Deck 12: Advanced Optimization Applications

Question 1

For a minimization problem,a point is a global minimum if there are no other feasible points with a smaller objective function value.

Answer 1

True

Question 2

For a typical nonlinear problem,duals price are relatively insensitive to small changes in right-hand side values.

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

Because most nonlinear optimization codes will terminate with a local optimum,the solution returned by the codes will be the best solution.

Question 6

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

Question 7

The goal of portfolio models is to create a portfolio that provides the best balance between risk and return.

Question 8

In portfolio models,risk is minimized by diversification.

Question 9

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

Question 10

Revenue management methodology was originally developed for the banking industry.

Question 11

The function f (x,y)= x ² + y ² has a single global minimum and is relatively easy to minimize.

Question 12

The interpretation of the dual price for nonlinear models is different than the interpretation of the dual price for linear models.

Question 13

A function is quadratic if its nonlinear terms have a power of 4.

Question 14

In the case of functions with multiple local optima,most nonlinear optimization software methods can get stuck and terminate at a local optimum.

Question 15

An index fund is an example of passive asset management.

Question 16

A feasible solution is a global optimum if there are no other feasible points with a better objective function value in the feasible region.

Question 17

A feasible solution is a global optimum if there are no other feasible solutions with a better objective function value in the immediate neighborhood.

Question 18

Nonlinear programming algorithms are more complex than linear programming algorithms.

Question 19

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

Question 20

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

Question 21

The logic of a DEA model is to determine whether _________ facility can achieve the same or more output than ________ facility while requiring less input.​

A)​an actual;another actual
B)​an actual;any other actual
C)​a hypothetical composite;an actual
D)​an actual;a hypothetical composite

Question 22

A key trade-off in most portfolio optimization models must be made between risk and return.

Question 23

Which of the following is incorrect?

A)A global optimum is a local optimum in a nonlinear optimization problem.
B)A local maximum is a global maximum in a concave nonlinear optimization problem.
C)A global minimum is a local minimum in a convex nonlinear optimization problem.
D)A local optimum is a global optimum in a nonlinear optimization problem.

Question 24

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

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 25

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

Question 26

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

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

Question 27

Portfolio manager Max Gaines needs to develop an investment portfolio for his conservative clients.His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides the best return possible with a minimum risk.Formulate the maximin linear program.

Question 28

The overall goal of portfolio models is to create a portfolio that provides the best balance between

A)short-term and long-term investments.
B)gains and losses.
C)risk and return.
D)liquidity and stability.

Question 29

To develop a portfolio that provides the best return possible with a minimum risk,the linear programming model will have an objective function which

A)minimizes the maximum risk.
B)minimizes total risk.
C)maximizes return and minimizes risk.
D)maximizes the minimum return.

Question 30

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

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

Question 31

Which of the following is not true regarding a concave function?

A)It is bowl-shaped down.
B)It is relatively easy to maximize.
C)It has multiple local maxima.
D)It has a single global maximum.

Question 32

Revenue management methodology was originally developed for

A)a cruise line.
B)an airline.
C)a car rental company.
D)a hotel chain.

Question 33

The objective for the Markowitz portfolio model is to minimize portfolio return variance.

Question 34

A linear programming application used to measure the relative efficiency of operating units with the same goals and objectives is

A)game theory.
B)asset allocation.
C)revenue management.
D)data envelopment analysis.

Question 35

The composite unit in data envelopment analysis

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 36

If the coefficient of each squared term in a quadratic function is positive,the function is

A)concave.
B)convex.
C)elliptical.
D)sinusoidal.

Question 37

A convex function is

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

Question 38

Revenue management methodology enables an airline to

A)maximize the number of full-fare seats it sells on each flight.
B)minimize the number of discount-fare seats it sells on each flight.
C)increase the average number of passengers per flight.
D)decrease the number of overbooked flights.

Question 39

Revenue management methodology enables an airline to maximize the number of full-fare seats it sells on each flight.

Question 40

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

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

Question 41

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

Question 42

Native Customs sells two popular styles of hand-sewn footwear: a sandal and a moccasin.The cost to make a pair of sandals is $18,and the cost to make a pair of moccasins is $24.The demand for these two items is sensitive to the price,and historical data indicate that the monthly demands are given by S = 400 − 10P₁ and M = 450 − 15P₂ ,where S = demand for sandals (in pairs),M = demand for moccasins (in pairs),P₁ = price for a pair of sandals,and P₂ = price for a pair of moccasins.To remain competitive,Native Customs must limit the price (per pair)to no more than $60 and $75 for its sandals and moccasins,respectively.Formulate this nonlinear programming problem to find the optimal production quantities and prices for sandals and moccasins that maximize total monthly profit.

Question 43

List several types of organizations with multiple operating units where data envelopment analysis might be applied and give examples of possible inputs and outputs for each organization.​

Question 44

Portfolio manager Max Gaines needs to develop an investment portfolio for his clients who are willing to accept a moderate amount of risk.His task is to determine the proportion of the portfolio to invest in each of the five mutual funds listed below so that the portfolio provides an annual return of no less than 3%.Formulate the appropriate linear program.

Question 45

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:
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.

a.Define the decision variables.
b.Formulate a linear programming model for this revenue management application.

Question 46

The output shows the solution to a DEA model where facilities in Seaview (S),Farmington (F),Lewiston (L),and San Domingo (D)are compared.The inputs,in order,are number of machines,size of work force,and goodness of location.The outputs,in order,are production,quality rating,and on-time completion percentage.The model examines the efficiency of Lewiston.
OPTIMAL SOLUTION
Objective Function Value = 0.510

a.Is the Lewiston plant efficient? Why or why not? If not,which plants should it emulate in order to improve?
b.How much more production does the composite facility provide than the Lewiston site?
c.What is the quality rating for the composite facility?

Question 47

Explain the differences between the LP formulations for a conservative portfolio and moderate-risk portfolio.​

Question 48

Mountainside State Park has four visitor centers.To study the operation of these centers,a DEA model has been developed that compares inputs (size,number of staff,weekly hours of operation)and outputs (% of visitors attending educational program,daily sales in gift shop).The computer solution is shown below.What can you conclude about the efficiency of the North center?
LINEAR PROGRAMMING PROBLEM
OPTIMAL SOLUTION
Objective Function Value = 1.000

Question 49

Skooter's Skateboards produces two models of skateboards,the FX and the ZX.Skateboard revenue (in $l,000s)for the firm is nonlinear and is stated as (number of FXs)(5 − 0.2 number of FXs)+ (number of ZXs)(7 − 0.3 number of ZXs).Skooter's has 80 labor-hours available per week in its paint shop.Each FX requires 2 labor-hours to paint and each ZX requires 3 labor-hours.Formulate this nonlinear production planning problem to determine how many FX and ZX skateboards should be produced per week at Scooter's.

Question 50

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
Develop the DEA model that would evaluate the efficiency of Ralston Elementary School.

Question 51

MegaSports,Inc.produces two high-priced metal baseball bats,the Slugger and the Launcher,that are made from special aluminum and steel alloys.The cost to produce a Slugger bat is $100,and the cost to produce a Launcher bat is $120.We can not assume that MegaSports will sell all the bats it can produce.As the selling price of each bat model - Slugger and Launcher - increases,the quantity demanded for each model goes down.
Assume that the demand,S,for Slugger bats is given by S = 640 − 4P_S and the demand,L,for Launcher bats is given by L = 450 − 3PL where P_S is the price of a Slugger bat and P_L is the price of a Launcher bat.The profit contributions are P_SS − 100S for Slugger bats and P_LL − 120L for Launcher bats.Develop the total profit contribution function for this problem.

Question 52

Provide several examples of both nonlinear objective functions and nonlinear constraints.​

Question 53

List several industries in which revenue management has been applied and list several different types of decisions being made with the aid of the methodology.​

Question 54

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.

Question 55

Explain the logic of a DEA model.On what basis can the facility being evaluated be judged as relatively inefficient?​

Question 56

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