Variable costs of shipment of gasoline/distillate in $/b From/To New Zealand |Philippines Australia 0.20 0.30 Japan 0.25 0.40 1.4 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 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 1,000 b/d) Between/and Australia Japan Saudi Arabia 0.12 0.11 Borneo 0.05 0.05 Philippines 0.02 0.01 New Zealand 0.01 0.06 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 1998. 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: Variable costs Tanker of shipments requirements New Zealand 1.40 0.18 Philippines 1.10 0.15 2 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 used in your formulation. 2. Solve your linear program using an optimization modeling/solver tool. How many barrels of crude should Global Oil purchase from Saudi Arabia for its Far Eastern operations? How