Deck 14: Optimization Models

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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 15

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

Question 16

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 17

Multiple optimal solutions are quite common in linear programming models.

Question 18

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 19

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

Question 20

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

Question 21

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 22

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 23

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

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

Question 24

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

A) Flow out
$\geq$ Flow in + Net supply
B) Flow in
$\geq$ Flow out + Net demand
C) Flow in = Flow out
D) Flow in
$\leq$ Flow out + Net demand
E) Flow out
$\leq$ Flow in + Net demand

Question 25

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 26

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 27

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 28

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

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

Question 29

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

Question 30

If $X _ { \text {iij } }$
Refers to the number of hours employee $f$
Works in week $\int$
,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)
$X _ { 11 } + X _ { 12 } + X _ { 13 } + X _ { 14 } \leq 160$
B)
$X _ { 13 } + X _ { 23 } + X _ { 33 } + { } _ { 43 } \leq 160$
 
C)
$X _ { 31 } + X _ { 32 } + X _ { 33 } + X _ { 34 } \leq 160$
D)
$X _ { 43 } \leq 160$

Question 31

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 32

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

Question 33

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

Question 34

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

Question 35

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 36

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

Question 37

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

Question 38

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 39

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

Question 40

The optimal solution to an LP problem was $X _ { 1 }$
3.69 and $X _ { 2 }$
1.21.If $X _ { 1 }$
and $X _ { 2 }$
were restricted to be integers,then $X _ { 1 }$
= 4 and $X _ { 2 } =$
1 will be a feasible solution,but not necessarily an optimal solution to the IP problem.

Question 41

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

A) Flow in
$\geq$ Flow out + Net supply
B) Flow out
$\geq$ Flow in + Net supply
C) Flow in = Flow out
D) Flow out
$\leq$ Flow in + Net supply
E) Flow in
$\leq$ Flow out + Net demand

Question 42

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 43

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 44

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 45

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

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

Question 46

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 47

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 48

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

Question 49

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 50

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 51

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

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

Question 52

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 53

To specify that $X _ { 1 }$
Must be at most 75% of the blend of $X _ { 1 } , X _ { 2 } , \text { and } X _ { 3 }$
We must have a constraint of the form

A)
$X _ { 1 } \geq 0.75 \left( X _ { 2 } + X _ { 3 } \right)$
B)
$X _ { 1 } \leq 0.25 \left( X _ { 1 } + X _ { 2 } + X _ { 3 } \right)$
C)
$X _ { 1 } \leq 0.75 \left( X _ { 1 } + X _ { 2 } + X _ { 3 } \right)$
D)
$0.75 X _ { 1 } \geq X _ { 1 } + X _ { 2 } + X _ { 3 }$
E)
$.25 X _ { 1 } \geq 0.75 \left( X _ { 2 } + X _ { 3 } \right)$

Question 54

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

Question 55

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 56

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 57

The decision variables in transportation problems are:

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

Question 58

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

A) Flow in
$\geq$ Flow out + Net supply
B) Flow out
$\geq$ Flow in + Net demand
C) Flow in = Flow out
D) Flow out
$\leq$ Flow in + Net supply
E) Flow in
$\leq$ Flow out + Net demand

Question 59

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 60

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 61

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 62

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 63

The objective in transportation problems is typically to:

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