 2
B) 5
C) 10
D) 18
The ________ property of linear programming models indicates that the rate of change
or slope of the objective function or a constraint is constant.
A) additive
B) divisibility
C) certainty
D) proportionality
Spring is right around the corner and that can mean only one thing: it's time to incubate
some eggs for a fresh crop of chickens to supplement the existing flock for the year.
There are three breeds that are popular: Leghorns, Buff Orpingtons, and Cochins, and
each has its own strengths and weaknesses. The Leghorns, for example, are superb
layers but easily excitable. The Cochins, on the other hand, are very even-tempered but
not the best layers. They do have marvelous plumage, with feathers that extend down to
their feet. The Buff Orpingtons are good layers, have interesting plumage, and are
mid-range in their temperament.
The chicken farmer would like this crop of chickens to produce as many eggs as
possible while keeping the noise to a dull roar and having a nice array of birds
free-ranging on his lawn during those lazy summer days. He has put the relevant data in
table form. Plumage numbers are on a scale from 1-10, with 10 being the most
desirable. The egg output is not on a scale, but is instead the average output for the
breed, based on years of collecting eggs.
Temperament is actually measured by the average volume of cackling, clucking, and
crowing and is measured in decibels per bird. Appetite is measured in ounces of layer
pellets per week consumed by each of the breeds, while fertilizer is measured as the
output in ounces per week.
Which of the following is an appropriate objective function?
A) Max Z = 5L + 2C + 4.5B
B) Max Z = 10L + 10C + 10B
C) Min Z = 5L + 2C + 4.5B
D) Min Z = 10L + 10C + 10B
A ________ is the probability of moving from one state to another during one time
period.
Comedy Pasture II
A horse and two llamas are discussing the key areas of their domain on a lazy summer
afternoon. The llamas favor the pond and shade and like to browse the fruit trees and
oaks on the property, making their way to the barn only when their owner favors them
with some oats. The horse prefers to graze the grass and hay for food and drink from the
pond but will race up to the barn when the owner is handing out oats up there. Between
the three of them, they have stepped off the distances between many of these key points
several times and believe that they have developed an accurate map, shown below. This
map shows the number of loads that can be hauled between all connected points on the
property. As incredible as it may seem, neither the horse nor the llamas have had any
training in management science, which is where you come in.
The llamas took pride in the centuries old use as pack animals in the South American
Andes. They decided to join forces with their grazing buddy the horse and lug ripe fruit
from the orchard (designated as Fruit) down to the Pond. Use the capacities indicated
on each of the branches to determine the maximal flow from the orchard down to the
pond.
Mad Over Donuts
An entrepreneurial resident of the Oklahoma City metropolitan area is interested in
securing a new franchise for Mad Over Donuts. Ideally this franchise would be
centrally located so delivery could be economically handled and all citizens could enjoy
fresh, delicious donuts delivered to the doorstep. The main cities and anticipated
demand (in thousands per day) are shown in the table.
Write the formulation for this problem
The following data summarizes the historical demand for a product.
Use exponential smoothing with α = .2 and a smoothed forecast for July of 32 to
determine August and September's smoothed forecasts.
Write the dual form of the following linear program.
MAX Z = 3 + 5
s.t. ≤ 4
2 ≤ 12
3 + 2 ≥ 18
A(n) ________ decision is one that has a better payoff than another decision under each
state of nature.
The variable with the largest positive cj - zj is the ________ variable.
If the absolute errors were calculated for 5 periods and the sum of the absolute
deviation is 60, what is the value of the MAD?
The ________ method evaluates all feasible solutions to determine the optimal solution.
In setting up the an intermediate (transshipment) node constraint, assume that there are
three sources, two intermediate nodes, and two destinations, and travel is possible
between all sources and the intermediate nodes and between all intermediate nodes and
all destinations for a given transshipment problem. In addition, assume that no travel is
possible between source nodes, between intermediate nodes, and between destination
nodes, and no direct travel from source nodes to destination nodes. Let the source nodes
be labeled as 1, 2, 3, the intermediate nodes be labeled as 4 and 5, and the destination
nodes be labeled as 6 and 7.
State the constraint for intermediate node 4.
A fair die is rolled 8 times. What is the probability that an even number (2, 4, or 6) will
occur between 2 and 4 times?
Consider a capital budgeting example with five projects from which to select. Let x1 = 1
if project a is selected, 0 if not, for a = 1, 2, 3, 4, 5. Projects cost $100, $200, $150, $75,
and $300, respectively. The budget is $450.
Write the appropriate constraint for the following condition: If project 3 is chosen,
project 4 must be chosen.
Billy Hill's Still
William J Hill runs a small batch artisnal bourbon distillery at a secluded location in the
hills of Kentucky. He makes two products, known among his customers as Rotgut and
White Lightning. The recipes for the two have been passed down in the Hill family for
generations and are Rotgut: 1 bushel of corn, 3 pounds of sugar, 2 hours of cooking
time. For the premium blend, White Lightning, he needs 2 bushels of corn, 2 pounds of
sugar, and 3 hours of cooking time. Both recipes make enough to fill two jugs, which
sell for $8 apiece for Rotgut and $12 apiece for White Lightning.
A quick inventory one crisp autumn morning reveals that William has on hand 40
bushels of corn, 70 pounds of sugar, and 50 jugs. He would like to brew up a few
artisnal batches, but has recently received a tip that certain agencies have taken an
interest in his talents and may be paying him a visit in three days, hence he plans to
restrict any brewing activity to 72 hours at most, before he retreats to his home away
from home, Lubbock.
William cleans his equipment, lights a fire, and ponders the objectives. Obviously the
first priority is restricting himself to 72 hours of work any more than that and he runs
the risk of an extended holiday. His second priority to make enough to acquire materials
for the next production run and fund his daughter's college tuition - he believes that
$500 would make this production run worth his while. His third and fourth priorities are
not to have too much perishable inventory, so he wants to make sure he doesn't have too
many bushels of corn on hand (third priority) nor does he want too many pounds of
sugar on hand (fourth priority).
What is the objective function?
A credit union wants to make investments in the following:
The firm will have $2,500,000 available for investment during the coming year. The
following restrictions apply:
- Risk-free securities may not exceed 30% of the total funds, but must comprise at least
5% of the total.
- Signature loans may not exceed 12% of the funds invested in all loans (vehicle,
consumer, other secured loans, and signature loans).
- Consumer loans plus other secured loans may not exceed the vehicle loans.
- Other secured loans plus signature loans may not exceed the funds invested in
risk-free securities.
How should the $2,500,000 be allocated to each alternative to maximize annual return?
What is the annual return?
The closer the value of α is to zero, the ________ will be the dampening or smoothing
effect.
The linear programming problem whose output follows determines how many red nail
polishes, blue nail polishes, green nail polishes, and pink nail polishes a beauty salon
should stock. The objective function measures profit; it is assumed that every piece
stocked will be sold. Constraint 1 measures display space in units, constraint 2
measures time to set up the display in minutes. Constraints 3 and 4 are marketing
restrictions.
MAX 100x1 + 120x2 + 150x3 + 125x4
Subject to 1. x1 + 2x2 + 2x3 + 2x4 ≤ 108
2. 3x1 + 5x2 + x4 ≤ 120
3. x1 + x3 ≤ 25
4. x2 + x3 + x4 > 50
x1, x2, x3,x4 ≤ 0
Optimal Solution:
Objective Function Value = 7475.000
Objective Coefficient Ranges
Right Hand Side Ranges
What is the profit?
The relationship d = 5000 - 25p describes what happens to demand (d) as price (p)
varies. Price can vary between $10 and $50. How many units can be sold when the
price is $10?
