ISYE 251- Operations Research I- Spring 2022 Semester Project and Instructions Notes: 1. Formulate the LP models careful
Posted: Wed Apr 27, 2022 1:51 pm
ISYE 251- Operations Research I- Spring 2022 Semester Project
and Instructions
Notes:
1. Formulate the LP models carefully, considering all the
information provided
2. The implementation of the model can be using LINGO, Excel or
your preferred optimization package
3. Your final report should contain the mathematical model,
definitions of the decision variables, program code, results, your
interpretation of the results and sensitivity analysis
4. Please provide detailed answers to the questions that follow
each question using the output, I am interested to know the logical
interpretations and conclusions from the model output
5. Submissions are due on 02 May, 2022, In class
6. This is a group project (max. three students per group),
please submit only one report per group with the team member names
and ID numbers in the cover sheet.
7. Your project report must be typed or printed via word
processor. The body of the report should be written in complete
sentences, augmented by equations and calculations. The report must
contain a clear statement of each question as it is addressed,
explain what your conclusions are, and the calculations made and
reasoning used to reach those conclusions.
Model-1
Smartships, a leading Korean manufacturer of sailboats must
determine how many sailboats should be produced during each of the
next four quarters. The demand during each of the next four
quarters is as follows: first quarter, 40 sailboats; second
quarter, 60 sailboats; third quarter, 75 sailboats; fourth quarter,
25 sailboats. Smartships must meet the demands on time. At the
beginning of the first quarter, Smartships has an inventory of 10
sailboats. At the beginning of each quarter, Smartships must decide
how many sailboats should be produced during that quarter. For
simplicity, we assume that sailboats manufactured during a quarter
can be used to meet for that quarter. During each quarter,
Smartships can produce upto 40 sailboats with regular-time labor at
a total cost of $400 per sailboat. By having employees work
overtime during a quarter, Smartships can produce additional
sailboats with overtime labor at a total cos of $450 per
sailboat.
At the end of each quarter (after production has occurred and
the current quarters demand has been satisfied), a carrying or
holding cost of $20 per sailboat is incurred.
Page 1 of 5 Formulate a LP model to determine a production
schedule to minimize the sum of production and inventory costs
during the next four quarters. Solve the model using any
optimization package and use the output to answer the following
questions:
a) If month 1 demand decreased to 35 sailboats, what would be
the total cost of satisfying the demands during the next four
months?
b) If the cost of producing a sailboat with regular-time labor
during month 1 were $420, what would be the new optimal solution to
the problem?
c) Suppose a new customer is willing to pay $425 for a sailboat.
If his demand must be met during month 1, should Smartships fill
the order? How about if the demand must be met during month 4?
Model-2
Ittihad produces four product types, requiring time on two
machines and two types (skilled and unskilled) of labor. The amount
of machine time and labor (in hours) used by each product and the
sales prices are given in the table below:
Product
Machine 1
Machine 2
Skilled
Unskilled
Sales ($)
1
11
4
8
7
300
2
7
6
5
8
260
3
6
5
4
7
220
4
5
4
6
4
180
Each month, 700 hours are available on machine 1 and 500 hours
are available on machine 2. Each month, Ittihad can purchase up to
600 hours of skilled labor at $6 per hour. Formulate an LP model
that will maximize month profit for Ittihad. Solve the LP model and
use the output to answer the following questions:
a) By how much does the price of product 3 have to increase
before it becomes optimal to produce it?
b) If product 1 is sold for $290, then what would be the new
optimal solution to the problem?
c) What is the most Ittihad would be willing to pay for an extra
hour of time on each machine?
d) What is the most Ittihad would be willing to pay for an extra
hour of each type of labor?
e) If up to 700 hours of skilled labor could be purchased each
month, then what would be Ittihad monthly profits?
Page 2 of 5 Model-3
Cornco produces two products: PS and QT. The sales price for
each product and the maximum quantity of each that can be sold
during each of the next three months are given below:
Month 1
Month 2
Month 3
Product
Price
Demand
Price
Demand
Price
Demand
PS
40
50
60
45
55
50
QT
35
43
40
50
44
40
Each product must be processed through two assembly lines: 1 and
2. The number of hours required by each product on each assembly
line are given in table below:
Hours
Product
Line 1
Line 2
PS
3
2
QT
2
2
The number of hours available on each assembly line during each
month are given in table below:
Month
Line
1
2
3
1
1200
160
190
2
2140
150
110
Each unit of PS requires 4 pounds of raw material, each unit of
QT requires 3 pounds of raw material. As many as 710 units of raw
material can be purchased at $3 per pound. At the beginning of
month 1, 10 units of PS and 5 units of QT are available. It costs
$10 to hold a unit of either product in inventory for a month.
Formulate and solve the LP model use the output to answer the
following questions:
a) Find the new optimal solution if it costs $11 to hold a unit
of PS in inventory at the end of month 1
b) Find the company’s new optimal solution if 210 hours of line
1 are available during month 1
c) Find the company’s new profit level if 109 hours are
available on line 2
Page 3 of 5 during month 3
d) What is the most Cornco should be willing to pay for an extra
hour of line 1 time during month 2
e) What is the most Cornco should be willing to pay for an extra
pound of raw material
f) What is the most Cornco should be willing to pay for an extra
hour of line 1 time during month 3
g) Find the new optimal solution if PS sells for $50 during
month 2
h) Find the new optimal solution if QT sells for $50 during
month 3
i) Suppose spending $20 on advertising would increase demand for
QT in month 2 by 5 units. Should the advertising be done?
Model-4
A leading supply chain company has two factories located in
Shanghai and Brisbane that produce two types of steel castings,
GRD100 and GRD 200. Due to the growing business needs and expanding
opportunities the company would like to develop a LP model to
enable better decisions. Shanghai factory can produce 800 tons and
Brisbane factory can produce 1000 tons of steel castings. The
company can sell upto 900 tons of GRD100 and 900 tons of GRD200
grade steel. The profit associated with each production site and
sale is as follows:
Profit Per ton
Shanghai
Brisbane
GRD100
600
1000
GRD200
800
1300
Labor costs $20 per hour and a total of 4000 hours of skilled
labor is available per year. The skilled labor required for
production site differs and are given by the following table:
Labor Required per ton (in hours)
Shanghai
Brisbane
GRD100
2
3
GRD200
2
4
Formulate and computationally solve the LP model for the above
problem, obtain and interpret the optimal solution. Include
sensitivity analysis of various model parameters.
Using the output answer the following questions:
Page 4 of 5 a) If 3,000 hours of skilled labor were available,
what will be the profit
b) By how much would the profit for GRD200 produced in Brisbane
have to increase before the company would want to produce GRD200 in
Brisbane
c) What is the most the company should pay for an extra hour of
labor
ISYE 251- Operations Research I- Spring 2022 Semester Project and Instructions Notes: 1. Formulate the LP models carefully, considering all the information provided 2. The implementation of the model can be using LINGO, Excel or your preferred optimization package 3. Your final report should contain the mathematical model, definitions of the decision variables, program code, results, your interpretation of the results and sensitivity analysis 4. Please provide detailed answers to the questions that follow each question using the output, I am interested to know the logical interpretations and conclusions from the model output 5. Submissions are due on 02 May, 2022, In class 6. This is a group project (max. three students per group), please submit only one report per group with the team member names and ID numbers in the cover sheet. 7. Your project report must be typed or printed via word processor. The body of the report should be written in complete sentences, augmented by equations and calculations. The report must contain a clear statement of each question as it is addressed, explain what your conclusions are, and the calculations made and reasoning used to reach those conclusions. Model-1 Smartships, a leading Korean manufacturer of sailboats must determine how many sailboats should be produced during each of the next four quarters. The demand during each of the next four quarters is as follows: first quarter, 40 sailboats; second quarter, 60 sailboats; third quarter, 75 sailboats; fourth quarter, 25 sailboats. Smartships must meet the demands on time. At the beginning of the first quarter, Smartships has an inventory of 10 sailboats. At the beginning of each quarter, Smartships must decide how many sailboats should be produced during that quarter. For simplicity, we assume that sailboats manufactured during a quarter can be used to meet for that quarter. During each quarter, Smartships can produce upto 40 sailboats with regular-time labor at a total cost of $400 per sailboat. By having employees work overtime during a quarter, Smartships can produce additional sailboats with overtime labor at a total cos of $450 per sailboat. At the end of each quarter (after production has occurred and the current quarters demand has been satisfied), a carrying or holding cost of $20 per sailboat is incurred. Page 1 of 5
and Instructions
Notes:
1. Formulate the LP models carefully, considering all the
information provided
2. The implementation of the model can be using LINGO, Excel or
your preferred optimization package
3. Your final report should contain the mathematical model,
definitions of the decision variables, program code, results, your
interpretation of the results and sensitivity analysis
4. Please provide detailed answers to the questions that follow
each question using the output, I am interested to know the logical
interpretations and conclusions from the model output
5. Submissions are due on 02 May, 2022, In class
6. This is a group project (max. three students per group),
please submit only one report per group with the team member names
and ID numbers in the cover sheet.
7. Your project report must be typed or printed via word
processor. The body of the report should be written in complete
sentences, augmented by equations and calculations. The report must
contain a clear statement of each question as it is addressed,
explain what your conclusions are, and the calculations made and
reasoning used to reach those conclusions.
Model-1
Smartships, a leading Korean manufacturer of sailboats must
determine how many sailboats should be produced during each of the
next four quarters. The demand during each of the next four
quarters is as follows: first quarter, 40 sailboats; second
quarter, 60 sailboats; third quarter, 75 sailboats; fourth quarter,
25 sailboats. Smartships must meet the demands on time. At the
beginning of the first quarter, Smartships has an inventory of 10
sailboats. At the beginning of each quarter, Smartships must decide
how many sailboats should be produced during that quarter. For
simplicity, we assume that sailboats manufactured during a quarter
can be used to meet for that quarter. During each quarter,
Smartships can produce upto 40 sailboats with regular-time labor at
a total cost of $400 per sailboat. By having employees work
overtime during a quarter, Smartships can produce additional
sailboats with overtime labor at a total cos of $450 per
sailboat.
At the end of each quarter (after production has occurred and
the current quarters demand has been satisfied), a carrying or
holding cost of $20 per sailboat is incurred.
Page 1 of 5 Formulate a LP model to determine a production
schedule to minimize the sum of production and inventory costs
during the next four quarters. Solve the model using any
optimization package and use the output to answer the following
questions:
a) If month 1 demand decreased to 35 sailboats, what would be
the total cost of satisfying the demands during the next four
months?
b) If the cost of producing a sailboat with regular-time labor
during month 1 were $420, what would be the new optimal solution to
the problem?
c) Suppose a new customer is willing to pay $425 for a sailboat.
If his demand must be met during month 1, should Smartships fill
the order? How about if the demand must be met during month 4?
Model-2
Ittihad produces four product types, requiring time on two
machines and two types (skilled and unskilled) of labor. The amount
of machine time and labor (in hours) used by each product and the
sales prices are given in the table below:
Product
Machine 1
Machine 2
Skilled
Unskilled
Sales ($)
1
11
4
8
7
300
2
7
6
5
8
260
3
6
5
4
7
220
4
5
4
6
4
180
Each month, 700 hours are available on machine 1 and 500 hours
are available on machine 2. Each month, Ittihad can purchase up to
600 hours of skilled labor at $6 per hour. Formulate an LP model
that will maximize month profit for Ittihad. Solve the LP model and
use the output to answer the following questions:
a) By how much does the price of product 3 have to increase
before it becomes optimal to produce it?
b) If product 1 is sold for $290, then what would be the new
optimal solution to the problem?
c) What is the most Ittihad would be willing to pay for an extra
hour of time on each machine?
d) What is the most Ittihad would be willing to pay for an extra
hour of each type of labor?
e) If up to 700 hours of skilled labor could be purchased each
month, then what would be Ittihad monthly profits?
Page 2 of 5 Model-3
Cornco produces two products: PS and QT. The sales price for
each product and the maximum quantity of each that can be sold
during each of the next three months are given below:
Month 1
Month 2
Month 3
Product
Price
Demand
Price
Demand
Price
Demand
PS
40
50
60
45
55
50
QT
35
43
40
50
44
40
Each product must be processed through two assembly lines: 1 and
2. The number of hours required by each product on each assembly
line are given in table below:
Hours
Product
Line 1
Line 2
PS
3
2
QT
2
2
The number of hours available on each assembly line during each
month are given in table below:
Month
Line
1
2
3
1
1200
160
190
2
2140
150
110
Each unit of PS requires 4 pounds of raw material, each unit of
QT requires 3 pounds of raw material. As many as 710 units of raw
material can be purchased at $3 per pound. At the beginning of
month 1, 10 units of PS and 5 units of QT are available. It costs
$10 to hold a unit of either product in inventory for a month.
Formulate and solve the LP model use the output to answer the
following questions:
a) Find the new optimal solution if it costs $11 to hold a unit
of PS in inventory at the end of month 1
b) Find the company’s new optimal solution if 210 hours of line
1 are available during month 1
c) Find the company’s new profit level if 109 hours are
available on line 2
Page 3 of 5 during month 3
d) What is the most Cornco should be willing to pay for an extra
hour of line 1 time during month 2
e) What is the most Cornco should be willing to pay for an extra
pound of raw material
f) What is the most Cornco should be willing to pay for an extra
hour of line 1 time during month 3
g) Find the new optimal solution if PS sells for $50 during
month 2
h) Find the new optimal solution if QT sells for $50 during
month 3
i) Suppose spending $20 on advertising would increase demand for
QT in month 2 by 5 units. Should the advertising be done?
Model-4
A leading supply chain company has two factories located in
Shanghai and Brisbane that produce two types of steel castings,
GRD100 and GRD 200. Due to the growing business needs and expanding
opportunities the company would like to develop a LP model to
enable better decisions. Shanghai factory can produce 800 tons and
Brisbane factory can produce 1000 tons of steel castings. The
company can sell upto 900 tons of GRD100 and 900 tons of GRD200
grade steel. The profit associated with each production site and
sale is as follows:
Profit Per ton
Shanghai
Brisbane
GRD100
600
1000
GRD200
800
1300
Labor costs $20 per hour and a total of 4000 hours of skilled
labor is available per year. The skilled labor required for
production site differs and are given by the following table:
Labor Required per ton (in hours)
Shanghai
Brisbane
GRD100
2
3
GRD200
2
4
Formulate and computationally solve the LP model for the above
problem, obtain and interpret the optimal solution. Include
sensitivity analysis of various model parameters.
Using the output answer the following questions:
Page 4 of 5 a) If 3,000 hours of skilled labor were available,
what will be the profit
b) By how much would the profit for GRD200 produced in Brisbane
have to increase before the company would want to produce GRD200 in
Brisbane
c) What is the most the company should pay for an extra hour of
labor
- Isye 251 Operations Research I Spring 2022 Semester Project And Instructions Notes 1 Formulate The Lp Models Careful 1 (153.78 KiB) Viewed 33 times