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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 42 ›› Issue (6): 1131-1148.doi: 10.3969/j.issn.1005-3085.2025.06.011cstr: 32411.14.cjem.CN61-1269/O1.2025.06.011

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带有修正延迟休假的库存系统

许青哲,  李建军,  刘力维   

  1. 南京理工大学数学与统计学院，南京 210094
  • 收稿日期:2023-02-14 接受日期:2023-07-13 出版日期:2025-12-15 发布日期:2026-02-15
  • 通讯作者: 李建军 E-mail: jjli@njust.edu.cn
  • 基金资助:
    国家自然科学基金(61773014).

Inventory System with Modified Delayed Vacation Strategy

XU Qingzhe, LI Jianjun, LIU Liwei   

  1. School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094
  • Received:2023-02-14 Accepted:2023-07-13 Online:2025-12-15 Published:2026-02-15
  • Contact: J. Li. E-mail address: jjli@njust.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61773014).

摘要：

提出了修正的延迟休假策略，研究了该策略下带有损失销售和$(s,S)$补货策略的库存系统。当库存为空时，服务员开始一段随机时间的“休假准备”，这期间，若补货成功，服务员仍然服务顾客，称“休假准备”这段时间为修正的延迟休假期。当修正的延迟休假结束时，服务员随即开始多重休假。利用Markov过程理论进行稳态分析，得到了该策略下库存系统的稳态分布，进而得到了系统的性能指标和平均费用函数。最后，我们采用遗传算法获得了最优库存策略，通过数值实验分析了参数对性能指标和最优费用的影响。

关键词: 库存系统, 损失销售, 马尔可夫过程, $(s,S)$策略, 延迟休假

Abstract:

We introduce a modified delayed vacation strategy. We consider an inventory system with lost sales and $(s,S)$ strategy under the vacation strategy. When the inventory level is zero, the server goes to a random time to prepare for vacation in which if the replenishment is successful, the server still serves the customer normally. The random time is called a modified delayed vacation time. When the delayed vacation is over, the server immediately takes multiple vacations. We analyze the stationary distributions of the inventory system under the vacation strategy by using the Markov theory. On the basis, some performance measures and the average cost function are obtained. Finally, we get the optimal inventory policy by a genetic algorithms. On the basis, some performance measures and expected cost also are discussed by numerical examples.

Key words: inventory system, lost sale, Markov process, $(s,S)$ strategy, delayed vacation

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