Application of MMPP to Manufacturing Systems of Multiple Unreliable Machines
In this chapter, we study an application of the queuing system discussed in Chapter 3. We apply the queuing system to modeling a manufacturing system of multiple failure prone machines under Hedging Point Production (HPP) policy. In a queuing system, there are servers, customers, and waiting spaces. To model a manufacturing system by a queuing system, one may regard a server as a machine. Depending on the type of manufacturing system, make-to-order or order-to-make,the customers can be regarded as the inventory of product or the jobs to be processed respectively; see Buzacott and Shanthikumar . In our context here, we only discuss the latter case. In a make-to-order system, the machine system produces only when there is an arrived order. But in an order-to-make system, a certain amount of inventory is kept to cope with the fluctuation of demand and therefore production control is necessary. Here we employ the HPP policy as the production control; the definition of the policy will be discussed shortly.
KeywordsManufacturing System Generator Matrix Inventory Level Markov Chain Model Machine System
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