We solve the transportation problem using the followings steps in order:
a. Structuring the problem into the transportation framework.
b. Finding an initial solution.
c. Moving from the initial solution to th e optimal solution suing the transportation algorithm of the transportation method & if solution is not optimal.
d. Revising the solution until an optimal solution is obtained.
Step1 :L Structure the problem into transportation framework as explained in the followings.
First of all the given information can be put into the transportation framework as under:
The above solution indicate that first of we have transport 13 units to warehouse A from factory X and Y this way the demand of warehouse A is met with. The remaining 2 units at factory X are Sent to warehouse Y and this meet the demand of warehouse B only partially but the supply of factory X is exhausted. Then we take the supply available at factory Y and from it transport 10 units to warehouse B thereby meeting it demand completely and the remaining 14 units are sent to warehouse C. Then we take the supply at factory Z and from it we send 2 units to warehouse C and the remaining 19 units to warehouse D. This way we meet the requirement of all warehouse from the available supply at various factories without considering the cost factor. The initial solution has been shown the above table. The relevant transportation cost of this initial solution will be as under:
Cost of transportation 13 units from X to A @ Rs. 3 per units =Rs. 39
Cost of transportation 2 units from X to AB@ Rs. 2 per units =Rs. 40
Cost of transportation 10 units from Y to B @ Rs. 1 per units = Rs. 10
Cost of transportation 14units from Y to C @ Rs. 4 per units = Rs.56
Cost of transportation 2 units from Z to C@ Rs. 4per units = Rs. 80
Cost of transportation 19 units from Z to C@ Rs. 4per units = Rs. 57
Total transportation cost if the initial transportation schedule is adopted = Rs. 174