Manufacturing Systems with Batch Arrivals
In this chapter, we study an unreliable one-machine manufacturing system. The manufacturing system consists of one machine producing one type of product; see Fig. 5.1. The machine M 1 is unreliable and is subject to random breakdowns and repairs. Finished product is stored in the buffer B 1. The processing time for one unit of product and the normal time of the machine are exponentially distributed. The demand of the product is modeled as finite batch arrival with the inter-arrival time being exponentially distributed. The batch size distribution is stationary (independent of time). If the arrival demand exceeds the maximum allowable backlog, the system will accept part of the demand (up to the maximum allowable backlog). The demand process is similar to that in Chapter 2. HPP policy is employed as the production control. We focus on finding optimal hedging point policies for the captured manufacturing systems.
KeywordsInventory Level Matrix Vector Multiplication Batch Arrival Preconditioned Matrix Preconditioned System
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