Compact Book Storage in Libraries

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Abstract
A method is developed for optimally shelving inventory items by size, with particular reference to large library collections. The area presented by n + 1 distinct shelf heights is minimized for any collection that can be characterized by an item-height distribution. When item-height is continuous, the necessary conditions for the extremum are recursive in the optimal shelf heights, and the solution reduces to a simple computational search. For certain distribution functions, as demonstrated in the example, an additional recursive relation between the solutions for different n further simplified the computation considerably. Geometrical representations of both the model and the solution method are presented. The maximum increase in storage capacity can be expressed generally as a simple function of the mean and the maximum item-height.

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