Abstract

In this study, we are primarily motivated by the research problem of recognizing heterogeneous customer behavior towards waiting for order fulfillment under the threshold rationing policy (also known as the critical level policy), and aim to find its effect on system stock levels and performance measures. We assume a continuous review one-for-one ordering policy with generally distributed lead times. In the first model, we consider the case in which the low-priority customer class exhibits zero patience for waiting if the demand is not satisfied immediately (a lost sale), whereas the demand of the high-priority customer class can be backordered. This is the first study in the literature to consider this model. We provide an exact analysis for the derivation of the steady-state probability distribution and the average infinite horizon cost per unit time. We then develop an efficient optimization procedure to minimize the average expected cost rate. We also determine the forms of the optimal solutions for the two service level optimization models that are common in practice. In the second model, we study the opposite case in which the high-priority customer class exhibits zero patience for waiting. We establish a theoretical basis for the rationale of using the Continuous-Time Markov Chain (CTMC) approach as an approximation. We show that under certain assumptions, the steady-state probabilities of the system with generally distributed lead times are identical to the steady-state probabilities of the CTMC system with the same mean. This result enables us to link the dynamics of the studied model to the CTMC model, which may open new doors for future research.

摘要

在这项研究中，我们主要受到以下研究动机的启发：在阈值配给策略（也称为关键级别策略）下，识别异构客户行为以等待订单履行），目的是发现其对系统库存水平和性能指标的影响。我们假设连续检查一对一的订购策略，且交货时间通常分布。在第一个模型中，我们考虑以下情况：如果不能立即满足需求（销售损失），则低优先级客户类别的等待耐心为零，而高优先级客户类别的需求可以重新订购。这是文献中首次考虑此模型的研究。我们对稳态概率分布和每单位时间的平均无限期成本的推导提供了精确的分析。然后，我们开发一种有效的优化程序以最小化平均预期成本率。我们还为实践中常见的两个服务水平优化模型确定了最佳解决方案的形式。在第二种模型中，我们研究了相反的情况，即高优先级客户类别的等待耐心为零。我们为使用连续时间马尔可夫链（CTMC）方法进行近似的理论基础建立了理论基础。我们表明，在某些假设下，具有通常分布的提前期的系统的稳态概率与具有相同均值的CTMC系统的稳态概率相同。这一结果使我们能够将研究模型的动力学与CTMC模型联系起来，这可能为将来的研究打开新的大门。我们为使用连续时间马尔可夫链（CTMC）方法进行近似的理论基础建立了理论基础。我们表明，在某些假设下，具有通常分布的提前期的系统的稳态概率与具有相同均值的CTMC系统的稳态概率相同。这一结果使我们能够将研究模型的动力学与CTMC模型联系起来，这可能为将来的研究打开新的大门。我们为使用连续时间马尔可夫链（CTMC）方法进行近似的理论基础建立了理论基础。我们表明，在某些假设下，具有通常分布的提前期的系统的稳态概率与具有相同均值的CTMC系统的稳态概率相同。这一结果使我们能够将研究模型的动力学与CTMC模型联系起来，这可能为将来的研究打开新的大门。