Using the following transportation matrix Market 1 Market 2 Market 3 Supply (tons) Factory 1 $ 41 $ 39 $ 40 130 Factory 2 $ 35 $ 38 $ 31 170 Factory 3 $ 33 $ 43 $ 39 150 Factory 4 $ 37 $ 35 $ 38 155 Demand (tons) 160 220 165 The company is considering whether it would be beneficial to switch from direct shipments to shipments through a transshipment terminal for all or some transportation routes The freight rates (per ton) the freight rates (per ton) mentioned below Freight charges in pre carriage (per ton) Terminal 1 Terminal 2 Factory 1 $ 19 00 $ 15 00 Factory 2 $ 14 00 $ 15 00 Factory 3 $ 15 00 $ 16 00 Factory 4 $ 16 00 $ 15 00 Freight charges in pre carriage (per ton) Market 1 Market 2 Market 3 Terminal 1 $ 22 00 $ 19 00 $ 22 00 Terminal 2 $ 17 00 $ 22 00 $ 20 00 Question 1 part i and ii First, discuss which additional aspects become relevant when considering transshipment terminals compared to the transportation problem with direct shipments Represent the new transportation network in a mathematical graph Which nodes have to be considered Which arrows are needed How are the arrows mentioned in b) evaluated Note It is useful that you divide both the nodes and the arrows into different groups or sets according to their function or type Based on the graph created in Task (i), sketch a linear optimization model for the transportation problem with transshipment terminals The goal is to identify the minimum cost transport quantities What are the parameters Which decision variables are needed What is the objective function Which restrictions are needed Idea Try to extend the model created for the transportation problem (Hitchock Distribution Problem) For the nodes representing the transshipment terminals, it must be ensured that the total number of tons flowing into each terminal node is equal to the total number of tons flowing out of it This means that the sum of the quantities brought to a terminal must be as large as the sum of the quantities leaving this terminal ( in bound transport quantities outbound transport quantities )

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Using the following transportation matrix: Market 1 Market 2 Market 3 Supply (tons) Factory 1 $ 41 $ 39 $ 40 130 Factory 2 $

Using the following transportation matrix:

	Market 1	Market 2	Market 3	Supply (tons)
Factory 1	$ 41	$ 39	$ 40	130
Factory 2	$ 35	$ 38	$ 31	170
Factory 3	$ 33	$ 43	$ 39	150
Factory 4	$ 37	$ 35	$ 38	155
Demand (tons)	160	220	165

The company is considering whether it would be beneficial to switch from direct shipments to shipments through a transshipment terminal for all or some transportation routes. The freight rates (per ton) the freight rates (per ton) mentioned below

Freight charges in pre carriage (per ton)
	Terminal 1	Terminal 2
Factory 1	$ 19.00	$ 15.00
Factory 2	$ 14.00	$ 15.00
Factory 3	$ 15.00	$ 16.00
Factory 4	$ 16.00	$ 15.00

	Freight charges in pre carriage (per ton)
	Market 1	Market 2	Market 3
Terminal 1	$ 22.00	$ 19.00	$ 22.00
Terminal 2	$ 17.00	$ 22.00	$ 20.00

Question 1- part i and ii:

First, discuss which additional aspects become relevant when considering transshipment terminals compared to the transportation problem with direct shipments. Represent the new transportation network in a mathematical graph.
1. Which nodes have to be considered?
2. Which arrows are needed?
3. How are the arrows mentioned in b) evaluated?

Note: It is useful that you divide both the nodes and the arrows into different groups or sets according to their function or type.

Based on the graph created in Task (i), sketch a linear optimization model for the transportation problem with transshipment terminals. The goal is to identify the minimum cost transport quantities.

What are the parameters?
Which decision variables are needed?
What is the objective function?
Which restrictions are needed?

Idea: Try to extend the model created for the transportation problem (Hitchock Distribution Problem). For the nodes representing the transshipment terminals, it must be ensured that the total number of tons "flowing into" each terminal node is equal to the total number of tons "flowing out" of it. This means that the sum of the quantities brought to a terminal must be as large as the sum of the quantities leaving this terminal ("in-bound transport quantities = outbound transport quantities").