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Due-time performance of production systems with Markovian machines. (English) Zbl 1059.90056
Gershwin, Stanley B. (ed.) et al., Analysis and modeling of manufacturing systems. Selected papers of the second Aegean international conference on analysis and modeling of manufacturing systems, Tinos Island, Greece, May 16–20, 1999. Boston, MA: Kluwer Academic Publishers (ISBN 1-4020-7303-8/hbk). International Series in Operations Research & Management Science 60, 221-253 (2003).
Summary: Customer demand satisfaction in serial production lines with Markovian machines and Finished Goods Buffers (FGB) is analyzed. The level of demand satisfaction is measured by the probability to ship to the customer a required number of parts during a fixed interval of time. This performance measure, referred to as Due-Time Performance (DTP), is analyzed using a simplification procedure termed stationarization. As a result, an iteration-based method for DTP calculation is obtained and utilized for analysis of various properties of DTP. In particular, it is shown that when the demand is relatively low ($$\sim\, 95\%$$ of the production capacity), FGB of 2-4 shipments is sufficient to ensure high DTP ($$\sim 0.98$$). When the demand is high ($$\sim 99\%$$), FGB of 6–9 shipments is required. Further increase of FGB leads to highiy diminishing return. Also, it is shown that a ramp, rather than an inverted bowl, of machine efficiency allocation leads to optimization of DTP.
For the entire collection see [Zbl 1048.90094].

##### MSC:
 90B30 Production models 90B25 Reliability, availability, maintenance, inspection in operations research