We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.
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机译：我们考虑了一个制造系统，其中最终产品的质量不确定，并在生产后分为几种质量水平之一。我们对每个质量水平，随机生产时间和随机质量收益率的随机需求。我们还承担了下行的可替代性（即，需要给定产品的客户，以相同的价格将满足更高质量的产品）。该公司生产股票，即使有货物有货物，也可以选择拒绝满足客户。我们将此问题作为Markov决策过程在一个简单的m / m / 1 make-to-show队列的上下文中，具有多个客户类，以获得以下问题的洞察：（i）公司如何决定何时产生更多单位（即，最佳生产政策是什么？）和（ii）该公司如何决定何时接受/拒绝订单以及何时满足客户要求使用更高质量的产品要求更低的产品的客户？在两个产品类别的情况下，我们完全表征了最佳生产和验收/替代政策的结构。但是，最佳政策的结构复杂，因此我们为任何数量表现得很好的类别，我们为任何数量的类开发了一个简单的启发式政策。我们终于将我们的启发式扩展到生产的系统，其中批量大于一个大于一个，系统出现了启动生产的设置成本，以及处理时间分布为Erlang的情况。
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