Question 1

Write a summary of the DEA approach and explain how you would interpret the solution.​

Accepted Answer

The DEA (Data Envelopment Analysis) approach is a non-parametric method used to evaluate the relative efficiency of decision-making units (DMUs) such as firms, organizations, or government agencies. It compares the inputs and outputs of each DMU to determine their efficiency in converting inputs into outputs.

To interpret the solution of a DEA analysis, you would first look at the efficiency scores assigned to each DMU. A score of 1 indicates that the DMU is efficient, while a score below 1 indicates inefficiency. You would then examine the weights assigned to each input and output in the analysis to understand which factors are driving the inefficiency. This can help identify areas for improvement and inform decision-making to enhance overall efficiency.

Additionally, the DEA approach can also identify benchmark DMUs that are considered the most efficient, providing a reference point for other DMUs to strive towards. Overall, the DEA approach provides a comprehensive assessment of efficiency and can guide strategic decision-making to improve performance.

Question 2

Explain how the local minimum,local maximum,local optimum,global minimum,global maximum,and global optimum relate to one another in nonlinear optimization problems.​

Accepted Answer

In nonlinear optimization problems, the concepts of local minimum, local maximum, local optimum, global minimum, global maximum, and global optimum are all related to each other in the context of finding the best solution for a given objective function.

A local minimum is a point in the function where the value is lower than all nearby points, but it may not be the lowest point in the entire function. Similarly, a local maximum is a point where the value is higher than all nearby points, but it may not be the highest point in the entire function.

A local optimum is a point that is either a local minimum or a local maximum, meaning it is the best solution within a small neighborhood of points. However, it may not be the best solution for the entire function.

On the other hand, a global minimum is the lowest point in the entire function, and a global maximum is the highest point in the entire function. These points represent the best possible solutions for the given objective function.

The global optimum is the overall best solution for the entire function, which can be either a global minimum or a global maximum.

In summary, local minimum, local maximum, and local optimum are related to each other as they represent the best solutions within a small neighborhood, while global minimum, global maximum, and global optimum are related to each other as they represent the best solutions for the entire function. The goal of nonlinear optimization problems is to find the global optimum, which is the best possible solution for the given objective function.

Question 3

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

Accepted Answer

A) True 
 B)False  False

Question 4

The Markowitz mean-variance portfolio model is a classic application of non-linear programming.

Accepted Answer

A) True 
 B)False

Question 5

Hervis Car Rental in Austin,TX has 50 high-performance Shelby-H Mustangs in its rental fleet.These cars will be in greater demand than usual during the last weekend in July when the Central Texas Mustang Club holds its annual rally in Austin.At times like this,Hervis uses a revenue management system to determine the optimal number of reservations to have available for the Shelby-H cars.
Hervis has agreed to have at least 60% of its Shelby-H Mustangs available for rally attendees at a special rate.Although many of the rally attendees will request a Saturday and Sunday two-day package,some attendees may select a Saturday only or a Sunday only reservation.Customers not attending the rally may also request a Saturday and Sunday two-day package,or make a Saturday only or Sunday only reservation.Thus,six types of reservations are possible.The cost for each type of reservation is shown here.
The anticipated demand for each type of reservation is as follows:
 $$\begin{array} { l l l l } 
& \text { Two-Day } & \text { Saturday } & \text { Sunday } \
& \text { Package } & \text { Only } & \text { Only } \
\hline \text { Rally } & \$ 125 & \$ 75 & \$ 65 \
\text { Regular } & \$ 150 & \$ 85 & \$ 75
\end{array}$$ Hervis Car Rental would like to determine how many Shelby-H Mustangs to make available for each type of reservation in order to maximize total revenue.
 $\begin{array}{llll} 
& \text { Two-Day } & \text { Saturday } & \text { Sunday } \
& \text { Package } & \text { Only } & \text { Only } \
\hline \text { Rally } & 20 & 10 & 15 \
\text { Regul ar } & 10 & 20 & 25
\end{array}$
 
a.Define the decision variables.
b.Formulate a linear programming model for this revenue management application.

Accepted Answer

a. RATW = number of reservations av aila

Question 6

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

Accepted Answer

A) True 
 B)False

Question 7

A DEA linear programming model involving 4 input measures and 3 output measures will have

Accepted Answer

A) 7 constraints. 
B) 8 constraints. 
C) 12 constraints. 
D) 13 constraints. 
A) 7 constraints. 
B) 8 constraints. 
C) 12 constraints. 
D) 13 constraints.

Question 8

In data envelopment analysis,the percentage of an individual operating unit's resources that are available to the composite operating unit is the

Accepted Answer

A) efficiency index. 
B) local optimum. 
C) global optimum. 
D) equilibrium point. 
A) efficiency index. 
B) local optimum. 
C) global optimum. 
D) equilibrium point.

Question 9

Each point on the efficient frontier graph associated with the Markowitz portfolio model is the

Accepted Answer

A) maximum possible risk for the given return. 
B) minimum possible risk for the given return. 
C) maximum return for the least risk. 
D) minimum diversification for the least risk. 
A) maximum possible risk for the given return. 
B) minimum possible risk for the given return. 
C) maximum return for the least risk. 
D) minimum diversification for the least risk.

Question 10

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

Accepted Answer

A) True 
 B)False

Question 11

Revenue management methodology can be applied in the case of nonperishable assets.

Accepted Answer

A) True 
 B)False

Question 12

A convex function is

Accepted Answer

A) bowl-shaped up. 
B) bowl-shaped down. 
C) elliptical in shape. 
D) sinusoidal in shape. 
A) bowl-shaped up. 
B) bowl-shaped down. 
C) elliptical in shape. 
D) sinusoidal in shape.

Question 13

In portfolio models,risk is minimized by diversification.

Accepted Answer

A) True 
 B)False

Question 14

An index fund is an example of passive asset management.

Accepted Answer

A) True 
 B)False

Question 15

LeapFrog Airways provides passenger service for Indianapolis,Baltimore,Memphis,Austin,and Tampa.LeapFrog has two WB828 airplanes,one based in Indianapolis and the other in Baltimore.Each morning the Indianapolis based plane flies to Austin with a stopover in Memphis,and the Baltimore based plane flies to Tampa with a stopover in Memphis.Both planes have a coach section with a 120-seat capacity.
LeapFrog uses two fare classes: a discount fare D class and a full fare F class.Leapfrog's products,each referred to as an origin destination itinerary fare (ODIF),are listed below with their fares and forecasted demand.
Develop a linear programming model for LeapFrog's problem situation and determine how many seats LeapFrog should allocate to each ODIF.
 \[\begin{array} { l l l l l l l } 
\text { ODIF } & \text { Origin } & \text { Destination } & \text { Fare Class } & \text { ODIF Code } & \text { Fare } & \text { Demand } \
\hline 1 & \text { Indianapolis } & \text { Memphis } & \text { D } & \text { IMD } & 175 & 44 \
2 & \text { Indianapolis } & \text { Austin } & \text { D } & \text { IAD } & 275 & 25 \
3 & \text { Indianapolis } & \text { Tampa } & \text { D } & \text { ITD } & 285 & 40 \
4 & \text { Indianapolis } & \text { Memphis } & \text { F } & \text { IMF } & 395 & 15 \
5 & \text { Indianapolis } & \text { Austin } & \text { F } & \text { IAF } & 425 & 10 \
6 & \text { Indianapolis } & \text { Tampa } & \text { F } & \text { ITF } & 475 & 8 \
7 & \text { Baltimore } & \text { Memphis } & \text { D } & \text { BMD } & 185 & 26 \
8 & \text { Baltimore } & \text { Austin } & \text { D } & \text { BAD } & 315 & 50 \
9 & \text { Baltimore } & \text { Tampa } & \text { D } & \text { BTD } & 290 & 42 \
10 & \text { Baltimore } & \text { Memphis } & \text { F } & \text { BMF } & 385 & 12 \
11 & \text { Baltimore } & \text { Austin } & \text { F } & \text { BAF } & 525 & 16 \
12 & \text { Baltimore } & \text { Tampa } & \text { F } & \text { BTF } & 490 & 9 \
13 & \text { Memphis } & \text { Austin } & \text { D } & \text { MAD } & 190 & 58 \
14 & \text { Memphis } & \text { Tampa } & \text { D } & \text { MTD } & 180 & 48 \
15 & \text { Memphis } & \text { Austin } & \text { F } & \text { MAF } & 310 & 14 \
16 & \text { Memphis } & \text { Tampa } & \text { F } & \text { MTF } & 295 & 11 \
\hline
\end{array}\]

Accepted Answer

Define the decision variables
There are

Question 16

The Eastern Washington County School Corporation is interested in comparing educational performance at four elementary schools and has hired you to prepare a DEA model to do so.After detailed conversations with the corporation administrative staff and the building principals,you have isolated the following input and output measurements:
Data is collected for each school on each measure
 $$\begin{array} { l l } 
\text { Input Measures } & \text { Output Measures } \
\hline \text { Average classroom size } & \text { Percent of children in remedial classes } \
\text { Percent of students on reduced price } 1 \text { unch } & \text { Average first grade score on standard test } \
\text { Average number of parent volunteer hours per week } & \text { Average fifth grade score on standard test }
\end{array}$$ Develop the DEA model that would evaluate the efficiency of Ralston Elementary School.

Accepted Answer

Let @#LAT-DLM& the weight applied to inputs and ou

Question 17

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

Accepted Answer

A) True 
 B)False

Question 18

The composite unit in data envelopment analysis

Accepted Answer

A) has as input a weighted average of the inputs of the individual units. 
B) has outputs greater than or equal to the outputs of any individual unit. 
C) has as output a weighted average of the outputs of the individual units. 
D) All of the alternatives are correct. 
A) has as input a weighted average of the inputs of the individual units. 
B) has outputs greater than or equal to the outputs of any individual unit. 
C) has as output a weighted average of the outputs of the individual units. 
D) All of the alternatives are correct.

Question 19

Functions that are convex have a single local maximum that is also the global maximum.

Accepted Answer

A) True 
 B)False

Question 20

Modern revenue management systems maximize revenue potential for an organization by helping to manage

Accepted Answer

A) pricing strategies. 
B) reservation policies. 
C) short-term supply decisions. 
D) All of the alternatives are correct. 
A) pricing strategies. 
B) reservation policies. 
C) short-term supply decisions. 
D) All of the alternatives are correct.

Write a summary of the DEA approach and explain how you would interpret the solution.

Explain how the local minimum,local maximum,local optimum,global minimum,global maximum,and global optimum relate to one another in nonlinear optimization problems.

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

The Markowitz mean-variance portfolio model is a classic application of non-linear programming.

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

A DEA linear programming model involving 4 input measures and 3 output measures will have

In data envelopment analysis,the percentage of an individual operating unit's resources that are available to the composite operating unit is the

Each point on the efficient frontier graph associated with the Markowitz portfolio model is the

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

Revenue management methodology can be applied in the case of nonperishable assets.

A convex function is

In portfolio models,risk is minimized by diversification.

An index fund is an example of passive asset management.

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

The composite unit in data envelopment analysis

Functions that are convex have a single local maximum that is also the global maximum.

Modern revenue management systems maximize revenue potential for an organization by helping to manage

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Exam 12: Advanced Optimization Applications

Write a summary of the DEA approach and explain how you would interpret the solution.​

Explain how the local minimum,local maximum,local optimum,global minimum,global maximum,and global optimum relate to one another in nonlinear optimization problems.​

The problem of maximizing a concave quadratic function over a linear constraint set is relatively difficult to solve.

The Markowitz mean-variance portfolio model is a classic application of non-linear programming.

There are nonlinear applications in which there is a single local optimal solution that is also the global optimal solution.

A DEA linear programming model involving 4 input measures and 3 output measures will have

In data envelopment analysis,the percentage of an individual operating unit's resources that are available to the composite operating unit is the

Each point on the efficient frontier graph associated with the Markowitz portfolio model is the

A nonlinear optimization problem is any optimization problem in which at least one term in the objective function or a constraint is nonlinear.

Revenue management methodology can be applied in the case of nonperishable assets.

A convex function is

In portfolio models,risk is minimized by diversification.

An index fund is an example of passive asset management.

Many linear programming algorithms such as the simplex method optimize by examining only the extreme points of the feasible region.

The composite unit in data envelopment analysis

Functions that are convex have a single local maximum that is also the global maximum.

Modern revenue management systems maximize revenue potential for an organization by helping to manage

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Project Scheduling

Inventory Models

Waiting Line Models

Simulation

Markov Processes

Filters

Write a summary of the DEA approach and explain how you would interpret the solution.

Explain how the local minimum,local maximum,local optimum,global minimum,global maximum,and global optimum relate to one another in nonlinear optimization problems.