Transportation Problem

A transportation problem fundamentally deals with the difficulty which aspires to find the best possible way to accomplish the demand of ‘n’ demand points using the capabilities of ‘m’ supply points. While attempting to find the best probable way, usually a variable cost of transporting the product from 1 supply point to a demand point or a related constraint ought to be taken into concern. This kind of problem is known as allocation or transportation problem in which the main idea is to reduce the charge or the time of transport. If the overall capacity is equivalent to the total requirement, the problem is referred to as balanced transportation problem or else it is referred as unbalanced transportation problem. The algorithm to decipher a transportation problem is as follows:

Step 1: Prepare the problem and devise it in a matrix form. In this step, the objective is to fill the table with total transportation cost and the restrictions are the supply and demand existing at each of the source and destination.

Step 2: The 2^nd step is to obtain an Initial Basic Feasible Solution (IBFS). An IBFS is a solution that satisfies all the supply and demands at all the source and destination. There are 3 methods to calculate the IBFS:

• North-West Corner Rule: In this method, the cell at the top left corner of the matrix is allocated much possible equal to the least amount of the rim values for the 1^st row and column. It is then moved vertically down to fulfill the demand of the next center. The procedure is repeated.
• Least Cost Method: Since the intention of this whole method is to reduce the transportation cost, we should attempt to transport as much as possible throughout those paths where the unit transportation charge is the cheapest.
• Vogel’s Approximation Method: This is the most preferred method out of all the three. In this method, the allotment is made based on the opportunity costs that would be incurred if allotments in cells with the least unit transportation cost were overlooked.

Step 3: The optimality of the solution is checked using the Modified Distribution (MODI) method.

Questions:

• Explain the working of North-West corner rule?
• What is IBFS?