New thoughts, transportation modle in operation research
New thoughts, transportation modle in operation research
INTRODUCTION
The objective of the transportation problem is to transport various quantities of a single homogeneous commodity that are initially stored at various origins to different destinations in such a way that the transportation cost is minimum. To achieve this objective we must know the amount and location of available supplies and the quantities demanded. In addition we must know the costs that result from transporting one unit of commodity from various origins to various destinations.
PREFACE
The solution of a transportation problem can be obtained in two stages, namely initial solution and optimum solution.
Initial solution can be obtained by using any one of the three methods viz,
North west corner rule
Least cost method or matrix minima method
Vogel's approximation method.
But we have invented a new method to know the initial feasible solution. This method helps to calculate directly the minimum transportation cost easily and correctly with minimum time, also calculate the minimum time if the unit transportation cost is replaced by the unit time required to transport the items from origin to destination.
PROCEDURE (If the number of rows is not equal to number of columns.)
Step1
Determine the maximum cost in the cost matrix of the transportation table.
Step2
Choose the smallest cost in the column, also containing the maximum cost selected in the first step of the procedure.
Step3
Allocate the selected smallest cell as much as possible, so that either the capacity of the row is exhausted or the destination requirement of the column is satisfied.
Step4
If a particular recruitment is satisfied then delete the entire column or the particular capacity is satisfied then delete the entire row of the transportation table and no element of that column or row take part in operation.
Step5
Repeat all the above process for the resulting reduced transportation until all the rim requirements are satisfied.
Step6
Then calculate the minimum transportation cost.
Note: - [whenever the maximum cost or the minimum cost is more than one (if there is a tie) then we have to choose the maximum requirement is presented in that selected cell. If requirements are equal then we chose the maximum capacity present in that selected cell.]
(If number of rows is equal to number of columns.)
In this case all the steps of the first case are same.
Note:-[In this case chose the lowest cost in either the row or the column both containing the maximum cost selected in the 1st step.]
UNBALANCED TRANSPORTATION PROBLEM:-
If the total supply is not equal to the total requirement is called unbalanced transportation problem.
In case of unbalanced transportation problem we first balance the problem by adding the dummy row or the dummy column as per the requirement.
If the total supply is less than the total demand a dummy row is increased.
If the total supply is greater than the total demand a dummy column is increased.
Now we get the balanced transportation problem. Then we fallow the above process for calculate the minimum transportation cost.
NOTE: - [In this case the dummy row or column should be filled up at last as per the requirement.]
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