This paper attempts to establish a mathematical model to analyze and study the following problems in combination with the establishment of a maintenance team and crude oil transportation in an oilfield:
(1) The attached figure in Annex B 1 gives a schematic diagram of the traffic road in Area A of an oilfield and the existing 20 maintenance teams. See Annex B2 for relevant data information. The daily work of the maintenance team is to inspect the oil production wells within its jurisdiction. Please allocate the jurisdiction for 20 maintenance teams reasonably, so that the workload of each maintenance team is as balanced as possible and can arrive as soon as possible in case of accidents in the oil wells under their jurisdiction.
(2) Assuming that an oil spill accident occurs at the 13 oil production point at the same time, 20 maintenance teams need to be dispatched to realize rapid maintenance and resume production. In practice, a team can maintain at most one oil production point, and each oil production point only needs one team. In order to minimize the oil leakage loss, please give a reasonable scheduling scheme for 20 maintenance teams. (Note: It is assumed that the crude oil production rate at the production point is directly proportional to the recoverable reserves)
(3) In order to transport crude oil from all oil producing points to O point (coordinate origin) quickly, it is planned to build some existing roads as high-grade highways and special lines for crude oil transportation. Assuming that the total maintenance cost of road construction and oil production period is 1 10,000 /km and the road transportation cost is 0. 1 10,000 tons /km, please design a reasonable road transportation network to minimize the road construction and transportation costs. It is assumed that after exploration, the recoverable reserves of each oil production point have increased by 10 times. Please redesign a reasonable road traffic network. (Note: It is assumed that each oil production point can build a straight road to point O)
(4) Pipeline oil transportation has the characteristics of high construction cost and low oil transportation cost. Assuming that the total cost of oil pipeline construction and maintenance during the oil production period is100000 /km, ignoring the oil transportation cost, the pipeline can only be built along the existing road. Please compare highway transportation to analyze the economy of building oil pipelines and design a reasonable crude oil transportation scheme. Suppose that after exploration, the recoverable reserves of each oil producing point have increased by 10 times, so please redesign a reasonable crude oil transportation scheme. (Note: It is assumed that all oil production points can build oil pipelines reaching point O in a straight line. )
This problem can be referred to the 2000 National Mathematical Modeling Competition for College Students.