Deck 12: Advanced Optimization Application

Question 1

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.

Answer 1

D

Question 2

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

Answer 2

False

Question 3

Revenue management methodology was originally developed for the banking industry.

Answer 3

False

Question 4

In portfolio models,risk is minimized by diversification.

Question 5

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

Question 6

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

Question 7

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

Question 8

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 9

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 10

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 11

Revenue management methodology was originally developed for

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

Question 12

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 13

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

Question 14

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 15

A convex function is

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

Question 16

Nonlinear programming algorithms are more complex than linear programming algorithms.

Question 17

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 18

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 19

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 20

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 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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

Question 27

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

Question 28

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 29

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

Question 30

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

Question 31

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

Question 32

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 33

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 34

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

Question 35

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 36

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 - 3P_L 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_S S - 100S for Slugger bats and P_L L - 120L for Launcher bats.Develop the total profit contribution function for this problem.

Question 37

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 38

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

Question 39

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

Question 40

An index fund is an example of passive asset management.

Question 41

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 42

Lymann Brothers has a substantial number of clients who wish to own a mutual fund portfolio that closely matches the performance of the S&P 500 stock index.A manager at Lymann Brothers has selected five mutual funds that will be considered for inclusion in the portfolio.The manager must decide what percentage of the portfolio should be invested in each mutual fund.
Minimize the variance of the portfolio subject to constraints on the expected return,assuming that Lymann Brothers' client requires the expected portfolio return to be at least 9 percent.