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We develop a method for determining the optimal size and placement of parking spaces and approach aisles for an automobile parking lot. In particular, our solution concerns a parking lot of size 100' x 200' located at the corner of an intersection of two streets in a New England town. We begin by arguing the superiority of driver operation over attendant operation of vehicles to be parked. Then a statistical analysis is performed on a sampling of 160 1987 model automobiles to determine upper bounds and ideal values for the length and width of a parking space and for the turning radius required to navigate entrance into said space. Using this data, we show that the optimal degree for diagonal parking which minimizes necessary lot area for a particular space can be expressed as a function of the turning radius of the automobile and the width of the parking space. However, concerning our particular lot, right-angle parking is established as the method by which optimal use of space can be achieved by showing that to minimize wasted area using the diagonal parking scheme requires a greater number of spaces than can be accommodated in the given dimensions. Using these preliminary results, a computer program which utilizes a 12-way tree structure and recursion is employed to generate possible lot designs. Next, other considerations not so conducive to programming—such as snow removal, lot use fees and effects of our design on the adjacent intersection—are discussed.

We develop a method of managing strategic reserves, in this case, the U.S. Strategic Cobalt Reserve. A rationale for the stockpiling of cobalt is presented, followed by a method for bringing the stockpiled amount from any level to a desired goal, in this case an amount determined by the Federal Emergency Management Agency to last through three years of conventional warfare. The method involves solving a stochastic programming problem in order to balance the expected values of the social benefit and the social cost of building the stockpile—Social benefit is accrued by decreasing the impact and the probability of a war or a major supply disruption occuring before the stockpile goal is realized; social cost is determined from the additional amount U.S. cobalt consumers must pay due to the increase in world demand brought about by stockpiling. The management of the filled stockpile is then discussed, introducing the idea of using the stockpile to assure stability in the world price of cobalt and of defraying maintenance costs by market speculation. Least-squares fitting is used to determine whether prices are high or low and how much to sell or buy, respectively, to bring prices back into line. Then the conditions under which the stockpile should be drawn down are considered, with the proper rate and total amount of released stockpile material determined for two cases, that of a major supply disruption and that of actual warfare. Finally, generalization of the method to cover other strategic stockpiles is discussed.