1985问题B 战略储备物资的管理
钴对许多工业是至关重要的(1979年全世界钴产旦的17％用于防务部门)但是美国本土不生产钴，所需钴的大部分来自于政治上不稳定的中非地区。
1946年制定的战略及稀有物资存储法令要求钴的储存量应足以保证美国度过三年的战争时期。50年代政府按此要求建立了钴储备，但是在70年代卖掉了其中的大部分， 70年代后期决定重建这—储备。储存的指标是8540万磅。到1982年．储备达到这一数字的一半左右。
试建立一个数学模型，对金属钴的战赂储备进行经营管理。你需要考虑以下一些问题：诸如储备量应多大?应以什么样的速率建立这一储备?购买这些钴的合理价格是多少?你还应当考虑以下问题当储备量达到多大时，储备的钴可以被动用；应以什么样的速率消耗这一储备?出售这些金属的合理价格如何？这些钴应您样分配?
关于钴的有关资料
1985年政府计划需要2500万磅金属钴．美国国内大约有一亿磅靠得住的钴矿储藏量，只有当价格达到22美元一磅时，在本土外采生产才是经济上可行的(1981年数据)。从开采起、需时四年才能有持续稳定的金属钴生产，此后每年可产销600万磅。又：1980年占总消耗且7％的120万磅钴被再次利用，即得到了回收处理。
Problem B Strategic Reserve Management
Cobalt, which is not produced in the US, is essential to a number of industries. (Defense accounted for 17% of the cobalt production in 1979.) Most cobalt comes from central Africa, a politically unstable region. The Strategic and Critical Materials Stockpiling Act of 1946 requires a cobalt reserve that will carry the US through a three-year war. The government built up a stockpile in the 1950s, sold most of it off in the early 1970s, and then decided to build it up again in the late 1970s, with a stockpile goal of 85.4 million pounds. About half of this stockpile had been acquired by 1982.
Build a mathematical model for managing a stockpile of the strategic metal cobalt. You will need to consider such questions as: How big should the stockpile be? At what rate should it be acquired? What is a reasonable price to pay for the metal? You will also want to consider such questions as: At what point should the stockpile be drawn down? At what rate should it be drawn down? At what price is it reasonable to sell the metal? How should it be allocated?
| 欢迎光临 数学建模社区-数学中国 (http://www.madio.net/) | Powered by Discuz! X2.5 |