Cost- and service-based comparison of practical policies for stochastic clearing under nonlinear delay penalty
研究了在订单到达为泊松过程且服务延迟受非线性惩罚时，三种清理策略（基于数量、基于时间和混合策略）在平均订单平方延迟和长期平均成本上的表现，发现混合策略可能优于成本最优的基于数量策略。
We revisit the traditional stochastic clearing problem widely applicable in various supply chain and service systems. We consider the case where the stochastic input (order/customer arrival) process is Poisson and service delay (order/customer waiting) associated with clearing frequency (service) is subject to a nonlinear penalty in the context of a continuous-time setting. The penalty is associated with average order squared delay. It is designed to capture the customers’ impatience/disutility related to waiting times caused by service delays (e.g., delay of delivery of orders to customers). We analyze three practical, renewal-type clearing protocols (known as quantity-based, time-based, and hybrid policies) for operating the system. Our goal is to compare and contrast these policies in terms of average order squared delay, as an indicator of service performance, along with long-run average cost, as an indicator of financial performance. Unlike the case of linear delay penalty in the continuous-time setting–investigated previously in the literature–we find that quantity-based policies are not necessarily optimal with respect to service- or financial performance. Further, one can potentially compute a hybrid policy that dominates the cost-optimal quantity-based policy in terms of both dimensions of performance. This new finding regarding bi-criteria dominance potential of hybrid policies validates the value and importance of consideration of this class of clearing protocols in establishing operational guidelines in practice. Our analysis reveals and builds on some new characteristics of truncated Poisson random variables. To the best of our knowledge, the current paper is the first to formally offer and utilize these properties while simultaneously investigating the financial and service performance of stochastic clearing operations.