Question

What are the rule of closed loop in transportation problem?

Answer 1

Degeneracy in Transportation Problem in Operational Research

Degeneracy in transportation problem in Operational Research are explained below

Step 3: Check for degeneracy

In a standard transportation problem with m sources of supply and n demand destinations, the test of optimality of any feasible solution requires allocations in m + n – 1 independent cells. If the number of allocations is short of the required number, then the solution is said to be degenerate.

If number of allocations, N = m + n – 1, then degeneracy does not exist. Go to Step 5.

If number of allocations, N ¹ m + n – 1, then degeneracy does exist. Go to Step 4.

Step 4: Resolving degeneracy

In order to resolve degeneracy, the conventional method is to allocate an infinitesimally small amount e to one of the independent cells i.e., allocate a small positive quantity e to one or more unoccupied cell that have lowest transportation costs, so as to make m + n – 1 allocations (i.e., to satisfy the condition N = m + n – 1).

In other words, the allocation of e should avoid a closed loop and should not have a path. Once this is done, the test of optimality is applied and, if necessary, the solution is improved in the normal was until optimality is reached. The following table shows independent allocations.

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