How to solve transportation cost problem?

How to solve transportation cost 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.

What is optimal solution in transportation problem?

Optimal Solution- a feasible solution is said to be optimal solution if it minimize total transportation cost Balanced Transportation Problem – a transportation problem in which the total supply from all sources is equal to the total demand in all the destinations.

How do you balance a transportation problem?

If the total demand is greater than the total supply, then problem is infeasible. If the total demand is equal to the total supply, the problem is said to be a balanced transportation problem. If the total supply is greater than the total demand, we can add a dummy demand node to create a balanced problem.

What is transportation problem with example?

The transportation problem is a special type of linear programming problem where the objetive consists in minimizing transportation cost of a given commodity from a number of sources or origins (e.g. factory, manufacturing facility) to a number of destinations (e.g. warehouse, store).

How do you find the lowest cost method?

Solution: According to the Least Cost Cell method, the least cost among all the cells in the table has to be found which is 1 (i.e. cell (O1, D2)). Now check the supply from the row O1 and demand for column D2 and allocate the smaller value to the cell. The smaller value is 300 so allocate this to the cell.

How an unbalanced problem is tackled?

These unbalanced problems can be easily solved by introducing dummy sources and dummy destinations. If the total supply is greater than the total demand, a dummy destination (dummy column) with demand equal to the supply surplus is added.

What is the difference between feasible solution and optimal solution?

A feasible solution satisfies all the problem’s constraints. An optimal solution is a feasible solution that results in the largest possible objective function value when maximizing (or smallest when minimizing). A graphical solution method can be used to solve a linear program with two variables.

What do we apply in order to determine the optimal solution of transportation problem?

Usually, the initial basic feasible solution of any transportation problem is obtained by using well known methods such as North-West corner method (NWCM) or Least-Cost Method (LCM) or Vogel’s Approximation Method (VAM), and then finally the optimality of the given transportation problem is checked by MODI.

What is unbalanced transportation problem how can we make a balanced one?

To make an unbalanced transportation problem, a balanced one, a dummy origin(s) or a dummy destination (s) (as the case may be) is introduced with zero transportation cost per unit.

What is the aim of transportation problem?

The transportation problem is a special type of linear programming problem where the objective is to minimise the cost of distributing a product from a number of sources or origins to a number of destinations. Because of its special structure the usual simplex method is not suitable for solving transportation problems.

When a transportation problem is called unbalanced?

Unbalanced: When the supply and demand are not equal then it is said to be an unbalanced transportation problem. In this type of problem, either a dummy row or a dummy column is added according to the requirement to make it a balanced problem. Then it can be solved similar to the balanced problem.

What is another name for least cost method?

North West Corner Method (NWCM) , Least Cost Method (LCM) and Vogel’s Approximation Method (VAM) are the classical methods for solving transportation problems and are well discussed in all the operation research books.

Can a transportation problem be solved using a dummy supply node?

Note that the solution could still be solved when there was an unbalanced excess supply. If a transportation problem has more demand than supply, we can balance the problem using a dummy supply node. Note that with excess demand, the problem is “Infeasible” when unbalanced.

How is a dummy destination added to a transportation table?

Thus, a dummy destination is added to the table, with a demand of 100 units. The modified table is shown in Table which has been converted into a balanced transportation table.

Is the supply at the dummy origin equal to zero?

The supply at the dummy origin is equal to the difference of the total supply and the total demand. The costs associated with the dummy origin are equal to zero. When solving a transportation problem by its special purpose algorithm, unacceptable shipping routes are given a cost of +M (a large number).

Which is the solution to the unbalanced transportation problem?

Solution: For the given problem, the total supply is not equal to the total demand. The given problem is an unbalanced transportation problem. To convert the unbalanced transportation problem into a balanced problem, add a dummy destination (dummy column). i.e., the demand of the dummy destination is equal to,