Misplacement of Books on Library Shelves: A Mathematical Model

Abstract

A mathematical model is developed to determine the optimal interval for reading the shelves of a library. The model is based on knowledge of the transition probabilities of books moving from one shelf to another. Optimization of the process requires information on the cost of shelf reading to the library, the cost of a misplaced book to a user, and the error rate of the shelf reader. Sample data are reported on the degree of misplacement of books in a university library. It was found that 5.6 percent of the books were misplaced, with 65 percent of them located on the correct shelves but not in correct locations. Books misplaced on correct shelves were likely to be found slightly to the right of their correct positions on the shelves. Books misplaced on incorrect shelves are much more likely to be located to the left than to the right of their correct shelves. Implementation of the model with the sample data indicated that libraries are prone to shift shelf-reading costs to the user by relatively infrequen...