UNBALANCED TRANSPORTATION PROBLEM ALGORITHM TO SOLVE EXAMPLE UNBALANCED TRANSPORTATION PROBLEM So far we have assumed that the total supply at the origins is equal to the total requirement at the destinations But in certain situations the total supply is not equal to the total demand Thus th ID: 1046306
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1. TRANSPORTATION PROBLEMTOPICUNBALANCED TRANSPORTATION PROBLEMALGORITHM TO SOLVEEXAMPLE
2. UNBALANCED TRANSPORTATION PROBLEMSo far we have assumed that the total supply at the origins is equal to the total requirement at the destinations. But in certain situations, the total supply is not equal to the total demand. Thus, the transportation problem with unequal supply and demand is said to be unbalanced transportation problem.
3. If the total supply is more than the total demand, we introduce an additional column, which will indicate the surplus supply with transportation cost zero. Similarly, if the total demand is more than the total supply, an additional row is introduced in the table, which represents unsatisfied demand with transportation cost zero.
4. Algorithm to solveTo solve this problem, we have to introduce an additional row or column (according to question) which is known as Dummy Row or Dummy column. Now the access Demand or Supply will allocate to that dummy row or column . Now our problem is balanced after that we can solve the question using any of method as we do in normal (balanced) transportation problem question.
5. ExampleSolve the following transportation problem using vogel’s approximation method. D1 D2 D3 ai O1 500 O2 300 bj 250 250 500281726191216
6. As we see in the following question, ai=500+300=800 and bj=250+250+500=1000Hence it is the case of unbalanced transportation problem . So we introduce an additional row or Dummy row and allocate 200 to dummy row to balanced them. Step-1 D1 D2 D3 ai O1 500 O2 300 O3 200 bj 250 250 500281726191216000
7. Step-2 D1 D2 D3 aj P O1 500 9 O2 300 4 O3 200 0 bj 250-200 250 500 P 19 12 16281726191216 0 20000
8. Step-3 D1 D2 D3 aj P O1 500 9 O2 300 4 bj 50 250 500-300 P 9 5 102817261912 16 300
9. Step-4 D1 D2 D3 aj O1 500 bj 50 250 200 28 50 17 250 26 200
10. Step-5 D1 D2 D3 aj O1 500 O2 300 O3 200 bj 250 250 500 28 50 17 250 26 2001912 16 300 0 20000
11. Step-6Z=0*200+16*300+28*50+17*250+26*200Z=15,650