带有服务员混合式休假策略的排队库存系统

doi:10.15960/j.cnki.issn.1007-6093.2025.02.019

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (2): 230-238.doi: 10.15960/j.cnki.issn.1007-6093.2025.02.019

• 论文 • 上一篇

带有服务员混合式休假策略的排队库存系统

许青哲¹, 李建军¹^,*(), 刘力维¹

1. 南京理工大学数学与统计学院, 江苏南京 210094

收稿日期:2022-09-03 出版日期:2025-06-15 发布日期:2025-06-12
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)

Queueing-inventory system with hybrid vacation strategy of server

Qingzhe XU¹, Jianjun LI¹^,*(), Liwei LIU¹

1. School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

Received:2022-09-03 Online:2025-06-15 Published:2025-06-12
Contact: Jianjun LI E-mail:jjli@njust.edu.cn

摘要/Abstract

摘要：

本文引入了一种新的休假策略, 研究在该策略下带有损失销售和(s, S)库存策略的排队库存系统。当库存为空时, 服务员开始工作休假, 工作休假期间, 若补货成功, 服务员立刻开始正常服务顾客; 当工作休假结束时, 若库存仍为空, 服务员开始多重休假过程, 否则转为正常工作状态。利用马尔可夫过程方法对此系统进行稳态分析, 得到该策略下排队库存系统的稳态分布, 进而获得系统的一些稳态性能指标以及系统的平均费用函数。通过数值分析研究系统参数对最优策略和最优费用的影响。

关键词: 排队库存系统, 损失销售, (s, S)策略, 工作休假, 马尔可夫过程

Abstract:

In this paper, we introduce a new vacation strategy. We consider an queueing-inventory system with lost sales and (s, S) strategy under the vacation strategy. When inventory level is zero, the server goes to a working vacation in which if the replenishment is successful, the server immediately begins to serve the customer normally. When the working vacation is over, if the inventory level is still zero, the server will take multiple vacations, otherwise he/she will return to the normal working state. We analyze the stationary distributions of the queueing-inventory system under the vacation strategy by using Markov process method. On this basis, some performance indices and average cost function are obtained. Finally, the optimal inventory policy and the optimal expected cost are also discussed by numerical examples.

Key words: queueing-inventory system, lost sale, (s, S) strategy, working vacation, Markov process

中图分类号:

O226

许青哲, 李建军, 刘力维. 带有服务员混合式休假策略的排队库存系统[J]. 运筹学学报（中英文）, 2025, 29(2): 230-238.

Qingzhe XU, Jianjun LI, Liwei LIU. Queueing-inventory system with hybrid vacation strategy of server[J]. Operations Research Transactions, 2025, 29(2): 230-238.

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参考文献 18

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$ \lambda $	10	12	14	16	18	20
$ (s,S) $	(5, 24)	(6, 28)	(7, 32)	(8, 36)	(10, 40)	(11, 44)
$ C(s,S) $	239.442 0	279.561 0	319.423 2	359.107 6	398.562 4	437.899 6

$ \theta_{w} $	2	7	12	17	22	27
$ (s,S) $	(5, 24)	(6, 25)	(7, 26)	(7, 26)	(7, 26)	(7, 26)
$ C(s,S) $	239.442 0	251.918 3	255.218 3	256.949 1	258.035 8	258.781 6

$ \theta_{v} $	1	3	5	7	9	11
$ (s,S) $	(5, 24)	(4, 23)	(4, 23)	(3, 22)	(3, 22)	(3, 22)
$ C(s,S) $	239.442 0	226.362 6	222.981 6	221.334 6	220.130 7	219.363 0

$ \eta $	5	8	11	14	17	20
$ (s,S) $	(5, 24)	(4, 21)	(3, 19)	(2, 18)	(2, 18)	(2, 17)
$ C(s,S) $	239.442 0	203.643 2	185.325 0	175.069 0	166.611 2	161.136 2

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[2]	王慧宁, 徐秀丽. 基于PH服务的工作休假排队的流体模型[J]. 运筹学学报, 2019, 23(2): 57-66.
[3]	潘取玉, 唐应辉, 兰绍军. 带负顾客和N-策略的Geo^{lambda_1, lambda_2/Geo/1(MWV)排队系统分析及最优控制策略N*[J]. 运筹学学报, 2017, 21(3): 65-76.
[4]	张宏波. 带有Bernoulli控制策略的M/M/1多重休假排队模型[J]. 运筹学学报, 2013, 17(3): 93-100.

带有服务员混合式休假策略的排队库存系统

Queueing-inventory system with hybrid vacation strategy of server

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