Linear Program

The Global Oil Company

The Global Oil Company 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.


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To deal with this dilemma, Global Oil Headquarters develops an annual corporate-wide plan that provides the pattern of shipments among the various subsidiaries. The plan sets annual targets for each of the subsidiaries. It does not detail their day-to-day operations. Within the framework of this annual plan, the operating companies can make their own decisions and plans. This corporate-wide plan is presently done on a trial and error basis and, unfortunately, this has several drawbacks. 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. Second, Global Oil’s CEO Pedro Kemikol is concerned that the plan does not optimize for the total company.


In fact, Pedro Kemikol has made it his top priority to optimize the entire supply chain, from the procurement of crude oil to the distribution of gasoline at the pump. Global Oil has hired recently some young graduates from the Northwestern. They have hinted to Pedro that linear programming can be used to optimize the flow of raw materials and finished products by averaging over a year. This way, they argued, a corporate-wide annual plan would be generated based on a sound quantitative approach. Although Pedro is somewhat skeptical, he is open minded and willing to give it a try. Before embarking on the development of a world-wide model, Pedro Kemikol asks you to build a model of the Far Eastern Operations. The details of the Year 2006 planning model for the Far Eastern Operations are now described.


( 1 )

Far Eastern Operations


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 80,000 barrels per day (b/d) at a cost of $62 per barrel during Year 2006. 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 30,000 b/d of Brunei crude, at a cost of $67 per barrel is to be supplied during Year 2006.

There are two subsidiaries that have refining operations. The first is in Australia, operating a refinery in Sydney with the capacity of processing 30,000 b/d of crude. The Australian subsidiary markets its refined products throughout Australia, as well as having a surplus available for shipment to other subsidiaries. The Australian subsidiary does not import refined products.

The second subsidiary is in Japan, which operates a 50,000 b/d capacity refinery. Refined products are marketed in Japan, and excess production is available for shipment to other Far Eastern subsidiaries. The Japanese subsidiary does not import refined products.

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 – (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 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 transportation costs from either Borneo or Saudi Arabia.


Table 1: Refinery Operations

  Australia Japan
Capacity (b/d of input) 30000 50000
Saudi Crude    
Transportation Cost ($/b) 0.75 0.8
High Process Intensity ($/b) 1.19 1.26
Yield of Gasoline 0.31 0.3
Yield of Distillate 0.61 0.62
Low Process Intensity ($/b) 0.89 0.88
Yield of Gasoline 0.19 0.18
Yield of Distillate 0.76 0.77
Brunei Crude    
Transportation Cost ($/b) 0.35 0.35
High Process Intensity ($/b) 0.93 0.91
Yield of Gasoline 0.36 0.35
Yield of Distillate 0.58 0.59
Low Process Intensity ($/b) 0.61 0.55
Yield of Gasoline 0.26 0.25
Yield of Distillate 0.72 0.73



Marketing Operations


Marketing is conducted in two home areas (Australia and Japan) as well as in New Zealand and the Philippines. Demand for gasoline and distillate in all areas has been estimated for Year 2006.


Year 2006 Demand

Area (thous. of b/d)

  Gasoline Distillate
Australia 6 15
Japan 8 21
New Zealand 5.4 14
Philippines 3 8
TOTAL 22.4 58


The variable costs of supplying refined products to New Zealand and the Philippines are as follows:


( Variable costs of shipment of gasoline/distillate in $/b To: New Zealand Philippines From: Australia 0.2 0.2 Japan 0.45 0.25 )



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 New Zealand and the Philippines. The variable costs of these operations are included above.

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.

Tanker Usage Factors

(Fraction of Standard Sized Tanker Needed to Deliver 1000 b/d)

Between and Australia   Japan
Saudi Arabia     0.11 0.14
Borneo     0.05 0.05
New Zealand     0.04 0.08
Philippines     0.05 0.04


It is also possible to charter independent tankers. The rate for this is $8,500 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 Year 2006. The cost of distillate at the loading port of Los Angeles is $74 per barrel. There is no excess gasoline capacity. The estimated variable shipping costs and tanker requirements of distillate shipments from the United States are:



  Variable costs

of shipments


Tanker requirements

New Zealand  




Philippines 1.2 0.13





Your Job

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, and clearly write the objective and constraints in algebraic form. Then you need to use EXCEL SOLVER (or ANALYTICAL SOLVER PLATFORM) to find the optimal decision and value. Your entire report should be at most 4 pages long (Times New Roman, 12pt, double spaced). Please submit your report and Excel file digitally via Blackboard link.

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