On establishing initial inventory levels in the rent-to-own industry: an empirical analysis

A theoretic model is developed to calculate the optimal inventory investment for a firm in the rent-to-own industry. This investment question is shown to be equivalent to a queueing problem and queueing technology is employed to fashion a solution. The initial inventory level is a critical decision which should be made to maximise expected profit. The decision is complicated by the fact that the arrival process of new customers, the total number of times that an item will be rented, and the length of time an item is kept by a customer are all random variables. Despite this, the model is able to provide closed-form solutions for various parameters, e.g., the probability that a potential customer will be lost due to product unavailability. A compelling feature of the current study is our access to a large and detailed transactional database. This is used to gain insight into actual contract usage and to numerically estimate the input parameters to our model. The resultant optimal inventory level is then compared against the actual levels providing a clear goodness-of-fit test for our overall approach.