Abstract We consider the production control problem of a production-inventory system with correlated demand inter-arrival and processing times that are modeled as Markovian Arrival Processes. The control problem is minimizing the expected average cost of the system in the steady-state by controlling when to produce an available part. We prove that the optimal control policy is the state-dependent threshold policy. We evaluate the performance of the system controlled by the state-dependent threshold policy by using the Matrix Geometric method. We determine the optimal threshold levels of the system by using policy iteration. We then investigate how the autocorrelation of the arrival and service processes impact the performance of the system. Finally, we compare the performance of the optimal policy with 3 benchmark policies: a state-dependent policy that uses the distribution of the inter-event times but assumes i.i.d.inter-event times, a single-threshold policy that uses both the distribution and also the autocorrelation, and a single-threshold policy that uses the distribution of the inter-event times but assumes they are not correlated. Our analysis demonstrates that ignoring autocorrelation in setting the parameters of the production policy causes significant errors in the expected inventory and backlog costs. A single-threshold policy that sets the threshold based on the distribution and also the autocorrelation performs satisfactorily for systems with negative autocorrelation. However, ignoring positive correlation yields high errors for the total cost. Our study shows that an effective production control policy must take correlations in service and demand processes into account.

中文翻译：

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具有相关需求到达间隔和处理时间的生产/库存系统的优化控制

摘要 我们考虑具有相关需求到达间隔和处理时间的生产-库存系统的生产控制问题，这些系统被建模为马尔可夫到达过程。控制问题是通过控制何时生产可用零件来最小化系统在稳态下的预期平均成本。我们证明了最优控制策略是状态相关的阈值策略。我们使用矩阵几何方法评估由状态相关阈值策略控制的系统的性能。我们通过使用策略迭代来确定系统的最佳阈值水平。然后我们研究到达和服务过程的自相关如何影响系统的性能。最后，我们将最优策略的性能与 3 个基准策略进行比较：使用事件间时间分布但假设事件间时间的状态相关策略，使用分布和自相关的单阈值策略，以及使用事件间时间分布的单阈值策略- 事件时间，但假设它们不相关。我们的分析表明，在设置生产策略参数时忽略自相关会导致预期库存和积压成本出现重大错误。基于分布和自相关设置阈值的单阈值策略对于具有负自相关的系统表现令人满意。然而，忽略正相关会导致总成本的高误差。