Page 133 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes
Table 6.2: TP of the Shipment
Warehouse
Facility Chennai Mumbai
Coimbatore 4 7
Pune 6 3

Warehouses Retail outlets
Delhi Hyderabad Bangalore Thiruvananthapuram
Chennai 7 4 3 5
Mumbai 5 6 7 8

Objective: The objective is to minimize the total cost
Minimize Z = 4X + 7X + 6X + 3X + 7X + 4X + 3X + 5X + 5X 6X + 7X +8X
13 14 23 24 35 36 37 38 45 46 47 48
Constraints: The number of units shipped from Coimbatore must be less than or equal to 800.
Because the supply from Coimbatore facility is 800 units. Therefore, the constraints equation is
as follows:
X + X  800 (i)
13 14
Similarly, for Pune facility
X + X  600 (ii)
23 24
Now, considering the node 3,
Number of units shipped out from node 1 and 2 are,
X + X
13 23
Number of units shipped out from node 3 is,

X + X + X + X
35 36 37 38
The number of units shipped in must be equal to number of units shipped out, therefore
X + X = X + X + X + X
13 23 35 36 37 38
Bringing all the variables to one side, we get

–X –X + X + X + X + X = 0 (iii)
13 23 35 36 37 38
Similarly for node 4
–X –X + X X + X + X =0 (iv)
14 24 45 46 47 48
Now considering the retail outlet nodes, the demand requirements of each outlet must be
satisfied. Therefore for retail node 5, the constraint equation is
X + X = 350 (v)
35 45
Similarly for nodes 6, 7, and 8, we get,

X + X = 200 (vi)
36 46
X + X = 400 (vii)
37 47
X + X = 450 (viii)
38 48

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