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 transportation problem Slideshare?

 DEGENERATE BASIC FEASIBLE SOLUTION: If a BFS contains less than m+n–1 non–negative allocations, it is said to be degenerate.  OPTIMAL SOLUTION:  A feasible solution is said to be optimal if it minimizes the total transportation cost.

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 …

What is degeneracy in assignment problem?

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.

When there is a degeneracy in transportation problem we add an 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

What do you understand by Modi method?

MODI method is an improvement over stepping stone method. This model studies the minimization of the cost of transporting a commodity from a number of sources to several destinations. The supply at each source and the demand at each destination are known.

Which of the following is a valid reason for causing degeneracy in a transportation problem?

Explanation: When the number of allocations is less than m+n−1, it causes degeneracy in transportation problem.

What are the main elements of transportation problem?

Transportation Problem

• m = number of sources (i = 1 … m)
• n = number of destinations (j = 1 … n)
• c i,j = unit cost of shipping from source i to destination j.
• x i,j = amount shipped from source i to destination j.
• a i = supply at source i.
• b j = demand at destination j.

What is the meaning of degeneracy in operation research?

Degeneracy is revealed when a basic variable acquires a zero value rather than a negative or positive value. In the final solution, either the number of basic variable is not equal to the number of constraints, or the number of zero variables does not equal the number of decision variables.

What is the meaning of degenerate solution?

Definition. A basic feasible solution is degenerate if at least one of the basic variables is equal to zero. A standard form linear optimization problem is degenerate if at least one of its basic feasible solutions is degenerate. If every basic variable is strictly positive in a basic feasible solution.

What do you mean by degeneracy in operations research model?

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.

What is degeneracy in a transportation problem?

In a transportation problem, degeneracy occurs when the number of Allocations are less than (Rows +Columns – 1), where M= number of rows

What is designdegeneracy in transportation problem in operational research?

Degeneracy in transportation problem in Operational Research are explained below In a standard transportation problem with m sources of supply and n demand destinations, the test of optimality of any feasible solution requ i res allocations in m + n – 1 independent cells.

What is meant by the term degeneracy at subsequent interactions?

Degeneracy at Subsequent Interactions: To resolve degeneracy which occurs during optimality test, the quantity may be allocated to one or more cells which have become unoccupied recently to have m + n -1 member of occupied cells in the new solution. Goods have to be transported from sources S 1, S 2 and S 3 to destinations D 1, D 2 and D 3.

What is balanced transportation problem?

This problem is balanced transportation problem as total supply is equal to total demand. Least Cost Cell Method will be used here to find the initial basic feasible solution. One can also use NorthWest Corner Method or Vogel’s Approximation Method to find the initial basic feasible solution.