When degeneracy occurs in a transportation problem?

When degeneracy occurs in a transportation problem?

In a transportation problem with m origins and n destinations, if a basic feasible solution has less than m + n – 1 allocations (occupied cells), the problem is said to be a degenerate transportation problem. Degeneracy can occur at two stages: At the initial solution. During the testing of the optimal solution.

In what situation does degeneracy arise?

Degeneracy in a linear programming problem is said to occur when a basic feasible solution contains a smaller number of non-zero variables than the number of independent constraints when values of some basic variables are zero and the Replacement ratio is same.

What is completely degenerate form of a transportation problem?

Degenerate Basic Feasible Solution: A basic feasible solution that contains less than m + n – 1 non- negative allocations is said to be a degenerate basic feasible solution. Optimal Solution: A feasible solution (not necessarily basic) is said to be an optimal solution if it minimises the total transportation cost.

When there is degeneracy in the transportation problem we add imaginary allocation called?

Q.	When there is a degeneracy in the transportation problem, we add an imaginary allocation called in the solution.
B.	penalty
C.	regret
D.	epsilon
Answer» d. epsilon

How is degeneracy calculated in transportation problem?

Using Least Cost Cell Method we get the following solution. Optimization of the solution using U-V Method: Check whether m + n – 1 = total number of allocated cells. In this case m + n – 1 = 4 + 5 – 1 = 8 where as total number of allocated cells are 7, hence this is the case of degeneracy in transportation problem.

What is degeneracy in simplex method?

A basic feasible solution of a simplex method is said to be degenerate basic feasible solution if at least one of the basic variable is zero and at any iteration of the simplex method more than one variable is eligible to leave the basis and hence the next simplex iteration produces a degenerate solution in which at …

How is degeneracy used in transportation problem?

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 …

What is degeneracy in a transportation problem how it is solved?

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.

What is meant by degeneracy in transportation?

If the basic feasible solution of a transportation problem with m origins and n destinations has fewer than m + n – 1 positive xij (occupied cells), the problem is said to be a degenerate transportation problem.

When there are M rows and N columns in a transportation problem degeneracy occurs when the number of allocation is?

The test of optimality of any of the feasible solutions requires allocations in m + n – 1 independent cell. If the number of allocations is less than m+n-1, then degeneracy in the transportation problems can exist.

When the total allocation of a transportation problem match with supply and demand values the solution is called?

Q.	When the total of allocations of a transportation problem match with supply and demand values, the solution is called solution.
B.	feasible solution
C.	optimum solution
D.	degenerate solution
Answer» b. feasible solution

What is introduced in the transportation problem to remove degeneracy?

In order to remove degeneracy we assign Δ to unoccupied cell (S2, D5) which has minimum cost among unoccupied cells as shown in table 2. To check optionality: We use MODI method and therefore first we have to find ui, vj & Δij with following relation.

When does a transportation problem become a degenerate problem?

In a transportation problem with m origins and n destinations, if a basic feasible solution has less than m + n – 1 allocations (occupied cells), the problem is said to be a degenerate transportation problem. Degeneracy can occur at two stages:

How can we resolve the problem of degeneracy?

To resolve degeneracy, we make use of an artificial quantity (d). The quantity d is assigned to that unoccupied cell, which has the minimum transportation cost. The quantity d is so small that it does not affect the supply and demand constraints. In the above table, there is a tie in selecting the smallest unoccupied cell.

When does degeneracy occur in modified distribution method?

Degeneracy can occur at two stages: If modified distribution method (MODI) is applied to test for optimality, it will not be possible to find all the variables ui and vj since the number of allocated cells and their corresponding cij values is not enough. The initial basic feasible solution (by north-west rule) is:

When is a solution said to be degenerate?

If the number of allocations is short of the requ i red 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.