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A Production-Inventory System with a Service Facility and Production Interruptions for Perishable Items

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Stochastic Models in Reliability, Network Security and System Safety (JHC80 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1102))

Abstract

In this paper, we consider a production-inventory system with a service facility and production interruptions. Customers arrive in the system according to a Poisson process and require a random time of the service from a single service facility. The service time is assumed to be exponentially distributed. The items are produced according to an (s, S) policy. Each customer leaves the system with one item from the inventory at his service completion epoch if the inventory is available. The production is interrupted for a vacation of random time once the inventory level becomes S. The vacations are exponentially distributed. On return from a vacation, if the inventory level depletes to s, then the production is immediately switched on. It then starts production and is kept in the on mode until the inventory level becomes S. The items in stock are perishable and have exponential life times. It is assumed that no customers is allowed to join the queue when the inventory level is zero. We first derive the stability condition of the system. Then, We obtain the product form solution for the stationary joint distribution of the number of customers and the on-hand inventory level. Based on this stationary distribution, we compute explicitly some performance measures and develop a cost function. Finally, some numerical results are presented.

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Acknowledgments

This work was supported by the Natural Science Foundation of Hebei Province, China (No. A2017203078).

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Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, 066004, China

    Dequan Yue & Sai Wang

  2. School of Economics and Management, Yanshan University, Qinhuangdao, 066004, China

    Yuying Zhang

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  1. Dequan Yue
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  2. Sai Wang
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  3. Yuying Zhang
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Correspondence to Dequan Yue .

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Editors and Affiliations

  1. School of Economics and Management, Beijing University of Technology, Beijing, China

    Quan-Lin Li

  2. School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China

    Jinting Wang

  3. School of Economics and Management, Beijing University of Technology, Beijing, China

    Hai-Bo Yu

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Yue, D., Wang, S., Zhang, Y. (2019). A Production-Inventory System with a Service Facility and Production Interruptions for Perishable Items. In: Li, QL., Wang, J., Yu, HB. (eds) Stochastic Models in Reliability, Network Security and System Safety. JHC80 2019. Communications in Computer and Information Science, vol 1102. Springer, Singapore. https://doi.org/10.1007/978-981-15-0864-6_21

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  • DOI: https://doi.org/10.1007/978-981-15-0864-6_21

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  • Print ISBN: 978-981-15-0863-9

  • Online ISBN: 978-981-15-0864-6

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