1. Formulation of the Problem The Stateline Shipping and Transport Company wanted to transport industrial wastes from the 6 plants to the 3 waste disposable sites. The problem can be represented in as a Transportation table as shown below. Our problem is to find roots to disposable sites, such that the cost of transportation is minimized..
Mathematical Formulation Let Xij i=1,2,3,4,5,6; j =1,2,3 denote the quantity of waste transported from i-th plant to Therefore, the original problem was modified and again solved using new reduced costs. The result showed that the new model caused a considerable reduction in transportation costs. The optimum cost of the Stateline Shipping Company reduced to $2630. To get this cost advantage company must use the following roots for transportation. Waste from Kingsport to Duras (19 bbl) must take to Danville first and then from take Danville to Duras. Waste from Shelma to White water (36 bbl) must be transported and dropped at Columbus first and from there it must be shipped to White water. Waste from Shelma to Duras ($17 bbl) must be transported and dropped at Macon first and from there it must be shipped to Duras. The main limitation is that we have considered the cost aspect only in this problem. Handling of very dangerous industrial wastes cannot be considered only based on cost aspect. In our problem, note that this waste contains hazardous elements and hence transportation of waste to many intermediate positions will increase the risk of the company. Drop the waste at some intermediate points and then pick up from there to get to the final destination for cost benefit may lead to considerable time delay. If the waste from the sites do not reach at the disposable sites at a proper time intervals, disposal of wastes may become difficult. We have not considered the fact that transporting and
