Managing Rentals with Usage-Based Loss

Abstract

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.

Condition-Based Production Planning: Adjusting Production Rates to Balance Output and Failure Risk

“…The literature on condition-based maintenance, not restricted to production systems, is rich and deterioration processes depending on time, the current deterioration level, and exogenously given operational modes are covered (Liu et al 2013, Khaleghei and Makis 2016, Samuelson et al 2017. A current trend in the literature is to study the use of condition monitoring for other operational decisions such as improved stock keeping of spare parts (Olde Keizer et al 2017, Zhang andZeng 2017), managing rentals like cars (Slaugh et al 2016), and determining optimal production lot-sizes (Peng and Van Houtum 2016). The latter study uses condition monitoring to determine whether a new lot is started or preventive maintenance is performed.…”

Cross docking for libraries with a depot

“…Stochastic rental models can be grouped into single and multilocation models, with or without a depot. Single location rental models involve no depot and deal with particular issues such as setting the total rental stock for a finite time horizon ( Pasternack & Drezner, 1999;Slaugh, Biller, & Tayur, 2016 ), allocating demand to different customer classes (Jain, Moinzadeh, & Dumrongsiri, 2015) , and analyzing usage of newly introduced products under a heterogeneous customer base (Bassamboo, Kumar, & Randhawa, 2009) . Multilocation rental models without a depot can be divided into two main streams.…”

The Future of Retail Operations

“…For instance, a typical rental business model in apparel requires 1.9 rentals of the inventory to roughly break even (Vow to Be Chic 2017). Slaugh et al (2016) provide heuristics for this inventory problem and show that it can increase profits by 7% and service level by six percentage points. Even in the rental models, products eventually have to be disposed of, so what to do with unsold inventories remains a valid question.…”