Page 103 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Subject to constraints,

 = a i = 1,2,…..m (supply constraints)
 i,

 = b j = 1,2,…..m (demand constraints)
j,

and x ³ 0 for all i = 1,2,…..m and,
ij
j = 1,2,…..m

5.1.2 Network Representation of Transportation Model

The transportation model is represented by a network diagram in Figure 3.1

Figure 5.1: Network Representation of Transportation Model
Factory Source Destination Ware house

11
c : x 11
1 1 D 1
S 1

Supply Demand
2 2 D 2
S 2

S m m n D n
c : x mn
mn

where,
m be the number of sources,
n be the number of destinations,
S be the supply at source m,
m
D be the demand at destination n,
n
c be the cost of transportation from source m to destination n, and
mn
x be the number of units to be shipped from source m to destination n.
mn
The objective is to minimize the total transportation cost by determining the unknowns x , i.e.,
mn
the number of units to be shipped from the sources and the destinations while satisfying all the
supply and demand requirements.

98 LOVELY PROFESSIONAL UNIVERSITY