ABSTRACT

Ph.D. Thesis for Purdue University, June 1964
Major Professor: Ferdinand F. Leimkuhler

In view of the increasing growth rate of published materials, librarians are becoming highly concerned about their ability to store their future collections in a manner which will permit retrieval in a reasonable length of time. A search of the literature did not reveal a thorough and systematic approach to this problem of storage, which had general applicability. This study offers a structure of the overall storage problem with emphasis upon one aspect - the saving of space through the use of compact storage. Thus, the primary purpose of this research is to develop, discuss, and demonstrate compact storage models.

Two-dimensional and three-dimensional unconstrained storage models are developed and demonstrated for continuous and discrete size distributions of books. These models assume known size distributions and a known number of shelf heights. Then, the values of the shelf heights are to be chosen such that the storage space is minimized. The two-dimensional model is rather completely developed while the three-dimensional model is developed for book width, an increasing function of book height. Limiting conditions on the models and an analogy with inventory theory are presented. Geometrical interpretations of the problem and the solution technique are also provided.

A proposed computational scheme is discussed and demonstrated for the unconstrained models by using hypothetical continuous distributions and a discrete distribution from the Purdue University collection. A simple measure of the maximum possible increase in capacity yields 58% for the two-dimensional model and 150% for the three-dimensional model. This measure is not very meaningful for the three-dimensional model because it ignores aisle space.

Three constrained models are developed which consider the restrictions of the stack height, shelf thickness, shelf length, and incremental shelf adjustment. The Within Shelf model assumes that shelf heights may vary within a a stack unit, but all stack unites are identical. A different arrangement is implied by the Within Stack model which assumes that the total set of stack units is divided into subsets, such that each subset contains only those units with identical height shelves. By using the criterion of minimum number of stack units, both the number of shelf heights and their values are obtained (or estimated). The third constrained model is called Random Shelf, because it permits the books to be randomly placed on the shelves with respect to size.

For the examples demonstrated, the Within Shelf model permitted a gain of one shelf in each stack unit. The Within Stack model offered a slightly higher percentage gain. Removal of the stack cover permitted another shelf for the Within Shelf model, but it was not nearly as effective for the Within Stack model. By removing the incremental shelf adjustment restriction (a design consideration), further slight increase in capacity resulted. The Random Shelf model did not show any improvement for the one discreet example considered.

In addition to the sample data from Purdue University, a large sample of sizing data from Auburn University, Auburn, Alabama, was collected. Application of the storage models to this data gave the same general results as for the Purdue data.

A very interesting and practical result of all of the examples for all the models was the small number of shelf heights (from 3 to 5) required to be near an optimal solution. Discussions of some other factors pertinent to the total storage problem are offered for librarians and other investigators. These discussions are based upon rather inconclusive exploratory studies, which were not within the scope of this research effort.