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# Transportation Problem

The objective of transportation problem is to determine the amount to be transported from each origin to each destinations such that the total transportation cost is minimized.

Transportation Problem

The objective of transportation problem is to determine the amount to be transported from each origin to each destinations such that the total transportation cost is minimized.

## The Structure of the Problem

Let there be m origins and n destinations. Let the amount of supply at the i th origin is ai. Let the demand at j th destination is bj.

The cost of transporting one unit of an item from origin i to destination j is cij and is known for all combinations (i,j). Quantity transported from origin i to destination j be xij

The objective is to determine the quantity xij to be transported over all routes (i,j) so as to minimize the total transportation cost. The supply limits at the origins and the demand requirements at the destinations must be satisfied.

The above transportation problem can be written in the following tabular form: Now the linear programming model representing the transportation problem is given by ## Some Definitions

Feasible Solution: A feasible solution to a transportation problem is a set of non-negative values xij(i=1,2,..,m, j=1,2,â€¦n) that satisfies the constraints.

Basic Feasible Solution: A feasible solution is called a basic feasible solution if it contains not more than m+nâ€“1 allocations, where m is the number of rows and n is the number of columns in a transportation problem.

Optimal Solution: Optimal Solution is a feasible solution (not necessarily basic) which optimizes(minimize) the total transportation cost.

Non degenerate basic feasible Solution: If a basic feasible solution to a transportation problem contains exactly m+nâ€“1 allocations in independent positions, it is called a Non degenerate basic feasible solution. Here m is the number of rows and n is the number of columns in a transportation problem.

Degeneracy :If a basic feasible solution to a transportation problem contains less than m+nâ€“1 allocations , it is called a degenerate basic feasible solution. Here m is the number of rows and n is the number of columns in a transportation problem.

Tags : Definition and formulation, Structure | Operations Research , 12th Business Maths and Statistics : Chapter 10 : Operations Research
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12th Business Maths and Statistics : Chapter 10 : Operations Research : Transportation Problem | Definition and formulation, Structure | Operations Research