# Transportation Model

1.

Define feasible solution

A set of non-negative values x ij

i=1,2,3……m, j=1,2,3……n that satisfies the constraints is called a feasible solution to the transportation problem.

2.

Define basic feasible solution?

A feasible solution to a m x n transportation problem that contains no more than m + n – 1 non-negative allocations is called a basic feasible solution to the transportation problem

3.

Define non-degenerate basic feasible solution?

A basic feasible solution to a m x n transportation problem is said to be a nondegenerate basic feasible solution if it contains exactly m + n – 1 non-negative allocations in independent positions.

4.

Define degenerate basic feasible solution.

A basic feasible solution that contains less than m + n – 1 non-negative allocations is said to be degenerate basic feasible solutions.

5.

State the methods of finding initial basic feasible solution.

I.

North-west corner rule

II.

Least cost methods (or ) Matrix maima method

III.

Vogel’s approximation method (VAM)

6.

What are the characteristics of a transportation problem?

I.

Objective function is to reduce the transportation cost to the minimum

II.

Maximum quantity available at the sources is limited. This is a constraint

III.

Maximum quantity required at the destination is specified. This cannot be exceeded. This is another constraint.

IV.

Transportation cost is specified for each item.

V.

Sum of the products available from all sources is equal to sum of the products distributed at various destinations.

VI.

Maximum quantity available at the source, maximum quantity required at the destination and the cost of transportation, all refer to a single product.

7.

Mention some of the uses of transportation techniques.

I.

To reduce distribution and transportation cost.

II.

To improve competitiveness of products.

III.

To assist in locating ware-houses properly.

IV.

To assist proper location of new factories or plants being planned.

V.

To close down ware-houses which are found costly and uneconomical.

8.

What do you understand by transportation problem?

Transportation problem is a special class of linear programming problem in which we transport a single product from the source to a destination in such a way that the total transportation cost is minimum.

9.

Define the optimal solution for the transportation problem.

The basic feasible solution for a transportation problem is said to be optimal if it minimize the total transportation cost.

10.

When does a transportation problem have a unique solution.

A transportation has a unique solution if the net evaluation is given by all d ij

>

0.

11.

What do you mean by degeneracy in a transportation problem?

If the no. of occupied cells in a m x n transportation problem is less than m + n

– 1, then it is called a degeneracy in a transportation problem.

12.

Explain how degeneracy in a transportation problem may be resolved?

This degeneracy in a transportation problem can be resolved by adding one empty cell having the least cost and is independent position with a non-negative allocation.

13.

What do you mean by an unbalanced transportation problem?

Any transportation problem is said to be unbalanced

m n

Σa i

‡ Σb i=1 j=1 j the total supply is not equal to the total demand. that means if

14.

How do you convert the unbalanced transportation problem into a balanced one?

The unbalanced transportation problem can be converted into a balanced one by adding a dummy row (source) with cost zero and the excess demand is entered as a requirement if total supply is less than the total demand.

On the otherhand if the total supply > total demand, then introduce a dummy column (destination) with cost zero and the excess supply is entered as the requirement for dummy destination.

15.

List any 3 approaches used with transportation problem for determining the starting solution?

I.

North-west corner rule

II.

Least cost methods (or ) Matrix maima method

III.

Vogel’s approximation method (VAM)

16.

State the necessary and sufficient condition for the existence of a feasible solution to a transportation problem.

The necessary and sufficient condition for the existence of a feasible solution is a solution that satisfies all conditions of supply and demand.

17.

List the merits and demerits of using north-west corner rule.

Merits: This method is easy to follow because we need not consider the transportation cost.

Demerits: The solution obtained may not be the best solution as the allocations have been made without considering the cost of transportation while performing optimality test it may need more iteration to get the optimal solution.