Trans World Oil Company

The Trans World Oil Company is an international producer, refiner, transporter, and distributor of oil, gasoline, and petrochemicals. Trans World is a holding company with subsidiary operating companies that are wholly or partially owned. A major problem for Trans World is to coordinate the actions of these various subsidiaries into an overall corporate plan, while at the same time maintaining a reasonable amount of operating autonomy for the subsidiary companies.

To deal with this dilemma, an annual corporate-wide plan that detailed the pattern of shipments among the various subsidiaries was developed. This plan was not rigid but provided general guidelines and the plan was revised periodically to reflect changing conditions. Within the framework of this plan, the operating companies could make their own decisions and plans.

This corporate plan was originally done on a trial-and error basis. There were two problems with this approach. First, the management of the subsidiaries complained that the planners did not take into account the operating conditions under which the subsidiary had to operate. The plan might call for operations or distribution plans that were impossible to accomplish. Second, the corporate management was concerned that the plan did not optimize for the total company.

The technique of linear programming seemed a possible approach to aid in the annual planning process that would be able to answer, at least in part, the two objections above. In addition, the building of such a model would make it possible to make changes in plans quickly when the need arose.

The details of the 1996 planning model for the Far Eastern Operations are now described.

There are two sources of crude oil, Iran and Borneo. The Iranian crude is relatively heavier ( $\left.24^{\circ} \mathrm{API}\right)$, and the Far Eastern sector could obtain as much as 60,000 barrels per day (b/d) at a cost of $\$ 18.50$ per barrel at Abadan during 1996. A second source of crude is from the Brunei fields in Borneo. This is a lighter crude oil ( \(36^{\circ}\) API). Under the terms of an agreement with the Netherlands Petroleum Company in Borneo, a fixed quantity of \(40,000 \mathrm{~b} / \mathrm{d}\) of Brunei crude, at a cost of $20.50 per barrel is to be supplied during 1996 .

There are two subsidiaries that have refining operations. The first is in Australia, operating a refinery in Sydney with a capacity of \(50,000 \mathrm{~b} / \mathrm{d}\) throughout. The company also marketed its products throughout Australia, as well as having a surplus of refined products available for shipment to other subsidiaries.

The second subsidiary is in Japan, which operates a \(30,000 \mathrm{~b} / \mathrm{d}.\) capacity refinery. Marketing operations are conducted in Japan, and excess production is available for shipment to their Far Eastern subsidiaries.

In addition, there are two marketing subsidiaries without refining capacity of their own. One of these is in New Zealand and the other in the Philippines. Their needs can be supplied by shipments from Australia, Japan, or the Trans World Oil subsidiary in the United States. The latter is not a regular part of the Far Eastern Operations, but may be used as a source of refined products.

Finally, the company has a fleet of tankers that move the crude oil and products among the subsidiaries.

The operation of a refinery is a complex process. The characteristics of the crudes available, the desired output, the specific technology of the refinery, and so on make it difficult to use a simple model to describe the process. In fact, management at both Australia and Japan have complex linear programming models involving approximately 300 variables and 100 constraints for making detailed decisions on a daily or weekly basis.

For annual planning purposes the refinery model is greatly simplified. The two crudes (Iranian and Brunei) are input. Two general products are output-(a) gasoline products; and (b) other products known collectively as distillate. In addition, although the refinery had processing flexibility that permitted a wide range of yields, for planning purposes it was decided to include only the use of the values at highest and lowest conversion rates (process intensity). Each refinery could use any combination of the two extreme intensities. These yields are shown in Table 1.

The incremental costs of operating the refinery depend somewhat upon the type of crude and process intensity. These costs are shown in Table 1. Also shown are the incremental. transportation costs from either Borneo or Iran.

Marketing is conducted in two home areas (Australia and Japan) as well as in the Philippines and New Zealand. Demand for gasoline and distillate in all areas has been estimated for 1996 and is shown in the following table.

Variable costs of supplying gasoline or distillate to New Zealand and the Philippines are shown in the following table.

Tankers are used to bring crude from Iran and Borneo to Australia and Japan and to transport refined products from Australia and Japan to the Philippines and New Zealand. The variable costs of these operations are included in the previous shipment table. However, there is a limited capacity of tankers available. The fleet had a capacity of $6.9$ equivalent (standardized) tankers.

The amount of capacity needed to deliver one barrel from one destination to another depends upon the distance traveled, port time, and other factors. The table below lists the fraction of one standard-sized tanker needed to deliver 1,000 b/d over the indicated routes. It is also possible to charter independent tankers. The rate for this was $\$ 8,600$ per day for a standard-sized tanker.

United States operations on the West Coast expected a surplus of \(12,000 \mathrm{~b} / \mathrm{d}\) of distillate during 1996 . The cost of distillate at the loading port of Los Angeles is $\$ 19.80$ per barrel. There is no excess gasoline capacity. The estimated variable shipping costs and tanker requirements of distillate shipments from the United States are:

Required

1. Formulate and optimize a linear program that could be used to generate a comprehensive plan for the whole Far Eastern Operations.
2. Use the model to respond to the following four new requests.

Price: $33.37

Solution: The downloadable solution consists of 18 pages, 1537 words and 4 charts.
Deliverable: Word Document