Which transportation problem will always have a feasible solution?

balanced transportation problem
Theorem 2 A balanced transportation problem always has a feasible solution. Theorem 3 A balanced transportation problem always has a basic feasible solution. Such a solution consists of m + n − 1 positive variables at most.

What is feasible transportation problem?

The objective of the problem is to find the amount of commodity to be transported from each source to each destination so that the destination requirements within the operating production capacity constraints are satisfied at minimum transportation cost. …

What are the methods to find the feasible solution of transportation problem explain any one of them?

Step 1: Find the cell with the least(minimum) cost in the transportation table. Step 2: Allocate the maximum feasible quantity to this cell. Step:3: Eliminate the row or column where an allocation is made. Step:4: Repeat the above steps for the reduced transportation table until all the allocations are made.

Which method is used to verify that solution is optimal in the transportation problem?

Least cost method is used to verify the optimality of the current solution of the transportation problem.

What do you mean by feasible and basic feasible solution of transportation problem?

A set of non-negative allocations xij ≥ 0 which satisfies the row and column restrictions is known as feasible solution. Basic Feasible Solution. A feasible solution to a m-origin and n-destination problem is said to be basic. feasible solution if the number of positive allocations are (m+n–1).

What feasible solution satisfies?

A feasible solution is one that satisfies all linear and non-linear constraints. If a linear constraint is defined using only decision variables, the OptQuest Engine can determine feasibility when it generates a solution, because it has all the information it needs to calculate a value and ensure its feasibility.

How can we solve the transportation problem?

To solve a transportation problem, the following information must be given:

1. m= The number of sources.
2. n= The number of destinations.
3. The total quantity available at each source.
4. The total quantity required at each destination.
5. The cost of transportation of one unit of the commodity from each source to each destination.

How do you solve degenerate transportation problems?

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 …

Which of the following methods is used to verify the optimality?

Solution(By Examveda Team) Modified distribution method (MODI) is used to verify the optimality of the current solution of the transportation problem.

What is feasible solution and non degenerate solution in transportation problem?

A basic feasible solution of an (m × n) transportation problem is said to be non- degenerate. if it has following two properties : (a) Initial basic feasible solution must contain exactly m+n–1 number of individual allocations. (b) These allocations must be in independent positions.

How feasible is a solution?

A feasible solution is a set of values for the decision variables that satisfies all of the constraints in an optimization problem. A local optimal solution is one where there is no other feasible solution “in the vicinity” with a better objective function value.

When is a feasible solution to a transportation problem optimal?

A feasible solution (not necessarily basic) is said to be optimal if it minimizes the total transportation cost. To solve a transportation problem first we need to find an initial basic feasible solution and then get an optimum solution.

How to solve the transportation problem?

Various methods have been developed to solve the transportation problem and obtain an optimal solution, such as the modified distribution (MODI) method. In order to proceed with these methods, it is necessary to obtain the initial feasible solution.

How to solve the transportation problem in linear programming?

The transportation problem has a large number of linear programming applications. Various methods have been developed to solve the transportation problem and obtain an optimal solution, such as the modified distribution (MODI) method. In order to proceed with these methods, it is necessary to obtain the initial feasible solution.

How do you find the basic feasible solution to a problem?

A number of methods are proposed to find the basic feasible solution, among which are Vogel’s approximation method (VAM), the row minima method, the column minima method, minimum cost method, the north-west corner method and Russell’s method.