Management Logistics - Questions & Answers

Running head: MANAGEMENT LOGISTICS
1
Management Logistics
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MANAGEMENT LOGISTICS 2
Management Logistics
Question 1
We will start by drawing a tour graph showing all the costs between different towns.
a. Farthest insertion
In this part we will be inserting the node whose minimal travel cost to a tour results to
minimum.
We use the tour T = { 4−1−5−4 }
Starting our ˇwitth node 2
Next, we try with node 3
57
53
8
57
65
68
49
84
85
6
1
66
24
89
47
71
19
5
4
32
4
53
19 12
65 5
47
4
85 13
57

MANAGEMENT LOGISTICS 3
Finally, we try with node 6
From the three diagrams we can conclude that:
Minimum cost of node 2 =19
Minimum travel cost of node 3 = 47
Minimum travel cost of node 6= 24
So, it is evident that has the maximum travel cost.
Therefore, the furthest insertion is Node 3.
b. Nearest insertion
Considering the TPS insertion schemes for the Nearest Insertion, we will chose a node among
the nodes which are inserted next to each other and we will give the minimum cost of the tour.
We will check the nodes apart from the nodes given in the current tour i.e. tour
T = { 4−1−5−4 } that gives the lowest increase in the cost of the tour.
The current node is T = { 4−1−5−4 }
The current cost of the tour cT¿ 57+84 +89=230
Starting with node 2
We insert node 2 and check the cost of the tour
T = { 4−2−1−5−4 }
¿ 53+19+84 ++89
cT =245
Inserting Node 3
T = { 4−3−1−5−4 }
5
83 4
66
6
1
57
5

MANAGEMENT LOGISTICS 4
¿ 47 +85+84 +89
cT =305
Now inserting Node 6
T = { 4−6−1−5− 4 }
¿ 83+66 +84+ 89
cT =322
From the above, we find that Node 2 causes the least increase in the cost of the tours.
Therefore, the nearest insertion = Node 2
Question 2.
Given that the current tour is T = {2−3− 4−2 } and node 1 to be inserted next in the current tour.
This will give us five possibilities
Now, Possibility 1
T = { 1−2−3−4−2 }
Corresponding cost values are ¿ 19+71+47 +53
¿ 190
Possibility 2
T = { 2−1−3−4−2 }
The corresponding cost values will be ¿ 19+85++ 47+53
¿ 204
Possibility 3
T = { 2−3−1−4−2 }
The corresponding cost values will be ¿ 71+85+57+53
¿ 266
Possibility 4
T = { 2−3− 4−1−2 }