Question 1

The default value of suboptimality tolerance in Solver is ​1%

Accepted Answer

A) True 
 B)False

Question 2

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below.   ​
Based on this ILP formulation of the problem what formulas should go in cells B13:B16, B20:E20, F20, and F23:F24 of the following Excel spreadsheet?
Let Xi = 1 if truck located in zone i, 0 otherwise   ​   ​

Accepted Answer

Question 3

​A problem in which some decision variables are restricted to assuming only integer values is called a 0-1 programming problem.

Accepted Answer

A) True 
 B)False

Question 4

The B & B algorithm solves ILP problems

Accepted Answer

A)  by solving for each variable separately. 
B)  by solving for the integer variables first. 
C)  by solving a series of LP problems. 
D)  by solving smaller ILP problems. 
A)  by solving for each variable separately. 
B)  by solving for the integer variables first. 
C)  by solving a series of LP problems. 
D)  by solving smaller ILP problems.

Question 5

How are binary variables specified in the Analytic Solver Platform (ASP)?

Accepted Answer

A)  By replacing RHS values in constraints with 0 or 1. 
B)  By specifying changing cells as INTEGER and as non-negative. 
C)  By specifying changing cells as BINARY in the Variable Type/Bound area of ASP. 
D)  By selecting Assume Binary Model in the ASP Options dialog box. 
A)  By replacing RHS values in constraints with 0 or 1. 
B)  By specifying changing cells as INTEGER and as non-negative. 
C)  By specifying changing cells as BINARY in the Variable Type/Bound area of ASP. 
D)  By selecting Assume Binary Model in the ASP Options dialog box.

Question 6

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table:   Formulate the ILP for this problem.

Accepted Answer

The answer of A cellular phone company wants to locate...

Question 7

A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.   The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
Formulate the ILP for this problem capturing the ship choice of ports and the supply-to-demand transportation from the ports to the destinations.

Accepted Answer

The answer of A certain military deployment requires supplies delivered...

Question 8

Consider the constraint ​
X3 + X4 + X5 + X6 + X7 ≥ 27
​
Representing Air Express' Monday minimum worker requirement. Why was a "≥" used versus an "="?

Accepted Answer

A)  The "≥" is needed to accommodate workers held over from Sunday. 
B)  Solver only accepts "≥" constraints. 
C)  The "≥" is less restrictive. 
D)  The "=" will always produce an infeasible constraint. 
A)  The "≥" is needed to accommodate workers held over from Sunday. 
B)  Solver only accepts "≥" constraints. 
C)  The "≥" is less restrictive. 
D)  The "=" will always produce an infeasible constraint.

Question 9

A wedding caterer has several wine shops from which it can order champagne. The caterer needs 100 bottles of champagne on a particular weekend for 2 weddings. The first supplier can supply either 40 bottles or 90 bottles. ​
The relevant decision variable is defined as
​
X1 = the number of bottles supplied by supplier 1
​
Which set of constraints reflects the fact that supplier 1 can supply only 40 or 90 bottles?

Accepted Answer

A)  X1 ≤ 40 Y11, X1 ≤ 90(1 − Y11) 
B)  X1 = 40Y11 + 90Y12, Y11 + Y12 ≤ 1 
C)  X1 = 40Y1 + 90(1 − Y1), Y1 = 0 OR 1 
D)  X1 = 40Y11 + 90Y12, Y11 + Y12 = 1 
A)  X1 ≤ 40 Y11, X1 ≤ 90(1 − Y11) 
B)  X1 = 40Y11 + 90Y12, Y11 + Y12 ≤ 1 
C)  X1 = 40Y1 + 90(1 − Y1), Y1 = 0 OR 1 
D)  X1 = 40Y11 + 90Y12, Y11 + Y12 = 1

Question 10

For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

Accepted Answer

A)  An upper bound. 
B)  A lower bound. 
C)  An alternative optimal solution. 
D)  An additional constraint for the ILP problem. 
A)  An upper bound. 
B)  A lower bound. 
C)  An alternative optimal solution. 
D)  An additional constraint for the ILP problem.

Question 11

Exhibit 6.2
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.   The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
The following is the ILP formulation and a spreadsheet model for the problem.    
-Refer to Exhibit 6.2. What formula would go into cells G8:G10?

Accepted Answer

The answer of Exhibit 6.2
The following questions pertain to the...

Question 12

How are general integrality requirements indicated in the Analytic Solver Platform?

Accepted Answer

A)  Specifying the INT option for the appropriate changing cells. 
B)  Specifying the INT option for the constraint rows. 
C)  Adding additional RHS values to constraints. 
D)  Choosing the BIN setting in the Value field in the Solver Parameters dialog box. 
A)  Specifying the INT option for the appropriate changing cells. 
B)  Specifying the INT option for the constraint rows. 
C)  Adding additional RHS values to constraints. 
D)  Choosing the BIN setting in the Value field in the Solver Parameters dialog box.

Question 13

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as

Accepted Answer

A)  quickest solution method. 
B)  LP satisficing. 
C)  LP relaxation. 
D)  LP approximation. 
A)  quickest solution method. 
B)  LP satisficing. 
C)  LP relaxation. 
D)  LP approximation.

Question 14

The concept of a lower bound in IP is associated with:

Accepted Answer

A)  LP relaxation of a minimization problem 
B)  LP relaxation of a maximization problem 
C)  a cutting plane technique 
D)  explicit enumeration of corner point solutions 
A)  LP relaxation of a minimization problem 
B)  LP relaxation of a maximization problem 
C)  a cutting plane technique 
D)  explicit enumeration of corner point solutions

Question 15

Exhibit 6.2
The following questions pertain to the problem, formulation, and spreadsheet implementation below.
A certain military deployment requires supplies delivered to four locations. These deliveries come from one of three ports. Logistics planners wish to deliver the supplies in an efficient manner, in this case by minimizing total ton-miles. The port-destination data, along with destination demand is provided in the following table.   The ports are supplied by one of two supply ships. These ships travel to a particular port where their supplies are off-loaded and shipped to the requesting destinations. Ship S1 carries 1200 tones of supplies while Ship S2 carries 1120 tons of supplies. These ships can only go to a single port and each port can only accommodate one ship. Assume the costs for a ship to travel to a port are not part of the objective function.
The following is the ILP formulation and a spreadsheet model for the problem.    
-Refer to Exhibit 6.2. What formula would go into cells B11:E11 and cells F8:F10?

Accepted Answer

The answer of Exhibit 6.2
The following questions pertain to the...

Question 16

A company will be able to obtain a quantity discount on component parts for its three products, X1, X2 and X3 if it produces beyond certain limits. To get the X1 discount it must produce more than 50 X1's. It must produce more than 60 X2's for the X2 discount and 70 X3's for the X3 discount. How many binary variables are required in the formulation of this problem?

Accepted Answer

A)  3 
B)  6 
C)  9 
D)  12 
A)  3 
B)  6 
C)  9 
D)  12

Question 17

One way to find an optimal solution to the IP problem is to:

Accepted Answer

A)  use a B&B technique 
B)  use LP relaxation and round the values of the decision variables up to the nearest integer value 
C)  use LP relaxation and round the values of the decision variables down to the nearest integer value 
D)  use LP relaxation and round 50 percent of the decision variable values down to the nearest integer value and the remaining 50 percent up to the nearest integer value 
A)  use a B&B technique 
B)  use LP relaxation and round the values of the decision variables up to the nearest integer value 
C)  use LP relaxation and round the values of the decision variables down to the nearest integer value 
D)  use LP relaxation and round 50 percent of the decision variable values down to the nearest integer value and the remaining 50 percent up to the nearest integer value

Question 18

The ILP problems are computationally

Accepted Answer

A)  more demanding than their LP relaxations 
B)  less demanding than their LP relaxations 
C)  equally demanding compared to their LP relaxations 
D)  less complex than the corresponding LP problems 
A)  more demanding than their LP relaxations 
B)  less demanding than their LP relaxations 
C)  equally demanding compared to their LP relaxations 
D)  less complex than the corresponding LP problems

Question 19

A company produces three products which must be painted, assembled, and inspected. The machinery must be cleaned and adjusted before each batch is produced. They want to maximize their profits for the amount of operating time they have. The unit profit and setup cost per batch are:   The operation time per unit and total operating hours available are:   Formulate the ILP for this problem.

Accepted Answer

Xi = amount of produ

Question 20

A company is planning next month's production. It has to pay a setup cost to produce a batch of X4's so if it does produce a batch it wants to produce at least 100 units. Which of the following pairs of constraints show the relationship(s) between the setup variable Y4 and the production quantity variable X4?

Accepted Answer

A)  X4 ≤ M4Y4, X4 ≥ 100 
B)  X4 ≤ M4Y4, X4 = 100 Y4 
C)  X4 ≤ M4Y4, X4 ≥ 100 Y4 
D)  X4 ≤ M4Y4, X4 ≤ 100 Y4 
A)  X4 ≤ M4Y4, X4 ≥ 100 
B)  X4 ≤ M4Y4, X4 = 100 Y4 
C)  X4 ≤ M4Y4, X4 ≥ 100 Y4 
D)  X4 ≤ M4Y4, X4 ≤ 100 Y4

The default value of suboptimality tolerance in Solver is 1%

A problem in which some decision variables are restricted to assuming only integer values is called a 0-1 programming problem.

The B & B algorithm solves ILP problems

How are binary variables specified in the Analytic Solver Platform (ASP)?

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table: Formulate the ILP for this problem.

Consider the constraint X₃ + X₄ + X₅ + X₆ + X₇ ≥ 27 Representing Air Express' Monday minimum worker requirement. Why was a "≥" used versus an "="?

For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

How are general integrality requirements indicated in the Analytic Solver Platform?

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as

The concept of a lower bound in IP is associated with:

One way to find an optimal solution to the IP problem is to:

The ILP problems are computationally

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Goal Programming and Multiple Objective Optimization

Nonlinear Programming Evolutionary Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

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Exam 6: Integer Linear Programming

The default value of suboptimality tolerance in Solver is ​1%

​A problem in which some decision variables are restricted to assuming only integer values is called a 0-1 programming problem.

The B & B algorithm solves ILP problems

How are binary variables specified in the Analytic Solver Platform (ASP)?

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table: Formulate the ILP for this problem.

Consider the constraint ​ X3 + X4 + X5 + X6 + X7 ≥ 27 ​ Representing Air Express' Monday minimum worker requirement. Why was a "≥" used versus an "="?

For maximization problems, the optimal objective function value to the LP relaxation provides what for the optimal objective function value of the ILP problem?

How are general integrality requirements indicated in the Analytic Solver Platform?

One approach to solving integer programming problems is to ignore the integrality conditions and solve the problem with continuous decision variables. This is referred to as

The concept of a lower bound in IP is associated with:

One way to find an optimal solution to the IP problem is to:

The ILP problems are computationally

Introduction to Modeling and Decision Analysis

Introduction to Optimization and Linear Programming

Modeling and Solving Lp Problems in a Spreadsheet

Sensitivity Analysis and the Simplex Method

Network Modeling

Goal Programming and Multiple Objective Optimization

Nonlinear Programming Evolutionary Optimization

Regression Analysis

Data Mining

Time Series Forecasting

Introduction to Simulation Using Analytic Solver Platform

Queuing Theory

Decision Analysis

Project Management Online

Filters

The default value of suboptimality tolerance in Solver is 1%

A problem in which some decision variables are restricted to assuming only integer values is called a 0-1 programming problem.

Consider the constraint X₃ + X₄ + X₅ + X₆ + X₇ ≥ 27 Representing Air Express' Monday minimum worker requirement. Why was a "≥" used versus an "="?