A queueing model for time-dependent rental systems with phase-type distributed rentals and substitutions of items
本文为租赁公司提供了一个基于连续时间马尔可夫链的排队模型，用于评估时变租赁系统的占用情况，并设计了启发式优化算法在控制缺货概率的同时最小化库存容量，通过数值实验和公司案例验证了方法的有效性。
Abstract Society currently experiences a growing interest in renting as an alternative to exclusive ownership (Fota et al., 2019; Yeganeh, 2021). This paper supports rental companies in this transition by providing a method to evaluate rental system occupancy. The method considers time-dependent systems in which customers rent substitutes during stockouts. Specifically, the paper provides a queueing model based on a continuous-time Markov chain for systems where rentals occur according to Poisson processes and rental times follow phase-type distributions. Additionally, the paper provides a heuristic optimization algorithm to minimize inventory capacity while maintaining an upper stockout probability limit. The paper evaluates these methods through numerical experiments, including a company case. The results indicate that the queueing model adequately reflects the occupancy distributions of the investigated items, and that the optimization algorithm minimizes the inventory capacity to near-optimality. In the company case, these methods reduce the inventory capacity while simultaneously improving the maximum stockout probability.