Manufacturing Systems of Two Machines in Tandem
In this chapter, we study a two-stage manufacturing system. The system consists of two reliable machines (one in each stage) producing one type of product. Each product has to go through the manufacturing processes in the two stages before it is finished. We assume an infinite supply of raw material for the manufacturing process at the first machine. The mean processing time for one unit of product in the first and second machine are exponentially distributed with parameters μ 1 −1 and μ 2 −1 respectively. A buffer B 1 of size b 1 is placed between the two machines to store the products which are finished by the first machine and waiting for further operations by the second machine. Finished products are put in a buffer B 2 of maximum size b 2. The interarrival time of a demand is assumed to be exponentially distributed with parameter λ−1. A finite backlog of finished product is allowed in the system. The maximum allowable backlog of product is m. When the inventory level of the finished product is −m, any arrival demand will be rejected. Hedging Point Production (HPP) policy is employed as the inventory control in both buffers B 1 and B 2. We focus on HPP policies for our manufacturing systems.
KeywordsManufacturing System Generator Matrix Inventory Level Continuous Time Markov Chain Fast Convergence Rate
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