Optimal loan periods

摘要

The influence of a library's loan period on user satisfaction is a topic of considerable current interest. In this paper a model is created that is useful for studying this interaction. A policy, possibly appropriate for a reserve book room, is assumed, in which no queues form. Users not able to take out a book either give up or return. Also, the model includes the effect of a patron not being able to use a book for a sufficient length of time. This model yields equations for the value of the loan period that minimizes the number of transactions at the circulation desk consistent with a constant level of real demand. An iterative solution procedure is described and its convergence proven. Other objective functions, and in particular, the probability of a user successfully using a book, are considered.The objective of the paper is not to detail an operating procedure for circulation systems, but to continue the discussion initiated by Philip Morse about how such systems can be modelled. Morse introduces a queuing model for circulating books, but neglects to consider the impact of queue formation on the arrival rate to the system. The intention of this paper is to emphasize the necessity of introducing such considerations and to indicate how such complications can be analytically treated. The specific system modelled is a simplified one, similar to the one discussed by Bruce in a recent article published in L.Q. This model, or variants adapted to local conditions should be useful in assisting decision-making regarding circulation, but it is the modelling process rather than the management aspect that is addressed by this paper.