Introduction to Quantitative Management

Assignment

The weighting of this assignment is 20% in your final grade. You are encouraged to discuss in groups, however, the final report and LINGO implementation must be completed individually. Your work must be submitted on 14 May 2018, in the lecture in hard copy. No late submission will be accepted. The final report should at least consist of the mathematical modeling and the LINGO solution parts.

• In the mathematical modeling part, describe all assumptions clearly. State decision variables, establish and explain the objective functions, and determine all constraints (restrictions) (60% of total marks).

• In the LINGO solution part, provide a printout of the set based LINGO model, a solution report of LINGO, and explain the solution (what is minimum/maximum, which strategy must be applied to achieve this, etc.) (40% of total marks).

Your report should follow the structure suggested below:

1) Title

2) Executive summary: a short description of the problem and summary of your results

3) Problem description: rewrite the problem according to your understanding

4) Formulation of the problem

5) LINGO implementation and interpretation of the solution report 6) Summary

A cover sheet with detailed instruction is included as the last page of this document.

Problem O.J. Juice Company sells bags of oranges and cartons of orange juice. O.J. grades oranges on a scale of 1(poor) to 10(excellent). The average quality of oranges sold in bags must be at least 6, and the average quality of the oranges used to produce orange juice must be at least 7.5. The average quality is calculated as the weighted average of the grades of oranges blended together. For example, the average quality of blending 2 lb of grade 2 oranges and 5 lb of grade 9 oranges is

O.J. purchases oranges from many different suppliers. Each supplier cannot provide more than its capacity. The capacity, cost and grade mix of the oranges purchased from five suppliers are given as an example in the Table below. For example, supplier 1 cannot provide more than 2,000 lb of oranges; if O.J. purchase 1,000 lb oranges from supplier 1, after sorting (separating the oranges according to grade), 50 lb of them will be of grade 3, 200 lb of them will be of grade 6, 500 lb will be grade 8 and 250 lb will be of grade 10.

Supplier capacity Cost $/lb grade 3(%) grade 6 grade 8 grade 10

1 2000 0.9 5 20 50 25

2 1500 0.8 8 25 50 17

3 2500 0.6 10 30 50 10

4 2000 0.4 30 30 30 10

5 1800 0.3 40 40 20 0

The purchased oranges are transported from suppliers to O.J’s different warehouses. The transportation cost per lb is shown as an example in the Table below

Shipping cost($ per lb)

Warehouse A Warehouse B Warehouse C

supplier1 0.10 0.15 0.05

supplier2 0.25 0.09 0.12

supplier3 0.13 0.12 0.10

The sorting process takes place in O.J’s different warehouses at different cost rate. The amount of oranges sorted by each warehouse must be within its capacity. The sorted oranges are transported to OJ’s plant to produce orange juice and bag of oranges. The transportation cost is $0.05 per lb. Each lb of orange can yield

0.95 lb of bags of orange at a cost of $0.1, while each lb of orange can yield only 0.6 lb of orange juice at a cost of $0.4. The orange juice can be sold at $3.5 per lb, and the bag of oranges is sold at $1.5 a pound. O.J.’s plant can process no more than 30,000 lb of oranges, and must produce at least 3000 lb of bags of oranges. Oranges not used must be sent to a recycling centre at the cost of $0.1 per lb.

The detailed data can be found in the Excel file with the name 2018AssignData.xlsx.

Questions:

1) Find the optimal production and shipping plan for the company to maximise profit with Linear Programming and LINGO.

2) O.J. is considering the opportunity to build a new plant. What data are critical for the evaluation of this decision?

37141 Introduction to Quantitative Management

ASSIGNMENT COVER SHEET

Please use BLOCK letters (i.e. CAPITALS ONLY) to fill in all details below.

Please DO NOT submit your assignment in a plastic cover, folder or an envelope. All attachments must be stapled.

Student name:

Student number:

Date due: In the lecture - Monday 14 May 2018 Date submitted:

INSTRUCTIONS TO STUDENTS

This is an individual assessment component of the final grade of this subject. Students must complete the declaration below.

Reports to be submitted:

Cover sheet

Problems & Mathematical models

LINGO codes and results

Solution reports

DECLARATION

I hereby certify that this assignment is my own work, based on my personal study and/or research and that I have acknowledged all material and sources used in the preparation of this assignment. I also certify that the assignment has not previously been submitted for assessment and that I have not copied in part or whole or otherwise plagiarised the work of other students or authors.

Signature: Date:

Assignment

The weighting of this assignment is 20% in your final grade. You are encouraged to discuss in groups, however, the final report and LINGO implementation must be completed individually. Your work must be submitted on 14 May 2018, in the lecture in hard copy. No late submission will be accepted. The final report should at least consist of the mathematical modeling and the LINGO solution parts.

• In the mathematical modeling part, describe all assumptions clearly. State decision variables, establish and explain the objective functions, and determine all constraints (restrictions) (60% of total marks).

• In the LINGO solution part, provide a printout of the set based LINGO model, a solution report of LINGO, and explain the solution (what is minimum/maximum, which strategy must be applied to achieve this, etc.) (40% of total marks).

Your report should follow the structure suggested below:

1) Title

2) Executive summary: a short description of the problem and summary of your results

3) Problem description: rewrite the problem according to your understanding

4) Formulation of the problem

5) LINGO implementation and interpretation of the solution report 6) Summary

A cover sheet with detailed instruction is included as the last page of this document.

Problem O.J. Juice Company sells bags of oranges and cartons of orange juice. O.J. grades oranges on a scale of 1(poor) to 10(excellent). The average quality of oranges sold in bags must be at least 6, and the average quality of the oranges used to produce orange juice must be at least 7.5. The average quality is calculated as the weighted average of the grades of oranges blended together. For example, the average quality of blending 2 lb of grade 2 oranges and 5 lb of grade 9 oranges is

O.J. purchases oranges from many different suppliers. Each supplier cannot provide more than its capacity. The capacity, cost and grade mix of the oranges purchased from five suppliers are given as an example in the Table below. For example, supplier 1 cannot provide more than 2,000 lb of oranges; if O.J. purchase 1,000 lb oranges from supplier 1, after sorting (separating the oranges according to grade), 50 lb of them will be of grade 3, 200 lb of them will be of grade 6, 500 lb will be grade 8 and 250 lb will be of grade 10.

Supplier capacity Cost $/lb grade 3(%) grade 6 grade 8 grade 10

1 2000 0.9 5 20 50 25

2 1500 0.8 8 25 50 17

3 2500 0.6 10 30 50 10

4 2000 0.4 30 30 30 10

5 1800 0.3 40 40 20 0

The purchased oranges are transported from suppliers to O.J’s different warehouses. The transportation cost per lb is shown as an example in the Table below

Shipping cost($ per lb)

Warehouse A Warehouse B Warehouse C

supplier1 0.10 0.15 0.05

supplier2 0.25 0.09 0.12

supplier3 0.13 0.12 0.10

The sorting process takes place in O.J’s different warehouses at different cost rate. The amount of oranges sorted by each warehouse must be within its capacity. The sorted oranges are transported to OJ’s plant to produce orange juice and bag of oranges. The transportation cost is $0.05 per lb. Each lb of orange can yield

0.95 lb of bags of orange at a cost of $0.1, while each lb of orange can yield only 0.6 lb of orange juice at a cost of $0.4. The orange juice can be sold at $3.5 per lb, and the bag of oranges is sold at $1.5 a pound. O.J.’s plant can process no more than 30,000 lb of oranges, and must produce at least 3000 lb of bags of oranges. Oranges not used must be sent to a recycling centre at the cost of $0.1 per lb.

The detailed data can be found in the Excel file with the name 2018AssignData.xlsx.

Questions:

1) Find the optimal production and shipping plan for the company to maximise profit with Linear Programming and LINGO.

2) O.J. is considering the opportunity to build a new plant. What data are critical for the evaluation of this decision?

37141 Introduction to Quantitative Management

ASSIGNMENT COVER SHEET

Please use BLOCK letters (i.e. CAPITALS ONLY) to fill in all details below.

Please DO NOT submit your assignment in a plastic cover, folder or an envelope. All attachments must be stapled.

Student name:

Student number:

Date due: In the lecture - Monday 14 May 2018 Date submitted:

INSTRUCTIONS TO STUDENTS

This is an individual assessment component of the final grade of this subject. Students must complete the declaration below.

Reports to be submitted:

Cover sheet

Problems & Mathematical models

LINGO codes and results

Solution reports

DECLARATION

I hereby certify that this assignment is my own work, based on my personal study and/or research and that I have acknowledged all material and sources used in the preparation of this assignment. I also certify that the assignment has not previously been submitted for assessment and that I have not copied in part or whole or otherwise plagiarised the work of other students or authors.

Signature: Date:

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