Operations Research Frank Lauren Hitchcock ( - ) Introduction Operations reserach (O.R.) is an analytical method of problem solving and decision-making, that is useful in management organisations. The transportation problem involves certain origins (sources) which may represent factories where we produce homogeneous items and a number of destinations where we supply a required quantity of the products. Each factory has a certain capacity constraint and each destination (dealer or customer) has a certain requirement. The unit cost of transportation of the items from the factory to the dealer/ customer is known.
American mathematician and physicist Frank Lauren Hitchcock ( - ) known for his formulation of transportation problem in . . 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. .
. Definition and formulation The Structure of the Problem Let there be m origins and n destinations. Let the amount of supply at the i th origin is a i . Let the demand at j th destination is b j .
The cost of transporting one unit of an item from origin i to destination j is c ij and is known for all combinations (i,j). Quantity transported from origin i to destination j be x ij The objective is to determine the quantity x ij to be transported over all routes ( i,j ) so as to XII Std - Business Maths & Stat EM Chapter - - Operations Research 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: Origins Destinations supply … ( x ) C ( x ) C ( x ) C … ( x n ) C n a ( x ) C ( x ) C ( x ) C … ( x n ) C n a m ( x m ) C m ( x m ) C m ( x m ) C m … ( x mn ) C mn a m demand b b b … b n Table- .
Now the linear programming model representing the transportation problem is given by The objective function is Minimize Z = ij j i m ij