Research Article
Volume 2 Issue 3 - August 2018
DOI: 10.19080/ETOAJ.2018.02.555586
Eng Technol Open Acc
Copyright © All rights are reserved by Palanivel M
A New Method to Solve Transportation
Problem - Harmonic Mean Approach
Palanivel M
1
* and Suganya M
2
1
Department of Mathematics, Mepco Schlenk Engineering College, India
2
Department of Mathematics, M Kumarasamy College of Engineering, India
Submission: July 06, 2018; Published: August 13, 2018
*
Corresponding author: M Palanivel, Department of Mathematics, Mepco Schlenk Engineering College, Sivakasi, TamilNadu, India;
Email:
Eng Technol Open Acc 2(3): ETOAJ.MS.ID.555586 (2018)
0066
Abstract
Transportation Problem is one of the models in the Linear Programming problem. The objective of this paper is to transport the item from the
origin to the destination such that the transport cost should be minimized, and we should minimize the time of transportation. To achieve this, a
new approach using harmonic mean is proposed in this model.
Keywords: Transportation; Harmonic mean;Optimum solution
Introduction

In transportation problem, different sourcessupply to different
destinations of demand in such a way that the transportation
cost should be minimized. We can obtain basic feasible solution
by three methods. They are
1. North West Corner method
2. Least Cost method
3. Vogel’s Approximation method (VAM)
In these three methods, VAM method is best according to the
literature. We check the optimality of the transportation problem
by MODI method.
       
They are balanced transportation problem and unbalanced
transportation problem. If the number of sources is equal to
number of demands, then it is called balanced transportation
problem. If not, it is called unbalanced transportation problem.
If the source of item is greater than the demand, then we should
add dummy column to make the problem as balanced one. If
the demand is greater than the source, then we should add
the dummy row to convert the given unbalanced problem to
balanced transportation problem.
         
optimum solution for the transportation problem. Pandian

       
discussed an improved Vogel’s Approximation method for the
        
        
        
global approach to transportation problem. Later Reena et al.
        
optimum solution of transportation problem. Amaravathy et


new transportation problem using stepping stone method and

approach to solve transportation problem with the average total
        
East Corner Method to give an initial basic feasible solution for
transportation problem.
      
world problems. In this paper, a new statistical method called
        

very closer to VAM Method. We also gave the numerical example
for the new method and we compared our method with existing
methods such as North West Corner method, Least cost method,
Vogel’s Approximation method. We checked the optimality of the
solution using MODI Method. Here, we considered the balanced
transportation problem also.
Harmonic mean = total number of observations/sums of the
reciprocal of number.
How to cite this article: Palanivel M, Suganya M. A New Method to Solve Transportation Problem - Harmonic Mean Approach. Eng Technol Open Acc.
2018; 2(3): 555586. DOI: 10.19080/ETOAJ.2018.02.555586
0067
Engineering Technology Open Access Journal
Algorithm
i. Step 1: Check whether the given transportation
problem is balanced or not. If not, balance or by adding
dummy row or column. Then go to the next step.
ii. Step 2:

iii. Step 3: Allocate the minimum supply or demand at the
place of minimum value of the related row or column.
iv. Step 4: Repeat the step 2 and 3 until all the demands

v. Step 5: Total minimum cost = sum of the product of
the cost and its corresponding allocated values of supply or
demand.
Numerical Example
Table 1,2
Table 1: Consider the following transportation problem.
D1 D2 D3 D4 Supply
S1 19 30 50 10
S2  30  60 9
S3  8  20 18
Demand 5 8 
Table 2: Solution:The given problem is balanced transportation problem since Total supply=total demand=34
D1 D2 D3 D4 Supply
S1
19
5
30 50
10
2
  16.13 16.13 15
S2 
30
2

60 9,2  
S3 
8
6

20
12
18 18.66 15 15 
Demand 5 8,6 
32.63 15.65 50.6 18
32.63 15.65 18
 12.63 13.33
12.63 0 
12.63 0 
The transportation cost is:

Table3: Illustrate.
D1 D2 D3 D4 Supply
S1 9 8 5 12
S2 6 8 
S3 5 8 9 5 16
Table 4: Solution: The given problem is balanced transportation problem since Total supply=total demand=42.
D1 D2 D3 D4 Supply
S1 9 8
5
12
12 6.9 6.9 6.6
S2
6

8  
S3
5
8
18
9
1
5
3
16,12 6.28 5.86 5.86
How to cite this article: Palanivel M, Suganya M. A New Method to Solve Transportation Problem - Harmonic Mean Approach. Eng Technol Open Acc.
2018; 2(3): 555586. DOI: 10.19080/ETOAJ.2018.02.555586
0068
Engineering Technology Open Access Journal
Demand 8  13,1 3
   
 8  5.83
  5.83
The transportation cost is:
Comparison of numerical results
The comparison between the existing method and proposed
method results are given below in Table5.
Table5: The comparison between the existing method and proposed
method.
Method Example-1 Example-2
Proposed method  
North west Corner rule 1015 320
Matrix Minima Method  
VAM  
  
Conclusion

solution obtained by the proposed method is less than that of
other methods and same that of MODI Method. But, the proposed
method is very easy since we have less computation works. So,
we can conclude that if we use harmonic mean approach to solve
transportation problem, we can get global optimum solution in
a lesser step.
References
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         
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DOI: 10.19080/ETOAJ.2018.02.555586