Quality and total value optimisation in Markovian tandem queues with time-dependent quality deterioration
研究了串联生产线中产品随遍历时间质量退化的问题，在给定服务率容量下优化分配以最大化最终质量，并考虑运营成本和逗留时间成本，量化了退化率与成本率之间的权衡。
We consider a tandem production line consisting of n Markovian single-server sites, where a product's quality deteriorates with its traversal time. Given an overall service-rate capacity, we determine the optimal capacity allocation among the queues that maximises product's final quality. We show that under light workload, the optimal allocation is governed solely by the deterioration rates, allocating higher service-rate to faster deteriorating sites. As the system's load increases, the allocation shifts towards a balanced distribution. Further, we consider two variants of associated costs. First, we incorporate heterogeneous operating costs and find the optimal allocation maximising the product's final quality under a limited budget. Second, since quality-driven capacity allocation reduces sojourn time at one queue but increases it at others, we incorporate sojourn time costs and obtain optimal allocation maximising product's total value. Then, we quantify the trade-off between a marginal change in quality deterioration rate at site i, and a marginal change in sojourn cost rate at site j, showing that it is a function of the final quality and the deterioration rate in site i. However, as the system approaches saturation, the impact of individual deterioration or cost rates becomes negligible, and the trade-off diminishes.