Decision Modeling: Linear Programming Project The Global Oil Company is an international producer, refiner, transporter, and distributor of oil, gasoline, and petrochemicals. Global is a holding company with subsidiary operating companies that are wholly or partially owned. A major problem for Global 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 Global 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, a recent MBA graduate. Linear Programming, as a planning tool, was being used for the first time in Global, and hence, Mr. Brown was keen to get the operating subdivisions in the Far East involved in the planning of 2010 operations. Far Eastern Operations For the Far Eastern Operations, there are two sources of crude oil, Saudi Arabia and Borneo. The Saudi Arabian crude is relatively heavier (24 API), and the Far Eastern sector could obtain as much as 300,000 barrels per day at a cost of $52.00 per barrel from Saudi Arabia during 2010. A second source of crude is from the Brunei fields in Borneo. This is a lighter crude oil (36 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 $57.00 per barrel was to be supplied during 2010. There are two subsidiaries that have refining operations. The first is in Australia, operating a refinery in Sydney with a capacity to refine 210,000 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 110,000 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 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 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 (Saudi 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 Saudi Arabia. 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 2010. Area Australia Japan Philippines New Zealand TOTAL 2010 Demand (in '000 b/d) Gasoline Distillate 35 85 14 50 20 35 22 36 91 206 The variable costs of supplying gasoline or distillate to New Zealand and the Philippines are as follows: Refinery Australia Japan Variable Cost of shipping Gasoline/Distillate ($/bbl) to: New Zealand Philippines $ 1.40 $ 1.60 $ 1.50 $ 1.80 2 Tanker Operations Tankers were 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 these operations are included above. However, Global 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, Global had defined an equivalent "standard" tanker. The capacities of tankers of various sizes it had available were then converted to the equivalent "standard" tankers. Global's fleet has a capacity of 26.5 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. FROM/TO Saudi Arabia Borneo Philippines New Zealand Tanker Usage Factor (Equivalent \"Standard\" tanker used per 1000 b/d) Australia Japan 0.15 0.12 0.06 0.05 0.03 0.02 0.02 0.10 It was also possible to charter capacity on independent tankers. This capacity could be obtained at the rate of $36,800 per standard tanker equivalent for 1,000 b/d delivery (and could be purchased in any tanker equivalent amounts). United States Supply United States operations on the West Coast expected a surplus of 52,000 b/d of distillate during 2010. The cost of distillate at the loading port of Los Angeles is $58.00 per barrel. There will be no excess gasoline capacity. The estimated variable shipping costs ($/bbl) and tanker requirements of distillate shipments from the Unites States are: Shipment of Distillate from USA to: New Zealand Philippines Variable Shipment Tanker Usage Factor Cost ($/bbl) $3.20 0.18 $2.50 0.16 Questions 1. Develop an optimal refining and shipping plan for Global's Far East operations for 2010. What is the operating cost for this plan for the year? 2. Athena Shipping, an independent shipping company, is offering a $1/bbl discount on all shipments from the USA to New Zealand. How will this affect Global's plans for 2010? Why? 3. A union dispute may cause a refinery shutdown in the USA which would lead to a reduction of 20,000 b/d of distillate in the US operations supply. If that happens, how will it affect Global's Far East plans for 2010, and how much money will they lose? Why? 3 EXHIBIT 1: REFINERY COSTS AND YIELDS (all costs in $/bbl) Yield (bbl output per bbl Inbound Cost of Refining Total crude)1 Location, Crude, Process Shipping Crude Cost Cost Cost Gasoline Distillate Australia Brunei Crude, Low (BLA) $57 $3.04 $0.96 $61.00 0.259 0.688 Brunei Crude, High (BHA) $57 $3.04 $2.12 $62.16 0.365 0.573 Saudi Crude, Low (SLA) $52 $3.48 $1.62 $57.10 0.186 0.732 Saudi Crude, High (SHA) $52 $3.48 $2.22 $57.70 0.312 0.608 Japan Brunei Crude, Low (BLJ) Brunei Crude, High (BHJ) Saudi Crude, Low (SLJ) Saudi Crude, High (SHJ) $57 $57 $52 $52 $1.96 $1.96 $3.36 $3.36 $1.64 $2.34 $1.80 $2.54 1 $60.60 $61.30 $57.16 $57.90 0.259 0.350 0.186 0.300 0.688 0.588 0.732 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 in 0.259 bbl of gasoline AND 0.688 bbl. of distillate 4