Managing Rentals with Usage-Based Loss

Motivated by new and innovative rental business models, this paper develops a novel discrete-time model of a rental operation with random loss of inventory due to customer use. The inventory level is chosen before the start of a finite rental season, and customers not immediately served are lost. Our analysis framework uses stochastic comparisons of sample paths to derive structural results that hold under good generality for demands, rental durations, and rental unit lifetimes. Considering different \recirculation" rules | i.e., which rental unit to choose to meet each demand | we prove the concavity of the expected profit function and identify the optimal recirculation rule. A numerical study clarifies when considering rental unit loss and recirculation rules matters most for the inventory decision: Accounting for rental unit loss can increase the expected profit by 7% for a single season and becomes even more important as the time horizon lengthens. We also observe that the optimal inventory level in response to increasing loss probability is non-monotonic. Finally, we show that choosing the optimal recirculation rule over another simple policy allows more rental units to be profitably added, and the profit-maximizing service level increases by up to 6 percentage points.

Usage-Based versus Measure-Based Unit Pricing: Is There a Better Index of Value?

In many product categories, unit prices facilitate price comparisons across brands and package sizes; this enables consumers to identify those products that provide the greatest value. However in other product categories, unit prices may be confusing. This is because there are two types of unit pricing, measure-based and usage-based. Measure-based unit prices are what the name implies; price is expressed in cents or dollars per unit of measure (e.g. ounce). Usage-based unit prices, on the other hand, are expressed in terms of cents or dollars per use (e.g., wash load or serving). The results of this study show that in two different product categories (i.e., laundry detergent and dry breakfast cereal), measure-based unit prices reduced consumers’ ability to identify higher value products, but when a usage-based unit price was provided, their ability to identify product value was increased. When provided with both a measure-based and a usage-based unit price, respondents did not perform as well as when they were provided only a usage-based unit price, additional evidence that the measure-based unit price hindered consumers’ comparisons. Finally, the presence of two potential moderators, education about the meaning of the two measures and having to rank order the options in the choice set in terms of value before choosing, did not eliminate these effects.