Deck 14: Optimization Modeling: Applications

Question 1

If refers to the number of hours employee works in week ,then to indicate that the number of working hours of 4 employees in week 3 should not exceed 160 hours,we must have a constraint of the form

A)
B)
C)
D)

Answer 1

B

Question 2

Which of the following statements are false?

A)Solver does not offer a sensitivity report for models with integer constraints
B)Solver's sensitivity report is not suited for questions about multiple input changes
C)Solver's sensitivity report is used primarily for questions about one-at-a time changes to input
D)None of these options

Answer 2

D

Question 3

A typical transportation problem requires which of the following sets of input numbers:

A)Capacities,demands and flows
B)Capacities,demands and unit shipping costs
C)Supplies,demands and flows
D)Supplies,demands and arcs

Answer 3

B

Question 4

The problem which deals with the direct distribution of products from supply locations to demand locations is called a(n)

A)transportation problem
B)assignment problem
C)network problem
D)transshipment problem

Question 5

A common characteristic of integer programming models is that they:

A)are easy to solve graphically
B)produce the same answer and standard linear programming models
C)often produce multiple optimal solutions
D)all of these options

Question 6

In a network representation of a transportation problem,the nodes generally represent:

A)warehouses
B)geographic locations
C)flows
D)capacities

Question 7

In formulating a transportation problem as linear programming model,which of the following statements are correct?

A)There is one constraint for each supply location
B)There is one constraint for each demand location
C)The sum of decision variables out of a supply location is constrained by the supply at that location
D)The sum of decision variables out of all supply locations to a specific demand location is constrained by the demand at that location
E)All of these options

Question 8

Which of the following statements is a type of constraint that is often required in blending problems?

A)Integer constraint
B)Binary constraint
C)Quality constraint
D)None of these options

Question 9

Many organizations must determine how to schedule employees to provide adequate service.If we assume that an organization faces the same situation each week,this is referred to as

A)static scheduling problem
B)dynamic scheduling problem
C)transportation scheduling problem
D)All of these options

Question 10

Which of the following is true regarding multiple optimal solutions?

A)All solutions have the same values for the decision variables
B)All solutions have the same value for the objective function
C)All solutions have the same shadow prices
D)All of these options

Question 11

The constraints in a blending problem can be specified in a valid way and still lead to which of the following problems?

A)Unboundedness
B)Infeasibility
C)Nonlinearity
D)None of these options

Question 12

Which of the following is not a required input for a typical transportation problem?

A)Capacities (or supplies)
B)Demands
C)Unit shipping (and possibly production)costs
D)Distance from origins to destinations

Question 13

To specify that must be at most 75% of the blend of , ,and ,we must have a constraint of the form

A)
B)
C)
D)
E)

Question 14

The decision variables in transportation problems are:

A)profits
B)costs
C)flows
D)capacities

Question 15

Many organizations must determine how to schedule employees to provide adequate service.If we assume that an organization faces the same situation each week,this is referred to as

A)static scheduling problem
B)dynamic scheduling problem
C)transportation scheduling problem
D)All of these options

Question 16

The objective in transportation problems is typically to:

A)maximize profits
B)maximize revenue
C)minimize costs
D)maximize feasibility

Question 17

Rounding the solution of a linear programming to the nearest integer values provides a(n)

A)integer solution that is optimal
B)integer solution that may be neither feasible nor optimal
C)feasible solution that is not necessarily optimal
D)infeasible solution

Question 18

Workforce scheduling problems are often integer programming models,which means that they have:

A)an integer objective function
B)integer decision variables
C)integer constraints
D)all of these options

Question 19

In a network representation of a transportation problem,the arcs generally represent:

A)warehouses
B)geographic locations
C)flows
D)capacities

Question 20

Which of the following does not represent a broad class of applications of linear programming models?

A)Blending models
B)Financial portfolio models
C)Logistics models
D)Set covering models
E)Forecasting models

Question 21

In a transshipment problem,shipments

A)can occur between any two nodes (suppliers,demanders,and transshipment locations)
B)cannot occur between two supply locations
C)cannot occur between two demand locations
D)cannot occur between a transshipment location and a demand location
E)cannot occur between a supply location and a demand location

Question 22

Solver may be unable to solve some integer programming problems,even when they have an optimal solution.

Question 23

A minimum cost network flow model (MCNFM)has the following advantage relative to the special case of a simple transportation model:

A)a MCNFM does not require capacity restrictions on the arcs of the network
B)the flows in a general MCNFM don't all necessarily have to be from supply locations to demand locations
C)a MCNFM is generally easier to formulate and solve
D)All of these options

Question 24

Integer programming (IP)models are optimization models in which all of the variables must be integers.

Question 25

The flow balance constraint for each transshipment node,in a minimum cost network flow model,takes the form

A)Flow in Flow out + Net supply
B)Flow out Flow in + Net supply
C)Flow in = Flow out
D)Flow out Flow in + Net supply
E)Flow in Flow out + Net demand

Question 26

Transportation and transshipment problems are both considered special cases of a class of linear programming problems called

A)minimum cost problems
B)minimum cost network flow problems
C)supply locations network problems
D)demand locations network problems

Question 27

In a minimum cost network flow model,the flow balance constraint for each supply node takes the form

A)Flow in Flow out + Net supply
B)Flow out Flow in + Net demand
C)Flow in = Flow out
D)Flow out Flow in + Net supply
E)Flow in Flow out + Net demand

Question 28

In nonlinear models,which of the following statements are correct?

A)Only the objective function is not a linear function of the decision variables
B)Only the constraints are not linear functions of the decision variables
C)The objective function and/or the constraints are not linear functions of the decision variables
D)All of these options

Question 29

In a typical minimum cost network flow model,the nodes indicate

A)roads
B)rail lines
C)geographic locations
D)rivers

Question 30

If an LP problem is not correctly formulated,Solver will automatically indicate that it is infeasible when trying to solve it.

Question 31

Many of the most successful applications of optimization in the real world have been in the areas of scheduling,blending,logistics and aggregate planning.

Question 32

If Solver fails to find an optimal solution to an integer programming problem,we might be able to find a near optimal solution by increasing the tolerance setting.

Question 33

In a minimum cost network flow model,the flow balance constraint for each demand node takes the form

A)Flow out Flow in + Net supply
B)Flow in Flow out + Net demand
C)Flow in = Flow out
D)Flow in Flow out + Net demand
E)Flow out Flow in + Net demand

Question 34

The binary variables in the fixed cost models correspond to:

A)the number of units or products produced
B)the total profit
C)the amount of labor hours
D)a process for which a fixed cost occurs

Question 35

In aggregate planning models,which of the following statements are correct?

A)The number of workers available influences the possible production levels
B)We allow the workforce level to be modified each month through the hiring and firing of workers
C)We eventually allow demand to be backlogged; that is,demand need not be met on time
D)All of these options

Question 36

Any integer program involving 0 - 1 variables with constraint(s)is called a knapsack problem.

A)three
B)two
C)one
D)zero

Question 37

Multiple optimal solutions are quite common in linear programming models.

Question 38

The optimal solution to an LP problem was 3.69 and 1.21.If and were restricted to be integers,then 4 and 1 will be a feasible solution,but not necessarily an optimal solution to the IP problem.

Question 39

The LP relaxation of an integer programming (IP)problem is the same model as the IP model except that some integer constraints are omitted.

Question 40

When we solve a linear programming problem with Solver,we cannot guarantee that the solution obtained is an optimal solution.

Question 41

Transshipment points are locations where goods neither originate nor end up,but goods are allowed to enter such points to be shipped out to their eventual destinations.

Question 42

In transportation problems,the three sets of input numbers that are required are capacities,demands and flows.

Question 43

A good shipping plan uses as many cheap routes as possible,but ultimately is constrained by capacities and demands.

Question 44

In network models of transportation problems,arcs represent the routes for getting a product from one node to another.

Question 45

In transportation problems,shipping costs are often nonlinear due to quantity discounts.

Question 46

A 0-1 variable,also called a binary variable,is a variable that must equal 0 or 1.

Question 47

Logistics problems are problems of finding the least expensive way to transport products from their origin to their destination.

Question 48

In a set-covering model,each member of a given set (set 1)must be "covered" by an acceptable member of another set (set 2).The objective of such problems is to minimize the number of elements in set 2 that are needed to cover all the elements in set 1.

Question 49

Aggregate planning models are usually implemented through a rolling planning horizon.

Question 50

In aggregate planning models,the number of workers available influences the possible production levels.

Question 51

In an optimized network flow model (MCNFM),all the available capacity will be used.

Question 52

A nonlinear programming problem (NLP)is an optimization problem in which the objective function and/or the constraints are not linear functions of the decision variables.

Question 53

The transportation model is a special case of the minimum cost network flow model (MCNFM).

Question 54

If all the supplies and demands for a transportation model are integers,then the optimal Solver solution may or may not have integer-valued shipments.

Question 55

Any integer programming problem involving 0-1 variables with only one constraint is called a knapsack problem.

Question 56

In blending problems,if a quality constraint involves a quotient,then the problem will be nonlinear.

Question 57

In transportation problems,shipments between supply points or between demand points are possible.

Question 58

In aggregate planning models,we can model backlogging of demand by allowing a month's inventory to be negative.

Question 59

In a transportation problem,if it costs $4 per item to ship up to 200 items between cities,and $2 per item for each additional item,the proportionality assumption of LP is satisfied.

Question 60

The flows in a general minimum cost network flow model (MCNFM)do all necessarily have to be from "left to right"; that is,from supply points to demand points.

Question 61

A company is considering investing a total amount of $2.50 million in four bonds.The expected annual return,the worst-case annual return on each bond,and the "duration" of each bond are given in the table below.
The duration of a bond is a measure of the bond's sensitively to interest rates.The company wants to maximize the expected return from its bond investments,subject to the following constraints:
-The worst-case return of the bond portfolio must be at least 90%.
-The average duration of the portfolio must be at most 7
-Because of diversification requirements,at most 35% of the total amount invested in a single bond.
Determine how the company can maximize the expected return on its investment.

Question 62

Assume that you are given the following means,standard deviations,and correlations for the annual return on three stocks.
The correlation between stocks 1 and 2 is 0.62,between stocks 1 and 3 is 0.72,and between stocks 2 and 3 is 0.39.You have $12,000 to invest and can invest no more than 55% of your money in any single stock.Determine the minimum variance portfolio that yields an expected annual return of at least 0.15

Question 63

A statistician is currently trying to maximize his profit in the bond market.Four bonds are available for purchase and sale at the bid and ask prices shown in the table below.The statistician can buy up to 1300 units of each bond at the ask price or sell up to 1300 units of each bond at the bid price.During each of the next three years the person who sells a bond will pay the owner of the bond the cash payments that are also shown in the table below.The statistician's goal is to maximize his revenue from selling bonds less his payments for buying bonds,subject to the constraint that after each year's payments are received,his current cash position (due only to cash payments from bonds and not purchases or sales of bonds)is nonnegative.His current cash position can depend on past coupons and that cash accumulated at the end of each year earns 12% annual interest.Determine how to maximize net profit from buying and selling bonds,subject to the constraints previously described.

Question 64

An oil delivery truck contains five compartments,holding up to 2800,2900,1200,1800,and 3200 gallons of fuel,respectively.The company must deliver three types of fuel (super,regular,and unleaded)to a customer.The demands,penalty per gallon short,and the maximum allowed shortage are shown in the table below.Each compartment of the truck can carry only one type of gasoline.Determine how to load the truck in a way that minimizes shortage costs.

Question 65

Suppose that on Monday morning you have $5000 in cash on hand.For the following seven days,the following cash requirements must be met: Monday,$6,000; Tuesday,$7,000; Wednesday,$10,000; Thursday,$3,000; Friday,$8,000; Saturday,$3,000; Sunday,$4,000.At the beginning of each day,you must decide how much money (if any)to withdraw from the bank.It costs $8 to make a withdrawal of any size.You believe that the opportunity cost of having $1 of cash on hand for a year is $0.25.Assume that opportunity costs are incurred on each day's ending balance.Determine how much money you should withdraw from the bank during each of the next 7 days.

Question 66

Chemical Bank is attempting to determine where its assets should be invested during the current year.At present,$800,000 is available for investment in bonds,home loans,auto loans,and personal loans.The annual rate of return on each type of investment is known to be the following: bonds,12%,home loans,18%,auto loans,15%,personal loans,22%.To ensure that the banks portfolio is not too risky,the bank's investment manager has placed the following restrictions on the bank portfolio:
-No more than 30% of the total amount invested may be in personal loans
-The amount invested in home loans cannot exceed the amount invested in auto loans
-The amount invested in personal loans cannot exceed the amount invested in bonds.
Determine how the bank can maximize the annual return on its investment portfolio.

Question 67

When we solve a nonlinear programming problem (NLP),it is very possible that Solver will obtain the wrong answer.

Question 68

(A)Use Solver to formulate and solve the post office's problem.
(B)Suppose the post office has 30 full-time employees and is not allowed to hire or fire any employees.Determine a schedule that maximizes the number of weekend days off received by the employees.

Question 69

A company has daily staffing requirements for two types of jobs,cleaning and customer service persons.The minimum numbers of workers required each day for each type of job are shown in the table below.To meet these requirements,the company can employ three types of workers: those who clean only,those who can perform customer service only,and those who are able to do both.In each of these three categories,the company wants to meet its daily requirements using only full-time workers.A full-time worker must work five consecutive days with two days off.Workers who are able to perform only one type of work (cleaning or customer service)earn $50 per day.Those who are able to perform both types of work earn $60 per day.As a matter of policy,the company wants to ensure that at least 20% of its total hours are staffed by "swing workers"; those who can do both types of jobs.The company wants to find a staffing policy that covers the daily worker requirements at minimum total costs per week.Use solver to formulate and solve the company's problem.

Question 70

For some types of integer programming problems,their LP relaxation solutions are optimal.

Question 71

Determine how to minimize the sum of shortage and shipping costs.

Question 72

An auto company must meet (on time)the following demands for cars: 5000 in quarter 1; 3000 in quarter 2; 6000 in quarter 3; 2000 in quarter 4.At the beginning of quarter 1,there are 500 autos in stock.The company has the capacity to produce at most 3600 cars per quarter.At the beginning of each quarter,the company can change production capacity.It costs $125 to increase quarterly production capacity by one unit.It also costs $60 per quarter to maintain each unit of production capacity (even if it is unused during the current quarter).The variable cost of producing a car is $2400.A holding cost of $200 per car is assessed against each quarter's ending inventory.It is required that at the end of quarter 4,plant capacity must be at least 5000 cars.Determine how to minimize the total cost incurred during the next four quarters.

Question 73

A local optimal solution is better than all nearby solutions,but a solution far away might be better than it.

Question 74

A Michigan company consists of three subsidiaries.Each has the respective average payroll,unemployment reserve fund,and estimated payroll shown in the table below (all figures are in millions of dollars).Any employer in the state of Michigan whose reserve to average payroll ratio is less than 1 must pay 25% of its estimated payroll in unemployment insurance premiums.Otherwise,if the ratio is at least one,the employer pays 13%.The company can aggregate its subsidiaries and label them as separate employers.For example,if subsidiaries 1 and 2 are aggregated,they must pay 25% of their combined payroll in unemployment insurance premiums.Determine which subsidiaries should be aggregated.

Question 75

(A)Determine how to minimize the cost of meeting demands at Dallas and Orlando
(B)Modify the answer to (A)if shipments between Los Angeles and Detroit are not allowed.

Question 76

A global optimal solution is not necessarily the best solution overall.

Question 77

A company manufactures two products.If it charges price for product ,it can sell units of product ,where and .It costs the company $20 to produce a unit of product 1 and $65 to produce a unit of product 2.How many units of each product should the company produce,and what prices should it charge,to maximize its profit?

Question 78

(A)Determine how to minimize the total (production plus distribution)costs of meeting the company's annual demand.
(B)How would you modify the model in (A)if at most 300 units can be shipped through Chicago?

Question 79

An electronic company is considering opening warehouses in New York,Los Angeles,Madison,and Tampa.Each warehouse can ship 125 units per week.The weekly fixed cost for keeping each warehouse open is $500 for New York,$600 for Los Angeles,$400 for Madison,and $200 for Tampa.Region 1 of the country requires 90 units per week,region 2 requires 80 units per week,and region 3 requires 50 units per week.The costs (including production and shipping costs)of sending one unit from a plant to a region are shown in the table below.
Show how the company can meet weekly demands at a minimum cost,subject to the above information and the following restrictions: If the New York warehouse is opened,then Los Angeles must be opened. At most two warehouses can be opened. Either the Tampa or the Los Angeles warehouses must be opened.

Question 80

Suppose that the company can purchase and ship extra units to either warehouse for a total cost of $125 per unit and that all customer demand must be met.Determine how to minimize the sum of purchasing and shipping costs.