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PART A: (40 marks) 773N1 Supply Chain Modeling

Company A is trying to create one or more warehouses to ship products to five customers. The
location of the five customers and the number of shipments per year needed by each customer are
given in Table 1. All locations are in miles, relative to the point x = 0 and y = 0. Following initial
investigation, the company has identified two possible warehouse locations: L1 (3, 4) with an annual
capacity of 750 shipments and L2 (100,110) with an annual capacity of 1500 shipments. Company A
can build either or both of these warehouses. The annualised costs to build a warehouse are £50,000
in L1 and £30,000 in L2 respectively. If only one warehouse is built, it will ship to all customers.
However, if both warehouses are built, then the company must decide which warehouse will ship to
each customer. There is a travelling cost of £1 per mile.
(1) Develop an appropriate model to minimise total annual cost, and then use the Solver to optimise
it. [20 marks]
(2) Discuss the limitations of the optimisation model developed in (1). [20 marks]
Customer Location Shipments/year
1 (5, 10) 200
2 (10, 5) 150
3 (0, 12) 200
4 (12, 0) 300
5 (7, 8) 250
Table 1 Company A’s customers’ location and shipments

PART B: (60 marks) 773N1 Supply Chain Modeling

Company B
Figure 1. The possible supply chain network
Company B needs to purchase and transport 3000 units of products from Tier 3 supplier S3 every
year. Due to the long distance between them, the purchased products need to be trans-shipped twice
at Tier 1 and Tier 2 suppliers, respectively. The company has chosen 3 possible Tier 1 suppliers:
S11, S12, and S13, and 3 possible Tier 2 suppliers, S21, S22, and S23, which can construct a possible
supply chain network as shown in Figure 1. At the moment, none of the suppliers have the
warehousing capacity available to handle the trans-shipped products. The company needs to pay an
upfront fee to each Tier 1 and Tier 2 supplier to expand their warehouse to store their products.
Tier 3 Tier 2 Tier 1
S21 S11
S3 S22 S12
S23 S13
After a fierce debate in the senior management team, Company B decided to only sign contract
with 2 suppliers on Tier 1 and Tier 2, respectively. In other words, one supplier on Tier 1 and
another supplier on Tier 2 will be excluded from the supply chain network shown in Figure 1.
Table 2 and Table 3 list the upfront fee Company B needs to pay to each individual supplier, and
the warehousing capacity they can gain to stock their products after paying the fee.
Tier 1 Suppliers
S11 S12 S13
Upfront fee 10000 12000 20000
Capacity obtained 2000 2000 2000
Table 2 Upfront fee (in pounds) to be paid to Tier 1 suppliers and obtained capacity
Tier 2 Suppliers
S21 S22 S23
Upfront fee 8000 20000 6000
Capacity obtained 2000 2000 2000
Table 3 Upfront fee (in pounds) to be paid to Tier 2 suppliers and obtained capacity
Apart from the upfront fee, another type of cost Company B needs to consider is the
transport cost. The transport rate between each pair of nodes on supply chain network has
been given in Table 4 – 6.
S21 S22 S23
S3 8 10 5
Table 4 Transport rate (pounds/ unit) betweenTier 3 suppliers and Tier 2 suppliers
S11 S12 S13
S21 11 10 15
S22 12 16 5
S23 15 12 22
Table 5 Transport rate (pounds/ unit) between Tier 2 suppliers and Tier 1 suppliers
S11 S12 S13
Company B 6 12 8
Table 6 Transport rate (pounds/ unit) between Tier 1 suppliers and the focal company B
Company B aims to minimise total transport costs and the upfront fee paid to Tier 1 and Tier 2
suppliers whilst meeting the requirements of transporting 3000 units of product from S3
to Company
B. The company would like to know:
(1) Which two suppliers on Tier 1 and Tier 2 should Company B keep respectively? How many
products should be transported between each pair of nodes on its supply chain network?
[40 marks]
(2) Using Company B’s network design as an example, discuss potential abuses/misuses of linear
programming beyond violation of basic assumptions.
[20 marks]

Guidelines for 773N1 Supply Chain Modeling

● Please refer to your assessment timetable on Canvas for the submission date.
● You will need to submit both your MS Word document and your Excel file to Canvas, and
name both files after your candidate number (e.g., 123456.docx and 123456.xlsx). Failing
to submit any of these files before the deadline will be considered as non-submission.
● This is an independent assignment and should be completely individual work. Students
may use library references, but collaboration between students will NOT be permitted for
the memo. For Part A (1) and B (1), you may be allowed to help each other on the
optimisation models, but collaboration between students will NOT be permitted for the
Excel spreadsheet and comparing of final answers or results will NOT be permitted.
● The solutions to Part A (1) and Part B (1) should (a) have separate spreadsheets (that use
the Solver to find the solution), but within a single Excel file; and (b) include the optimisation
models in the MS word document clearly stating decision variables, objective function and
all constraints.
● You should construct your spreadsheet models with readability in mind. Features that
improve readability include:
○ A clear, logical layout to the overall model
○ Separation of different parts of a model
○ Clear headings for different sections of the model and for all inputs, decision
variables and outputs
○ Use of Excel formatting features such as boldface, italics, larger font size,
colouring, indentation and cell comments
● The recommended word count for each discussion question is between 300-400 words.

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