MthSc 810 Mathematical Programming Case Study: The Global Oil Company

Transcription

1 MthSc 810 Mathematical Programming Case Study: The Global Oil Company October 30, 1996 Students may work in groups of up to three people. You may consult only your textbook, your notes, the AMPL manual, and me. Please submit a written report, a printout of your AMPL model and data files, and any AMPL output needed to support your answers. 1 Introduction Global Oil is an international producer, refiner, transporter, and ditributor of oil, gasoline, and petrochemicals. Global Oil is a holding company with a number of subsidiary operating companies that are wholly or partially owned. A major problem for Global Oil is to coordinate the actions of the various subsidiaries into a coherent corporate plan while maintaining a reasonable amount of operating autonomy for the subsidiary companies. The annual corporate-wide plan deals with this dilemma by providing shipping patterns among the subsidiaries. This plan is not rigid and is revised periodically to reflect changing conditions. Within the framework of the plan, the subsidiaries make their own decisions and plans. The corporate plan was originally done on a trial and error basis. There were two problems with this approach. First, the subsidiaries complained that the planners did not take into account the operating conditions under which the subsidiary had to operate. Second, the corporate management was concerned that the plan did not optimize for the total company. The technique of linear programming seems like a possible approach to aid in the annual planning process. With a suitable model, it seems possible 1

2 to at least partially counter the two problem above. In addition, such a model will be easily modified to reflect changing conditions. 2 Far Eastern Operations The details of the 1996 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 costs $19.15 per barrel. This oil is bought on the spot market and there is no more than 60,000 barrels per day (b/d) available. The Borneo fields produce a lighter crude (36 API). Global Oil receives this on a fixed contract with the Netherlands Petroleum Company. Under this contract, 40,000 b/d will be purchased at a cost of $22.17 throughout There are two subsidiaries that have refining operations. The first is in Australia, operating a refinery in Sydney with a capacity of 45,000 b/d throughput. The company markets its products throughout Australia, as well as having surplus of refined products to ship to other subsidiaries. The second refining subsidiary is in Japan, which has a capacity if 30,000 b/d throughput. This subsidiary markets in Japan and also has excess production for other subsidiaries. Additionally, there are two marketing subsidiaries without refining capacity of their own. One is based in New Zealand and the other in Philippines. They receive refined products from either Japan or Australia or from the Global Oil subsidiary on 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 to move the crude oil and the refined products among the subsidiaries. 3 Refinery Operations The operations 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 2

3 fact, management at both Australia and Japan use complex linear programming models on a weekly basis to plan production. For annual planning purposes, the refinery model is greatly simplified. The two crudes (from Saudi and Borneo) are inputs. Two general products are produced: gasoline (G) and distillate (D). This distillate indicates products like fuel oil, tar, and wax. Although each refinery has the processing flexibility for a wide range of yields, for planning purposes it was decided to include only two extreme conversion rates: high and low. For our purposes, it is sufficient to note that one barrel of crude can use any mixture of high and low conversion and that the conversion will result in different amount of G and D. These yields are shown in Table 1. Note that processing a barrel of crude results in less than a barrel of G and D combined. The cost of conversion depends somewhat on the type of crude and the process. There are also costs for transporting the crude from either Borneo or Saudi Arabia. These values are also given in Table 1. 4 Marketing Operations Marketing is conducted in the two refinery areas (Australia and Japan) as well as in Philippines and New Zealand. Demand for gasoline and distillate is set by contract and hence must be met exactly. For 1993, this has been estimated in Table 2. The variable cost of supplying one barrel of either gasoline or distillate are as follows: 5 Tanker Operations Philippines New Zealand Australia $0.30 $0.20 Japan $0.40 $0.20 Tankers are used to bring crude from Saudi Arabia and Borneo to Australia and Japan and to transport refined products from there to Philippines and New Zealand. The variable costs of these are given above. There is, however, a limited capacity of tankers available. The equivalent of 6.9 standard tankers are available for shipping each day. 3

4 The amount of capacity needed to deliver one barrel from one destination to another depends upon the distance traveled, port time, and other factors. Table 3 lists the fraction of one standard tanker needed to deliver 1,000 b/d over the indicated routes. It is also possible to charter independent tankers for $5,400 per day for a standard tanker. 6 United States Supply United States operations on the West Coast expects a surplus of 12,000 b/d of distillate during The cost at Los Angeles is $19.00 per barrel. There is no gasoline available. The estimated variable shipping cost from the U.S. are $1.40 to New Zealand and $1.10 to the Philippines. In either case, the tanker equivalents is 0.16 tanker equivalents to ship 1000 b/d. 7 Questions 1. Formulate a linear program which can be used to generate a comprehensive plan for the whole Far Eastern operations. Clearly define every variable in your formulation. Explain every constraint including coefficients (only simple and obvious coefficients such as +1 and 1 and those taken directly from the tables need not be explained). 2. Solve your linear program using AMPL. As simply as you can, describe thesolutioninwords. 3. Use sensitivity analysis to answer the following questions. Try to answer them without re-solving the linear program. (a) What would be the cost of a shutdown of the refinery in Australia for three days per year? What about a similar shutdown in Japan? [Hint: Treat shutting down 3 days per year as shutting down a small fraction of a day, every day, over the year]. (b) What is the marginal value of increasing the 40,000 b/d supplied from Borneo? Can this marginal value be used to estimate the total savings if 41,000 b/d are supplied instead of 40,000? Explain. 4

5 (c) What is the marginal value of increasing the tanker fleet? (d) What is the additional cost if demand for gasoline in the Philippines increases to 6,000 b/d? What is the minimum price of gasoline in the Philippines that would make it profitable to consider such an increase in distribution? (e) By how much should the production costs be reduced in Australia when operating at low process in order to make it cost effective to use such a process? 4. Several opportunities present themselves to the Global Oil company (see attached memos). Consider all the options and prepare a recommendation. Document your report. Note that you might have to re-solve the linear program a few times to gauge the interactions of the proposals. Use sensitivity analysis to guide you to appealing combinations. 5

6 8 Memos To: Global Oil Headquarters From: Australian Affiliate Since submitting data for annual planning, two additional opportunities have arisen. We would like to include these in the plans. A. Bid on Gasoline Contract with the Australian Government The government of Australia will submit a bid for a contract for 1,500 b/d of gasoline. We expect that we could win this bid at a price of $29.50 per barrel. We estimate the variable cost per barrel at $26.00 for a profit of $3.50 per barrel. We would like permission to bid on this contract. B. Expansion of Australian Refinery For the past three years, the Australian refinery has been operating at full capacity. We require authorization for capital expenditures to increase the refinery capacity to 50,000 b/d. There are several reasons for the need for this expansion: 1. Australia can supply the current requirements in New Zealand and the Philippines cheaper than Japan can. 2. The proposed bid on the government contract will further increase our demand. 3. The New Zealand affiliate is considering increasing its requirements [see below]. The cost of this expansion is 4 million dollars. To recover this investment, we need an annual savings of $702,000. To: Global Oil Headquarters From: New Zealand Affiliate Negotiations have begun with the NOZO Oil Company in New Zealand. Our intentions are to purchase this company and to make it a subsidiary. This company is a distributor with sales of 1600 b/d gasoline and 3200 b/d distillate. If we succeed, these requirements would be added to the current requirements for New Zealand. The anticipated revenue from this acquisition is $30 per barrel of gasoline and $22 per barrel of distillate. 6

7 The purchase cost of NOZO will be roughly $21 million. On an annual basis, this would require additional profits of $3.5 million to justify purchase. To: Global Oil Headquarters From: Borneo Office Our supplier of Brunei crude is willing to supply an additional 5,000 b/d at the current price. Should we accept the offer? To: Global Oil Headquarters From: Tanker Affiliate We are aware that expansions in requirements are being considered in New Zealand and Australia. The tanker fleet is currently operating at capacity. Additional requirements will increase the transport necessary for both crude and refined products. An unlimited number of additional tankers can be leased on a long term basis at a rate of $4,800 per day per tanker equivalent. We propose to lease 0.5 tanker equivalents at a cost of $2,400 per day. What do you think? 7

8 9 Tables Australia Japan Capacity (b/d) 45,000 30,000 SAUDI CRUDE Transporation Cost ($/b) High Process ($/b) Fraction yield of Gasoline Fraction yield of Distillate Low Process ($/b) Fraction yield of Gasoline Fraction yield of Distillate BRUNEI CRUDE Transporation Cost ($/b) High Process ($/b) Fraction yield of Gasoline Fraction yield of Distillate Low Process ($/b) Fraction yield of Gasoline Fraction yield of Distillate Table 1: Refinery Operations 8

9 1993 Demand (in 1000 b/d) Gasoline Distillate Australia Japan Philippines New Zealand Table 2: 1996 Demand Australia Japan Saudi Arabia Borneo Philippines New Zealand Table 3: Shipping Requirements 9