Management Science and Modeling Exam Solutions
Course Introduction
Management Science and Modeling explores the application of quantitative and analytical methods to solve complex decision-making problems in business and organizational contexts. The course introduces students to the principles and techniques of operations research, including linear programming, simulation, decision analysis, and forecasting. Emphasis is placed on constructing mathematical models to represent real-world business scenarios, utilizing computer-based tools for analysis, and interpreting results to support effective management decisions. Through case studies and practical exercises, students gain hands-on experience in formulating and solving models that drive operational efficiency, resource optimization, and strategic planning.
Recommended Textbook
Practical Management Science 6th Edition by Wayne L. Winston
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14 Chapters
421 Verified Questions
421 Flashcards
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Chapter 1: Introduction to Modeling
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Sample Questions
Q1) Models that suggest a desirable course of action are called descriptive models
A)True
B)False
Answer: False
Q2) Which of the following is not necessarily a property of a good model
A) The model represents the client's real problem accurately
B) The model is as simple as possible
C) The model is based on a well-known algorithm
D) The model is one the client can understand
Answer: C
Q3) Which of the following is <u>not</u> one of advantages of mathematical models
A) Mathematical models enable managers to understand the problem better
B) Mathematical models allow analysts to employ a variety of mathematical solution procedures
C) The mathematical modeling process itself, if done correctly, often helps "sell" the solution
D) Mathematical models help reduce the cost of obtaining a solution
Answer: D
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3
Chapter 2: Introduction to Spreadsheet Modeling
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Sample Questions
Q1) Refer to Exhibit 2-1.What Excel function is useful for calculating revenue
Explain why it is useful.
Answer: The IF function is useful for calculating revenue.This because there are two difference cases; demand could exceed production,in which case only the amount produced can be used to calculate revenue,and demand could be less than production,in which case only the demand can be used to calculate revenue.
Q2) A chart is typically much more informative to a business manager than the table of numbers it is based on.
A)True
B)False
Answer: True
Q3) [Part 2] Refer to Exhibit 2-2.Use the same scatterplot constructed for the previous question,fit an exponential trendline to the data.What are the coefficients of the exponential model,and what is the MAPE of an exponential model forecast,compared to the company's forecast
Answer: The exponential model fit produces a constant of 17.684 and an exponent of 0.115.Forecasting with this model and comparing against the company forecast results in a MAPE of 0.47%
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4
Chapter 3: Introduction to Optimization Modeling
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Sample Questions
Q1) [Part 3] Refer to Exhibit 3-1.Implement the model in Part 1 in Excel Solver and obtain an answer report.Which constraint(s)are binding on the optimal solution
Answer: The constraints section of the answer report (below)shows that the labor and process constraints are binding. 11ea5c70_d2e9_ee52_945b_7197f78516a8_TB6954_00
Q2) [Part 2] Refer to Exhibit 3-2.Obtain a sensitivity report for the solution reported in Part 1.Which constraints are binding
Answer: Steel available,Aluminum available,Assembly SS,and Market Deluxe SS all have nonzero shadow prices,so they are binding. 11ea5c70_d2ea_6384_945b_f15aeb52ba4e_TB6954_00
Steel available, Aluminum available, Assembly SS, and Market Deluxe SS all have nonzero shadow prices, so they are binding.
Q3) Refer to Exhibit 3-2.What is the value of additional capacity on the polisher How much increase and decrease in this capacity is possible before a change occurs in the optimal production schedule
Answer: The value of additional capacity on the polisher is zero,since it is not binding.The allowable increase is unbounded,and the allowable decrease is 1000.
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Chapter 4: Linear Programming Models
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Sample Questions
Q1) [Part 1] Refer to Exhibit 4-3.Suppose that later in the year,venison will be out of season,but the market will be able to obtain an additional 300 pounds of pork for the same costs.Develop a processing plan in that case.How does the solution change
Q2) In aggregate planning models,we can model backlogging of demand by allowing a month's inventory to be negative.
A)True
B)False
Q3) If we round the optimal values in the changing cells of a linear programming model,this is a good approximation of the integer programming solution.
A)True
B)False
Q4) Refer to Exhibit 4-1.Suppose the hospital has 40 nurses and is not allowed to hire or fire any employees,and cannot temporarily schedule nurses on their on call days.Determine a schedule that maximizes the number of weekend days off received by the nurses.
Q5) Refer to Exhibit 4-3.Determine the optimal processing plan for the meat market.
Q6) [Part 2] Refer to Exhibit 4-3.What happens to the revenue when the optimal plan changes to the one given in Part 1
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Chapter 5: Network Models
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Sample Questions
Q1) Refer to Exhibit 5-1.Formulate (write out algebraically)an LP transportation model to help Sinclair minimize its shipping costs.
Q2) It is useful to model network problems by listing all of the arcs and their corresponding flows in one long,comprehensive list.
A)True
B)False
Q3) Which of the following is not an example of a condition that a more complex logistics model might include
A) Multiple products
B) Multiple modes of transportation
C) Multiple time periods
D) Multiple objectives
Q4) In an assignment model of machines to jobs,the machines are analogous to which of the following in a transportation problem
A) Suppliers
B) Customers
C) Flows
D) Unit capacities
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Chapter 6: Optimization Models With Integer Variables
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Sample Questions
Q1) Solver may be unable to solve some integer programming problems,even when they have an optimal solution.
A)True
B)False
Q2) Many inherently nonlinear problems can be transformed into linear models with the use of:
A) integer variables
B) integer constraints
C) binary variables
D) binary constraints
Q3) Refer to Exhibit 6-2.Suppose the shipping capacity for all routes is 3000 tons per month.What is Sinclair's optimal shipping plan in that case What is the total cost in that case
Q4) Rounding the solution of a linear programming to the nearest integer values provides an:
A) integer solution that is optimal
B) integer solution that is not optimal
C) integer solution that might be optimal
D) infeasible solution
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Chapter 7: Nonlinear Optimization Models
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Sample Questions
Q1) Solver is guaranteed to solve certain types of nonlinear programming models.
A)True
B)False
Q2) Which of the following types of fit should be selected in Excel's Trendline function if a constant elasticity curve is to be used to model demand
A) Exponential
B) Logarithmic
C) Polynomial
D) Power
Q3) Refer to Exhibit 7-4.Suppose you set the weights in the portfolio to a maximum of 0.45 for each stock.Is it possible to achieve a 12% return What is the portfolio standard deviation in that case
Q4) [Part 1] Refer to Exhibit 7-3.Formulate a nonlinear optimization model to find the parameters of a function of the form: f(x)= axb to model demand for its product as a function of ad exposures (x).
Q5) [Part 1] Refer to Exhibit 7-4.Determine the minimum variance portfolio that yields an expected annual return of at least 0.10
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Chapter 8: Evolutionary Solver: An Alternative Optimization
Procedure
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Sample Questions
Q1) Which of the following is not one of the Excel functions that necessitate the use of Evolutionary Solver to obtain solutions
A) SUM
B) IF
C) MAX
D) MIN
Q2) Evolutionary Solver works best when constraints are applied as:
A) penalties
B) shortages
C) capacities
D) targets
Q3) Genetic algorithms are not guaranteed to be fast,but they make up for it by being flexible.
A)True
B)False
Q4) The number of possible paths in a shortest path problem with n locations is:
A) n
B) n 1
C) n<sup>2</sup>
D) n!
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Chapter 9: Decision Making Under Uncertainty
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Sample Questions
Q1) All problems related to decision making under uncertainty have three common elements:
A) the mean, median, and mode
B) the set of decisions, the cost of each decision and the profit that can be made from each decision
C) the set of possible outcomes, the set of decision variables and the constraints D) the set of decisions, the set of possible outcomes, and a value model that prescribes results
Q2) Refer to Exhibit 9-1.Suppose the farmer is not risk-neutral,but instead his behavior can be modeled using an exponential utility function with a risk tolerance parameter of 100,000.What is the most he would be willing to pay for insulation in that case
Q3) Refer to Exhibit 9-2.What should the credit union do What is their expected profit
Q4) Refer to Exhibit 9-2.Construct a decision tree to help the credit union decide whether or not to make the loan.Make sure to label all decision and chance nodes and include appropriate costs,payoffs and probabilities.
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Chapter 10: Introduction to Simulation Modeling
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Sample Questions
Q1) If x is a random number between 0 and 1,then we can use x to simulate a variable that is uniformly distributed between 100 and 200 using the formula:
A) 100 + x
B) 200 x
C) 100 + 100x
D) 200x
Q2) Refer to Exhibit 10-2.Total sales is a product of three different types of input distributions.What does the output distribution look like What is the standard deviation of the total sales
What are the 5th and 95th percentiles of this distribution
Q3) Refer to Exhibit 10-2.Finally,suppose the apparel company receives an uncertain fraction of the total retail revenue from its retailers,modeled as a Triangular(0.70,0.75,0.80)distribution,and then must subtract production and operations costs,which are modeled as a Lognormal distribution with mean of $1,000,000 and standard deviation of $300,000.In that case,what is the expected net profit from the jacket line
Q4) Refer to Exhibit 10-2.What is the probability that the apparel company will exceed a profit at least $0.5M from the jacket line
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Chapter 11: Simulation Models
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Sample Questions
Q1) In cash flow models,we are typically interested in investigating:
A) the value at risk (VAR)
B) the net present value (NPV)
C) the amount of loans required to maintain a minimum cash balance
D) the interest on loans taken out by a firm
Q2) [Part 6] Refer to Exhibit 11-1.Given your answers to Parts 1 through 5,would you invest in this project
Q3) [Part 2] Refer to Exhibit 11-1.Suppose that the forecasted price levels shown in the pro forma cash flow sheet are not deterministic,but rather are expected to fluctuate due to market forces.The prices are expected to be normally distributed in each year,with the following means and standard deviations:
Using the appropriate @RISK functions in the pro forma,what is the expected NPV
Would you recommend investing in this project
Explain. \[\begin{array} { c c c c c c }
\text { Year } & 1 & 2 & 3 & 4 & 5 \\
\text { Mean } & \$ 27.40 & \$ 26.60 & \$ 25.50 & \$ 24.80 & \$ 23.50 \\
\text { Std. Dev. } & \$ 5.50 & \$ 5.30 & \$ 5.00 & \$ 4.50 & \$ 4.10 \end{array}\]
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Chapter 12: Queueing Models
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Sample Questions
Q1) In queuing systems with a finite number of customers allowed,there is no need to require that the traffic intensity be less than 1 to ensure stability.
A)True
B)False
Q2) The exponential distribution is:
A) flat
B) bell-shaped
C) heavily right-skewed
D) heavily left-skewed
Q3) The decision to balk at entering a queuing system can be made by the customer or the system.
A)True
B)False
Q4) Refer to Exhibit 12-3.What percentage of all customers have to spend at least some small amount of time waiting in line
Q5) Refer to Exhibit 12-2.How many of the servers are busy on average
Q6) [Part 2] Refer to Exhibit 12-1.Assuming an exponential distribution with the parameter you obtained in Part 1,what is the probability that a customer interarrival time will be less than 2 minutes
Page 14
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Chapter 13: Regression and Forecasting Models
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Sample Questions
Q1) Winter's method is an exponential smoothing method,which is appropriate for a series with trend but no seasonality.
A)True
B)False
Q2) A time series can consist of four different components: trend,seasonal,cyclical,and random (or noise).
A)True
B)False
Q3) The percentage of variation explained R<sup>2</sup> is the square of the correlation between the observed Y values and the fitted Y values.
A)True
B)False
Q4) Which of the following is not one of the commonly used summary measures for forecast errors
A) MAE (mean absolute error)
B) MFE (mean forecast error)
C) RMSE (root mean square error)
D) MAPE (mean absolute percentage error)
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Chapter 14: Data Mining
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Sample Questions
Q1) SQL Server Analysis Services (SSAS)concentrates on which types of data mining
A) classification and clustering
B) market basket and forecasting
C) clustering and prediction
D) forecasting and classification
Q2) The logistic function 1/(1+e<sup> -x</sup> )
A) is concave.
B) is convex.
C) is S-shaped.
D) takes on values between -1 and 1.
Q3) The last step of cluster analysis is to understand the shared characteristics of the observations in each cluster.
A)True
B)False
Q4) See Exhibit 14.1 - How well can logistic regression classify the people as having the illness or not
Q5) See Exhibit 14-1 Use neural nets via Palisade's NeuralTools to classify the people as being diagnosed as having an illness or not. (Reserve 20% of the observations for testing.) How well does this method correctly classify people
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