Abstract We investigate a new class of separable systems which exhibit a product-form stationary distribution. These systems consist of parallel production systems (servers) at several locations, each with a local inventory under base stock policy, connected with a common supplier network. Demand of customers arrives at each production system according to a Poisson process and is lost if the local inventory is depleted (“lost sales”). To satisfy a customer’s demand a production server needs raw material from the associated local inventory. The supplier network is a classical queueing network. We investigate two different lost sales regimes, either based on total inventory or on available inventory. We perform cost analysis to find the optimal base stock levels, which is due to the product-form stationary distribution a separable optimization problem. Finally, we demonstrate that the explicit product forms for both stationary distributions enable us to compare main performance metrics of the systems under the different lost sales admission regimes.

中文翻译：

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互连生产-库存系统的可分离模型

摘要 我们研究了一类新的可分离系统，其表现出产品形式的平稳分布。这些系统由多个地点的并行生产系统（服务器）组成，每个系统都有一个符合基本库存政策的本地库存，并与一个公共供应商网络相连。客户的需求根据泊松过程到达每个生产系统，如果本地库存耗尽（“销售损失”），客户需求就会丢失。为了满足客户的需求，生产服务器需要相关本地库存中的原材料。供应商网络是一个经典的排队网络。我们调查了两种不同的销售损失制度，要么基于总库存，要么基于可用库存。我们进行成本分析以找到最佳的基本库存水平，这是由于产品形式平稳分布是一个可分离的优化问题。最后，我们证明了两种固定分布的显式产品形式使我们能够在不同的销售损失准入制度下比较系统的主要性能指标。