Management Science I: Homework 3
Spring 2024 | Due Friday 2/16/2024 (@ 11:59 PM)
There are three problems in this homework assignment, totaling 60 points. You may submit
either typed or handwritten solutions (in addition to screenshots where requested). You will
submit the homework using Gradescope (“Homework 3”), and you will submit the
accompanying spreadsheet on Canvas.
General reminders for assignments:
● Different questions build off each other in the homework. You will receive partial credit
if you do the right thing using an upstream incorrect answer (e.g., if you use the wrong
formula in an Excel cell in one part, and then rely on that cell later). We can only know
whether you were doing the right thing if you include an explanation of how you got
your numbers – so include brief (1 sentence or phrase) explanations of your logic if you
want to be eligible for partial credit.
● As stated in the syllabus, you may work in groups of up to 4 people. A couple of
reminders: do not collaborate outside of these groups, and do not use Generative AI
tools to assist with any of the problem solutions.
, Problem 1: Transshipment problem (general) [26 pts]
[Modified Ragsdale 5.17] Consider the transshipment problem in the figure below. A furniture
manufacturer sells living room sofas and needs to ship the sofas from warehouses to various
cities (with varied demands). The values on the arcs indicate the per unit shipping costs
required to transport the sofas between the various cities.
Following the standard conventions from class, the b i values are given next to each node (e.g.,
node 1 has b 1=−30) and the costs for each arc are given next to each arc (e.g., each unit
shipped from node 1 to 3 has a cost c 1,3=20).
A) [2 pts] Which cities are the suppliers in this network? In other words, which nodes are
the warehouses?
Nodes 1, Nodes 2, and Nodes 3 are the suppliers cities in this network.
B) [2 pts] If you were to solve this in Excel using the matrix approach, adding arcs for each
pair of nodes, how many decision variables would you have? How would you handle the
pairs of nodes that are not connected by an arc (e.g., 1 and 5)?
With the pairs of nodes that are not connected by an arc we would represent this in
the matrix with a zero. Since all 6 of the nodes have pairs of nodes that are not
connected by an arc, the decision variables will be 6*(6-1) = 30 dvs.
C) [2 pts] If you were to solve this in Excel using the node-arc incidence approach, how
many decision variables would you have? Would you add a dummy node and arcs?
Explain your answer.
If we were to use the node-arc incidence approach, there would be a total of 12 total
decision variables (9 DV and 3 Dummy DV). A dummy node of +10 (noted with 0)
has arcs from nodes 1, 2, and 3. We need a dummy node because there is an excess of
Spring 2024 | Due Friday 2/16/2024 (@ 11:59 PM)
There are three problems in this homework assignment, totaling 60 points. You may submit
either typed or handwritten solutions (in addition to screenshots where requested). You will
submit the homework using Gradescope (“Homework 3”), and you will submit the
accompanying spreadsheet on Canvas.
General reminders for assignments:
● Different questions build off each other in the homework. You will receive partial credit
if you do the right thing using an upstream incorrect answer (e.g., if you use the wrong
formula in an Excel cell in one part, and then rely on that cell later). We can only know
whether you were doing the right thing if you include an explanation of how you got
your numbers – so include brief (1 sentence or phrase) explanations of your logic if you
want to be eligible for partial credit.
● As stated in the syllabus, you may work in groups of up to 4 people. A couple of
reminders: do not collaborate outside of these groups, and do not use Generative AI
tools to assist with any of the problem solutions.
, Problem 1: Transshipment problem (general) [26 pts]
[Modified Ragsdale 5.17] Consider the transshipment problem in the figure below. A furniture
manufacturer sells living room sofas and needs to ship the sofas from warehouses to various
cities (with varied demands). The values on the arcs indicate the per unit shipping costs
required to transport the sofas between the various cities.
Following the standard conventions from class, the b i values are given next to each node (e.g.,
node 1 has b 1=−30) and the costs for each arc are given next to each arc (e.g., each unit
shipped from node 1 to 3 has a cost c 1,3=20).
A) [2 pts] Which cities are the suppliers in this network? In other words, which nodes are
the warehouses?
Nodes 1, Nodes 2, and Nodes 3 are the suppliers cities in this network.
B) [2 pts] If you were to solve this in Excel using the matrix approach, adding arcs for each
pair of nodes, how many decision variables would you have? How would you handle the
pairs of nodes that are not connected by an arc (e.g., 1 and 5)?
With the pairs of nodes that are not connected by an arc we would represent this in
the matrix with a zero. Since all 6 of the nodes have pairs of nodes that are not
connected by an arc, the decision variables will be 6*(6-1) = 30 dvs.
C) [2 pts] If you were to solve this in Excel using the node-arc incidence approach, how
many decision variables would you have? Would you add a dummy node and arcs?
Explain your answer.
If we were to use the node-arc incidence approach, there would be a total of 12 total
decision variables (9 DV and 3 Dummy DV). A dummy node of +10 (noted with 0)
has arcs from nodes 1, 2, and 3. We need a dummy node because there is an excess of
