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Problem Title: The Strategic Reserve Problem

  Year: 1985      
  Student Level: Undergraduate      
  Source: MCM      
  Commentary: No      
  Student Papers: Yes (1)      

Cobalt, which is not produced in the U.S., 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 U.S. through a three-year war. The government built up a cobalt stockpile in the 1950s, sold most of it 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 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 would the stockpile be drawn down?
  • At what rate should it be drawn down?
  • What is a reasonable price at which to sell the metal?
  • How should sold metal be allocated?

Below we give more information on the sources, cost, demand, and recycling aspects of cobalt.

Useful Information on Cobalt

The government has projected a need of 25 million pounds of cobalt in 1985.
The U.S. has about 100 million pounds of proven cobalt deposits. Production becomes economically feasible when the price reaches $22/lb (as occurred in 1981). It takes four years to get operations rolling, and then six million pounds per year can be produced.
In 1980, 1.2 million pounds of cobalt were recycled, 7% of total consumption.
Please see Figures 1-3, whose source is Mineral Facts and Problems, U.S. Bureau of Mines (Washington, DC: Government Printing Office, 1980).

Figure 1. U.S. primary demand for cobalt, 1960-1980.

Figure 2.
Cobalt prices in the U.S. market, 1960-1982.

Figure 3.
Producers of refined metal and/or oxide, 1979. An asterisk denotes a country with domestic production.

  Student Papers      

Managing a Strategic Reserve

Calvin College, MI