Identify the linear programming problem apparent in the case, that will help the company achieve their goals. Excel file with model and optimal solution (optimal purchasing, refining, shipping schedule), as well as any written documentation to support the model (including formulations).

 

• The number of decision variables should be greater than or equal to 19 and strictly less than 30.
• Dont assume any variables were integer valued.
• Do assume all 160,000 b/d of Brunei crude will be taken (nothing less).
• Volumes: Observe that a bbl of oil does not equal a bbl of gas and distillate. A bbl of oil is cracked to produce a fraction of a bbl of gas and a fraction of a bbl of distillate. These fractions do not add up to 1 (i.e., there is no volumetric equivalence between oil as an input and gas & distillate as outputs). Use your cracking fractions!

Use the follow case as a basis for case study 

 

Trans Pacific Oil Company (TPO)

 

The Trans Pacific Oil Company is an international producer, refiner, transporter, and distributor of oil, gasoline, and petrochemicals. Trans Pacific is a holding company with subsidiary operating companies that are wholly or partially owned. A major problem for Trans Pacific 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 which 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. In particular, the plan might call for operations or distribution plans that were impossible to accomplish. And secondly, 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. It 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 corporate planning department of Trans Pacific Oil Company was given the responsibility of developing the necessary Linear Programming Model. Mr. Brown, chief of the corporate planning department, had assigned this task to his assistant, Ms. Jamias, a recent MBA graduate of a well-known southern business school. Linear Programming, as a planning tool, was being used for the first time in TPO, and hence, Mr. Brown was keen to get the operating subdivisions in the Far East involved in the planning of 2009 operations. 

 

Far Eastern Operations

The details of the Far Eastern Operations are now described.

 

There are two sources of crude oil, Iran and Borneo. The Iranian crude is relatively heavier (24E API), and the Far Eastern sector could obtain as much as 350,000 barrels per day at a cost of $60.00 per barrel at Abaian during 2009. A second source of crude is from the Brunei fields in Borneo. This is a lighter crude oil (36E API). Under the terms of an agreement with Netherlands Petroleum Company in Borneo, a fixed quantity of 160,000 b/d of Brunei crude, at a cost of $68.00 per barrel was to be supplied during 2009.

 

There are two subsidiaries that have refining operations. The first is in Australia, operating a refinery in Sydney with a capacity to refine 200,000 b/d of crude oil. The company also marketed its products throughout Australia, as well as having a surplus of refined products available for shipment to other Far Eastern subsidiaries.

 

The second subsidiary is in Japan, which operates a 120,000 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 were two marketing subsidiaries without refining capacity of their own.  One of these was in New Zealand and the other in the Philippines. Their needs can be supplied by shipments from Australia, Japan, or the Trans Pacific 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 had a fleet of tankers that moved 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 (Iranian and Brunei) are input. Two general products are output -- (a) gasoline products; and (b) other products such as distillate fuel oil. 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 Exhibit 1. The incremental costs of operating the refinery depended somewhat upon the type of crude and process intensity. These costs are shown in Exhibit 1. Also shown are the incremental transportation costs from either Borneo or Iran.

 

Marketing Operations

Marketing is conducted in two home areas (Australia and Japan) as well as in the Philippines and New Zealand.  Demands for gasoline and distillate in all areas have been estimated for 2009.

Area	2009 Demand (in '000 b/d)
	Gasoline	Distillate
Australia	36.0	84.0
Japan	12.0	48.0
Philippines	20.0	32.0
New Zealand	21.5	35.5
Total	89.5	199.5

 

Variable costs of supplying gasoline or distillate to New Zealand and the Philippines are:

 

Refinery	Variable Cost of Shipment of Gasoline/Distillate ($/bbl.) to:
	New Zealand	Philippines
Australia	1.60	2.40
Japan	1.60	3.20

 

Tanker Operations

Tankers were 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 above.

 

However, TPO had a limited capacity of tankers -- company owned and leased -- available. The amount of capacity needed to deliver one barrel from one destination to another depended upon the distance traveled, port time, and other factors. To simply the estimation of its tanker capacity, TPO had defined an equivalent "standard" tanker. The capacities of tankers of various sizes it had available were then converted to the equivalent "standard" tankers. TPO's fleet has a capacity of 26.4 equivalent standard tankers. The table below lists the fraction of one equivalent "standard" tanker needed to deliver 1,000 b/d over the indicated routes.

 

	Tanker Usage Factor (Equivalent "standard" tanker used per 1000 b/d)
To From	Australia	Japan
Iran	0.12	0.11
Borneo	0.05	0.045
Philippines	0.02	0.01
New Zealand	0.01	0.06

 

It was also possible to charter independent tankers (to add to the existing tanker capacity). The rate for this was $51,200 per day for a standard tanker equivalent.

 

United States Supply

United States operations on the West Coast expected a surplus of 68,000 b/d of distillate during 2009. The cost of distillate at the loading port of Los Angeles is $60.00 per barrel. There will be no excess gasoline capacity. The estimated variable shipping costs ($/bbl) and tanker requirements of distillate shipments from the Unites States are:

 

Shipment of Distillate from USA to:	Variable Shipment Cost ($/bbl.)	Tanker Usage Factor
New Zealand	11.20	0.18
Philippines	8.80	0.15

 

 

 

EXHIBIT 1
REFINERY COSTS AND YIELDS (All costs in $/bbl.)
Location, Crude, Process	Cost of Crude Oil	Inbound Shipping Cost	Refining Cost	Total Cost	Yield (bbl. output per bbl. of crude input)1
					Gasoline	Distillate
Australia
Brunei Crude, Low (BLA)	68.00	4.16	1.92	74.08	0.259	0.688
Brunei Crude, High (BHA)	68.00	4.16	4.48	76.64	0.365	0.573
Iran Crude, Low (ILA)	60.00	9.92	2.40	72.32	0.186	0.732
Iran Crude, High (IHA)	60.00	9.92	4.80	74.72	0.312	0.608
Japan
Brunei Crude, Low (BLJ))	68.00	3.84	2.56	74.40	0.259	0.688
Brunei Crude, High (BHJ)	68.00	3.84	5.44	77.28	0.350	0.588
Iran Crude, Low (ILJ)	60.00	9.44	3.20	72.64	0.186	0.732
Iran Crude, High (IHJ)	60.00	9.44	6.24	75.68	0.300	0.620
Consider, for example, refining of Brunei crude oil at low intensity in Australia, i.e., BLA. The yield data shows that refining one barrel of crude oil results into 0.259 bbl. of gasoline and 0.688 bbl. of distillate