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时间：2021-03-17
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 1 of 6
Assignment-1
Data-Driven Decision-Making
MGT7180
2020-2021
Deadline: Friday, March 19, 2021, 23:59, CANVAS
The following four problems comprise assignment-1, which is an individual assignment. Use
mathematical programming models and techniques to solve these problems. For each problem, besides
formulating the model, clearly explain why each part, e.g., expression, inequality/equation, condition, etc,
is being included or used in the model for that problem (to what information in the problem setting it
corresponds). Also, include any intermediate calculation you perform to formulate the model, e.g., unit
conversion.
Use appropriate mathematical typesetting, e.g., the MS-Word Equation editor, for presenting your models
and equations. When solving the model, use succinct comments in your R-code: one or at most two lines
each, relating the important parts of the code to their corresponding parts in the mathematical model.
Include the R-code and the R output text (solution) in the assignment report paper right after the model
formulation of the problem. At the end of each solution, explicitly state the decision in terms of the
variables and the objective.
Also, upload the functional R-code files (i.e., they run without any errors and generate the same results as
those which you report in your paper) to the “dummy assignment” on Canvas for each problem that you
solve. Use recognizable filenames: e.g., “problem-2.R”. Note that you must upload all three (or four if
you split the file of problem 1) R files to the dummy assignment at the same time (see the figure
below). Your assignment paper must be uploaded to the main assignment (not the dummy
assignment). The assignment on Canvas that has the text of the four problems is the Main assignment for
uploading your assignment paper.
K = kilo =
M = million =
B = billion =
( B≢ )
NB: Please carefully read the important administrative information at the end (on the last
page) of this assignment.
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 2 of 6
1) Supermarket Shelf Space [30 marks]
Jumbo supermarket sells its own brand of peanut butter among other brands, where the profit
per jar is € 0.35 for its own brand and € 0.25 for all other brands. The shelf space allocated to
peanut butter is 0.5 m2, and each jar of any brand of peanut butter takes 50 cm2.
a) The daily sales records indicate that the number of jars sold of their own brand never
exceeds half as many jars of the other brands combined. The supermarket’s operations
manager wants to know how many jars of their own brand and how many jars of
other brands combined to stock each day on the allocated shelf space for maximum
profit.
b) Sales records have also shown that when their own brand is on discount, it sells at least
1.2 times as many jars as other brands combined. However, the profit of their own brand
drops to € 0.20 when on discount and that of the other brands is unchanged. How many
jars of their own brand and how many jars of other brands combined should be
placed in the allocated shelf space when their own brand is on discount?
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 3 of 6
2) Fleet Planning [25 marks]
NederVerzend is planning to buy ships from a British shipbuilder in three traveling range
categories, long, medium, and short, where the price of a unit ship is £ 70 M, £ 55 M, £ 40 M,
respectively. The spending limit for buying these ships is £ 2 B. Shipment orders are expected to
be more than enough to fully utilize any number of ships (that they would purchase within their
budget) in each category. The annual net profit is calculated after subtracting the ship’s
purchase price. From utilizing one ship, the net profit is £ 4.2 M, £ 3.1 M, £ 2.6 M, respectively.
The company has foreseen the hiring of enough personnel to manage 40 ships. However, the
overall facilities capacity is equivalent to 60 short-rang ships, where a medium-range ship is
equivalent to 1.5 short-range ship, and a long-range ship is equivalent to 2 short-range ships.
The CEO of NederVerzend wants to know how many of each category to purchase for
maximum total profit, and the amount of that total profit.
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 4 of 6
3) Production and Distribution [35 marks]
Ontgifter is a company that produces a special detoxifying supplement. Although they can
produce the supplement at eight plants, because of limited resources, they have to choose only
some of the plants in any given month to maximize profit. Operating any of the plants incurs a
fixed cost of € 70 K for each month the supplement is produced there. Each plant can produce at
most 120 kg of the supplement per month at a cost of € 10 per kilogram. The shipment cost of
the packaged end product to customers is € 0.01 per kilogram per kilometer. The pairwise
distances among the eight cities where all eight plants and eight customers are located are given
in Table 1. Each city has one plant and one customer (wholesaler active in that city). However,
the customer is not necessarily coupled to the plant of its city, i.e., it is not necessary to choose
both in the planned solution. But if a plant ships to the customer in the same city, their distance
is assumed to be zero. The order amount of the customers for the month being planned in this
problem and what they are willing to pay are given in Table 2. Ontgifter can decide to fill each
of the eight orders or not. However, if a customer’s order is filled, it must be by only one plant.
Orders cannot be partially filled: an order is either fully delivered to the customer or the
customer’s offer is declined.
The chief operating officer (COO) wants to know which plants should produce the
supplement in that month and for which customers.
Table 1. City Distances (km)
City A B C D E F G H
A 0 976 1808 1984 3029 1532 206 2657
B 976 0 1198 1043 2105 1383 833 1722
C 1808 1198 0 794 1418 1325 1597 1020
D 1984 1043 794 0 1167 2058 1773 829
E 3029 2105 1418 1167 0 2750 2818 391
F 1532 1383 1325 2058 2750 0 1251 2352
G 206 833 1597 1773 2818 1251 0 2435
H 2657 1722 1020 829 391 2352 2435 0
Table 2. Purchase Orders
Customer Order
Amount
(kg)
Bid
Price
(€)
A 68 75,840
B 41 44,470
C 37 46,420
D 54 87,880
E 33 43,950
F 39 21,100
G 58 74,950
H 51 84,080
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 5 of 6
4) Question! [10 marks]
When the objective function involves an absolute value of a variable, but all constraints are
linear, how can the problem be reformulated as a linear program: without the absolute value
function? Consider the following small problem as an example to answer the question: min 3|1| + 2 s. t. 1 + 32 ≥ 7 1, 2 ≥ 0
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 6 of 6
This assignment assesses the understanding and ability to use mixed integer linear
programming models. The assignment must be submitted via CANVAS by 11:59 pm on
Friday, 19th March 2021. Students must ensure their name and student ID is included on the
title page of their individual assignment.
Please note that the School has a number of policies governing the submission of student
work. For all elements of assessment associated with this course, you must be familiar with
the School’s policies on:
• Participation, Preparation for Classes and Private Study;
• Preparation and Submission of Assessed Work; and
• Plagiarism, Collusion and Fabrication.
These policies are detailed in the Queen’s Management School Postgraduate Student
Handbook.
The individual assignment will be marked using the postgraduate conceptual marking scale
as recommended by the University (please refer to the Queen’s Management School
Postgraduate Student Handbook for further information).
The following criteria are also considered when assessing the assignment:
• Demonstration of wide reading and understanding of the assignment task
• Ability to synthesise and critically evaluate relevant material
• Quality and relevance of evidence/example presented to support position/claims
• Structure including planning, organizing, flow and coherence
• Overall presentation
学霸联盟
Assignment-1
Data-Driven Decision-Making
MGT7180
2020-2021
Deadline: Friday, March 19, 2021, 23:59, CANVAS
The following four problems comprise assignment-1, which is an individual assignment. Use
mathematical programming models and techniques to solve these problems. For each problem, besides
formulating the model, clearly explain why each part, e.g., expression, inequality/equation, condition, etc,
is being included or used in the model for that problem (to what information in the problem setting it
corresponds). Also, include any intermediate calculation you perform to formulate the model, e.g., unit
conversion.
Use appropriate mathematical typesetting, e.g., the MS-Word Equation editor, for presenting your models
and equations. When solving the model, use succinct comments in your R-code: one or at most two lines
each, relating the important parts of the code to their corresponding parts in the mathematical model.
Include the R-code and the R output text (solution) in the assignment report paper right after the model
formulation of the problem. At the end of each solution, explicitly state the decision in terms of the
variables and the objective.
Also, upload the functional R-code files (i.e., they run without any errors and generate the same results as
those which you report in your paper) to the “dummy assignment” on Canvas for each problem that you
solve. Use recognizable filenames: e.g., “problem-2.R”. Note that you must upload all three (or four if
you split the file of problem 1) R files to the dummy assignment at the same time (see the figure
below). Your assignment paper must be uploaded to the main assignment (not the dummy
assignment). The assignment on Canvas that has the text of the four problems is the Main assignment for
uploading your assignment paper.
K = kilo =
M = million =
B = billion =
( B≢ )
NB: Please carefully read the important administrative information at the end (on the last
page) of this assignment.
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 2 of 6
1) Supermarket Shelf Space [30 marks]
Jumbo supermarket sells its own brand of peanut butter among other brands, where the profit
per jar is € 0.35 for its own brand and € 0.25 for all other brands. The shelf space allocated to
peanut butter is 0.5 m2, and each jar of any brand of peanut butter takes 50 cm2.
a) The daily sales records indicate that the number of jars sold of their own brand never
exceeds half as many jars of the other brands combined. The supermarket’s operations
manager wants to know how many jars of their own brand and how many jars of
other brands combined to stock each day on the allocated shelf space for maximum
profit.
b) Sales records have also shown that when their own brand is on discount, it sells at least
1.2 times as many jars as other brands combined. However, the profit of their own brand
drops to € 0.20 when on discount and that of the other brands is unchanged. How many
jars of their own brand and how many jars of other brands combined should be
placed in the allocated shelf space when their own brand is on discount?
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 3 of 6
2) Fleet Planning [25 marks]
NederVerzend is planning to buy ships from a British shipbuilder in three traveling range
categories, long, medium, and short, where the price of a unit ship is £ 70 M, £ 55 M, £ 40 M,
respectively. The spending limit for buying these ships is £ 2 B. Shipment orders are expected to
be more than enough to fully utilize any number of ships (that they would purchase within their
budget) in each category. The annual net profit is calculated after subtracting the ship’s
purchase price. From utilizing one ship, the net profit is £ 4.2 M, £ 3.1 M, £ 2.6 M, respectively.
The company has foreseen the hiring of enough personnel to manage 40 ships. However, the
overall facilities capacity is equivalent to 60 short-rang ships, where a medium-range ship is
equivalent to 1.5 short-range ship, and a long-range ship is equivalent to 2 short-range ships.
The CEO of NederVerzend wants to know how many of each category to purchase for
maximum total profit, and the amount of that total profit.
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 4 of 6
3) Production and Distribution [35 marks]
Ontgifter is a company that produces a special detoxifying supplement. Although they can
produce the supplement at eight plants, because of limited resources, they have to choose only
some of the plants in any given month to maximize profit. Operating any of the plants incurs a
fixed cost of € 70 K for each month the supplement is produced there. Each plant can produce at
most 120 kg of the supplement per month at a cost of € 10 per kilogram. The shipment cost of
the packaged end product to customers is € 0.01 per kilogram per kilometer. The pairwise
distances among the eight cities where all eight plants and eight customers are located are given
in Table 1. Each city has one plant and one customer (wholesaler active in that city). However,
the customer is not necessarily coupled to the plant of its city, i.e., it is not necessary to choose
both in the planned solution. But if a plant ships to the customer in the same city, their distance
is assumed to be zero. The order amount of the customers for the month being planned in this
problem and what they are willing to pay are given in Table 2. Ontgifter can decide to fill each
of the eight orders or not. However, if a customer’s order is filled, it must be by only one plant.
Orders cannot be partially filled: an order is either fully delivered to the customer or the
customer’s offer is declined.
The chief operating officer (COO) wants to know which plants should produce the
supplement in that month and for which customers.
Table 1. City Distances (km)
City A B C D E F G H
A 0 976 1808 1984 3029 1532 206 2657
B 976 0 1198 1043 2105 1383 833 1722
C 1808 1198 0 794 1418 1325 1597 1020
D 1984 1043 794 0 1167 2058 1773 829
E 3029 2105 1418 1167 0 2750 2818 391
F 1532 1383 1325 2058 2750 0 1251 2352
G 206 833 1597 1773 2818 1251 0 2435
H 2657 1722 1020 829 391 2352 2435 0
Table 2. Purchase Orders
Customer Order
Amount
(kg)
Bid
Price
(€)
A 68 75,840
B 41 44,470
C 37 46,420
D 54 87,880
E 33 43,950
F 39 21,100
G 58 74,950
H 51 84,080
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 5 of 6
4) Question! [10 marks]
When the objective function involves an absolute value of a variable, but all constraints are
linear, how can the problem be reformulated as a linear program: without the absolute value
function? Consider the following small problem as an example to answer the question: min 3|1| + 2 s. t. 1 + 32 ≥ 7 1, 2 ≥ 0
Data-Driven Decision-Making (MGT7180, 2020-2021, S2), QMS/QUB Page 6 of 6
This assignment assesses the understanding and ability to use mixed integer linear
programming models. The assignment must be submitted via CANVAS by 11:59 pm on
Friday, 19th March 2021. Students must ensure their name and student ID is included on the
title page of their individual assignment.
Please note that the School has a number of policies governing the submission of student
work. For all elements of assessment associated with this course, you must be familiar with
the School’s policies on:
• Participation, Preparation for Classes and Private Study;
• Preparation and Submission of Assessed Work; and
• Plagiarism, Collusion and Fabrication.
These policies are detailed in the Queen’s Management School Postgraduate Student
Handbook.
The individual assignment will be marked using the postgraduate conceptual marking scale
as recommended by the University (please refer to the Queen’s Management School
Postgraduate Student Handbook for further information).
The following criteria are also considered when assessing the assignment:
• Demonstration of wide reading and understanding of the assignment task
• Ability to synthesise and critically evaluate relevant material
• Quality and relevance of evidence/example presented to support position/claims
• Structure including planning, organizing, flow and coherence
• Overall presentation
学霸联盟
