Page 106 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 5: Transportation Problem

Notes
Table 5.2 (c): Transportation Cost per Unit
Supply Destination
Bangalore Hyderabad Cochin Goa
Chennai 5 6 9 7
Coimbatore 7 8 2 4
Madurai 6 3 5 3

A linear programming model can be used to solve the transportation problem.

Let,
X be number of units shipped from source1 (Chennai) to destination 1 (Bangalore).
11
X be number of units shipped from source1 (Chennai) to destination 2 (Hyderabad).
12
X number of units shipped from source 1 (Chennai) to destination 3 (Cochin).
13
X number of units shipped from source 1 (Chennai) to destination 4 (Goa).
14
:
and so on.
X = number of units shipped from source i to destination j, where i = 1,2,……..m and,
ij
j = 1,2,………n.
5.3 Minimizing Case

Objective Function

The objective is to minimize the total transportation cost. Using the cost data table, the following
equation can be arrived at:

 Transportation cost for units shipped from Chennai = 5x +6x +9x +7x
11 12 13 14
 Transportation cost for units shipped from Coimbatore = 7x +8x +2x +4x
21 22 23 24
 Transportation cost for units shipped from Madurai = 6x +3x +5x +3x
31 32 33 34
Combining the transportation cost for all the units shipped from each supply point with the
objective to minimize the transportation cost, the objective function will be,
Minimize Z = 5x +6x +9x +7x +7x +8x +2x +4x +6x +3x +5x +3x
11 12 13 14 21 22 23 24 31 32 33 34
Constraints: In transportation problems, there are supply constraints for each source, and demand
constraints for each destination.
Supply constraints:
For Chennai, x + x + x + x  6000
11 12 13 14
For Coimbatore, x + x + x + x  5000
21 22 23 24
For Madurai, x + x + x + x  4000
31 32 33 34
Demand constraints:
For B’lore, x + x + x = 5000
11 21 31
For Hyderabad, x + x + x = 4000
12 22 32

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