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Operations Research Transactions >

2025 , Vol. 29 >Issue 4: 1 - 13

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.04.001

Research Article

Analysis of M/M/1 production-inventory system with working vacations

  • Wenye LIU ,
  • Dequan YUE
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  • School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China

Received date: 2022-01-27

  Online published: 2025-12-11

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, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

This paper studies the M/M/1 production inventory system with working vacations. The server takes multiple working vacations when there is no customers in the system. Based on the (s, S) inventory strategy, a four-dimensional Markov process of the number of customers in the system, the inventory level, the server state and the production state is established. We obtain the steady-state condition of the system by using quasi-birth-death process theory. Furthermore, we derive the steady-state performance indexes of the system and the system cost function. The effect of various parameters of the system on the performance indexes and inventory strategy is analyzed. Then the optimal inventory strategies and optimal costs with different service rates under working vacation are compared.

Key words： production inventory system; working vacation; (s, S) inventory strategy; cost function; quasi-birth-death process

Cite this article

Wenye LIU , Dequan YUE . Analysis of M/M/1 production-inventory system with working vacations[J]. Operations Research Transactions, 2025 , 29(4) : 1 -13 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.04.001

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