Problem Statement: Traveling Salesman Problem
Consider
C
id 6 cities
iti shown
h
as nodes
d 1,
1 2,
2 . 6 in
i the
th figure
fi
b l
below.
A traveling
t
li salesman
l
based in node 1 has to make a tour of all other 5 nodes before returning to node 1. The

Quiz No. 2 Problem:
Consider the schematic of the network
off n
nodes
d
shown
h
i the
in
h figure
fi
below. The time taken to travel
between two nodes is given by
Tij, where i is the startingg node and j
j
is the ending node. Travel is allowed
both ways

Network: General
Series of nodes (or junctions or vertices) connected by a set of links (or branches)
In the network above, every
y node is connected to at least one other node byy a link. Such a
network is termed connected.
This network is also planar, s

Balanced Transportation Problem
S1
S2
S3
1
5
2
6
3
7
D5
D6
D7
A product from 4 production centers, with
production capacities of S1, S2, S3 and S4
must be supplied to 4 demand centers with
d
demand
d off D1,
D1 D2,
D2 D3 andd D4.
D4 Assume
A
total product

Linear Programming: Bus Routing Problem
Suppose
pp
in a bus route, the minimum number of ppublic buses required
q
at the ith hour of the
day is bi, i = 1, 24. Each bus runs for 6 consecutive hours. If the number of buses in period
i exceeds the minimum re

Solution:
Here,
i = 1, , 7
and
j = 1, 2, 3, 4
Let Xij be a binary variable, i.e., taking values of either 0 or 1
7
4
Maximize S Wi .Sij .X ij
i 1 j1
7
4
Minimize C Cij .X ij
i 1 j1
4
Constraints:
X
j1
1j
4
X
j1
4j
1
4
X
j1
1
2j
4
X
j1
5j
1
4
X
j1
1
3j
4
X

Problem 2: The Hydroelectric Dam Problem
The plan view of a hydroelectric power project, constructed at the confluence of two rivers is shown
in the figure below. The project consists of two dams. Water from reservoir 1 is used to generate
po er through
p

System Analysis
Whatt is
Wh
i a System?
S t ?
A system may be defined as a collection of physical and human elements
which are interconnected and organized in such a way as to achieve some
specified objectives.
objectives
A fundamental property of a syste