Prof. Hitesh Arora
Abhay Sawhney (201055)
Transportation Problem involves distribution of a certain commodity from several origins to a number of destinations. The aim in the whole process is to minimize the costs involved. A necessary condition for the solving of the transportation problem is that the problem must be balanced, i.e the demand for the product at the destinations must equal the capacity of the suppliers.
The Texago Corporation is a large, fully integrated petroleum company based in the United States. The company produces most of its oil in its own oil fields and then imports the rest of what it needs from the Middle East. An extensive distribution network is used to transport the oil to the company’s refineries and then to transport the petroleum products from the refineries to Texago’s distribution centers.
Table 1.1 The location of the facilities of Texago Corporation Type of Facility| Location|
Oil Fields| * Texas * California * Alaska|
Refineries| * New Orleans, Louisana * Charleston, South Carolina * Seattle, Washington| DistributionCentres| * Pittsburg, California * Atlanta, Georgia * Kansas City, Missouri * San Francisco, California|
Texago is a growing organization & so is its market share. The Board of Directors have therefore decided to add another Refinery to expand the output. The three prospective Refineries are Los Angeles, Galveston & St. Louis, Missouri. The addition of the new refinery will have a great impact on the operation of the entire distribution system, including decisions on how much crude oil to transport from each of its Oil Fields to each refinery (including the new one) and how much finished product to ship from each refinery to each distribution center. Therefore, the three key factors for management’s decision on the location of the new refinery are: 1. The cost of transporting the oil from the Oil Fields to all the refineries, including the new one. 2. The cost of transporting finished product from all the refineries, including the new one, to the distribution centers. 3. Operating costs for the new refinery, including labor costs, taxes, the cost of needed supplies (other than crude oil), energy costs, the cost of insurance, the effect of financial incentives provided by the state or city, and so forth. (Capital costs are not a factor since they would be essentially the same at any of the potential sites.) Now the production data for Texago Corporation is as follows:
Table 1.2 The Crude Oil Requirement at various Refineries
Refinery| Crude Oil Requirement (Million Barrels) |
New Orleans| 100|
New One| 120|
Table 1.3 The Capacity of the three Oil Fields
Oil Field| Capacity (Million Barrels)|
Therefore, there is a shortfall of 120 Million Barrels, which Texago Corporation needs to fulfill by means of imports. Management wants all the refineries, including the new one, to operate at full capacity. Since the amounts of crude oil produced or purchased will be the same regardless of which location is chosen for the new refinery, the management concludes that the associated production or purchase costs (exclusive of shipping costs) are not relevant to the site selection decision. The costs for transporting the crude oil from its source to a re-finery are very relevant, which are as follows: Table 1.4 Cost of transporting Cruse Oil from an Oil Field to the refinery | New Orleans| Charleston| Seattle| Los Angeles| Galveston| St. Louis| Texas| 2| 4| 5| 3| 1| 1|
Claifornia| 5| 5| 3| 1| 3| 4|
Alaska| 5| 7| 3| 4| 5| 7|
Imports| 2| 3| 5| 4| 3| 4|
Table 1.5 Cost of shipping the Finished product from the Refineries to the Distribution...