Shortage decision policies for a fluid production model with MAP arrivals
研究连续生产库存系统中，面对马尔可夫加性过程到达的需求时，两种短缺策略（延期交货和订单供应/损失销售）的成本优化问题，并考虑安全库存的影响。
We consider on a continuous production/inventory process where a single machine produces a certain product into a finite buffer. The demands arrive according to a Markov Additive Process governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. Two shortage policies are considered: the backorder policy, in which any demand that cannot be satisfied immediately is backlogged, and the order policy, in which any demand that cannot be satisfied immediately is supplied (alternatively, the latter policy can be considered as lost sales). We assume that the total cost includes a production loss cost, a penalty cost, a fixed cost for an order and a variable cost for the ordered amount. By applying the regenerative theory, we use tools from the exit-time theorem for fluid processes to obtain the discounted cost functionals under both policies. In addition, the models are extended to include a non-zero safety stock. Numerical examples, sensitivity analysis and comparative study are included.