Research Article
Characteristics of Optimal Rental Periods for the Rental Industry
1 Chung-Ang University
Published: January 2010 · Vol. 39, No. 3 · pp. 835-849
Full Text
Abstract
There have been many studies trying to understand and construct sound theoretical schemes analyzing the characteristics of the rental industries such as DVD rental industry. Most of the researches have concentrated on finding the optimal rental price to maximize the profit of a retail rental company. On the other hand, we observe few efforts to optimize another important managerial factor, which is the rental period. Especially, if the rental demand is affected by the rental price or the rental period, then it is not that simple to solve such problems, and we find some meaningful implications though. We investigate the characteristics of the optimal rental period which maximizes the profit of a retail rental company, and we produce several managerial implications based on the results. We assume the rental price is already given exogenously and the rental demand is affected by the length of the rental period. In other words, the model assumes the corresponding rental demand increases if the rental period increases. On the other hand, the corresponding rental demand decreases if the rental period decreases. First, we analyze the shape of the profit function as a function of the rental period, and find that there is a certain upper-bound value for the optimal rental period. Also we find that the profit function is a concave function of the rental period if the rental period exists below a certain threshold, otherwise the concavity cannot be guaranteed. Based on those analyses, we provide some conditions and limitations for the optimal rental period to be a relatively short term such as 1 or 2 periods. Also, we develop a theoretical scheme which shows patterns of the optimal rental period when some important managerial factors such as unit inventory holding cost, unit inventory shortage cost, and unit cost of the product changes, respectively. For instance, if unit inventory holding cost increases, then a manager should make the optimal rental period shorter than the present period to depend their profitability as much as possible. Similarly, if unit inventory shortage cost increases, then a manager should make the optimal rental period shorten either. Finally if the unit cost of the product increases, then a manager also should make the optimal rental period shorten in the same manner.
