The Global Oil Company (Global Oil) is an international producer, refiner, transporter and distributor of oil, gasoline and petrochemicals. Global Oil is a holding company with subsidiary operating companies that are wholly or partially owned. A major problem for Global Oil 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, the logistics department at Global Oil Headquarters develops an annual corporate-wide plan which details the pattern of shipments among the various subsidiaries. The plan is not rigid but provides general guidelines and the plan is revised periodically to reflect changing conditions. Within the framework of this plan, the operating companies can make their own decisions and plans. This corporate-wide plan is presently done on a trial and error basis. There are two problems with this approach. First, the management of the subsidiaries often complains that the plan does not reflect properly the operating conditions under which the subsidiary operates. The plan sometimes calls for operations or distribution plans that are impossible to accomplish. And secondly, corporate management is concerned that the plan does not optimize for the total company.

The technique of linear programming seems a possible approach to aid in the annual planning process that will be able to answer, at least in part, the two objections raised above. In addition, the building of such a model will make it possible to make changes in plans quickly when the need arises. Before embarking on the development of a world-wide model, Global Oil asks you to build a model of the Far Eastern operations for the coming year.

Far Eastern Operations
The details of the 2008 planning model for the Far Eastern Operations are now described.

There are two sources of crude oil, Saudi Arabia and Borneo. The Saudi crude is relatively heavier (24 API), 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 during 2008. A second source of crude is from the Brunei fields in Borneo. This is a light crude oil (36 API). Under the terms of an agreement with the Netherlands Petroleum Company in Borneo, a fixed quantity of 40,000 b/d of Brunei crude, at a cost of $19.90 per barrel is to be supplied during 2008.

There are two subsidiaries that have refining operations. The first is in Australia, operating a refinery in Sydney with a capacity of 50,000 b/d throughput. The company markets 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 b/d capacity refinery. Marketing operations are conducted in Japan, and excess production is available for shipment to other 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 is in the Philippines. Their needs can be supplied by shipments from Australia, Japan, or the Global 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 refined products among the subsidiaries.

Refinery Operations
The operation of a refinery is a complex process. The characteristics of the crudes available, the desired output, the specific technology of the refinery, etc., 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 (Saudi and Brunei) are input. Two general products are output. They are: (a) gasoline products, and (b) other products such as distillate, fuel oil, etc. In addition, although the refinery has processing flexibility that permits a wide range of yields, for planning purposes it was decided to include only 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 Saudi Arabia.

Marketing Operations
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 2008.

Table 1. Refinery Operations

Area 2008 Demand (000s of b/d)
                          Gasoline             Distillate
Australia                   9                           21
Japan                         3                          12
Philippines               5                             8
New Zeeland        5.4                          8.7
Total                    22.4                        49.7

Tanker Operations

Tankers are used to bring crude from Saudi Arabia 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 supplying gasoline or distillate to New Zealand and the Philippines are:

Variable costs of shipment of
gasoline/distillate in $/b
From To New Zealand Japan
Australia                             0.2               0.3
Japan                                 0.25               0.4

However, there is a limited capacity of tankers available. The fleet has a capacity of 6.5 equivalent (standard sized) 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 is $5,400 per day for a standard sized tanker.

United States Supply
United States operations on the West Coast expect a surplus of 12,000 b/d of distillate during 2008. The cost of distillate at the loading port of Los Angeles is $20.70 per barrel. There is no excess gasoline capacity. The estimated variable shipping costs and tanker requirements of distillate shipments from the United States are:

Questions

Formulate a linear program which can be used to generate a comprehensive plan for the whole Far Eastern operations. Clearly define every variable used in your formulation.