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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 ›› 2025, Vol. 42 ›› Issue (5): 806-822.doi: 10.3969/j.issn.1005-3085.2025.05.002cstr: 32411.14.cjem.CN61-1269/O1.2025.05.002

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两阶段生产服务库存系统的性能分析与库存策略的优化控制

岳德权,  迟艳伟,  魏伊宁   

  1. 燕山大学理学院，秦皇岛  066004
  • 收稿日期:2023-02-27 接受日期:2024-06-23 出版日期:2025-10-15 发布日期:2025-12-15
  • 基金资助:
    国家自然科学基金 (71971189)；河北省高等学校科技计划重点项目 (ZD2018042).

Performance Analysis and Optimal Control of the Inventory Strategy of Two-stage Production-service Inventory System

YUE Dequan,  CHI Yanwei,  WEI Yining   

  1. School of Science, Yanshan University, Qinhuangdao 066004
  • Received:2023-02-27 Accepted:2024-06-23 Online:2025-10-15 Published:2025-12-15
  • Supported by:
    The National Natural Science Foundation of China (71971189); the Science and Technology Project of Higher Education Institutions of Hebei Education Department (ZD2018042).

摘要：

研究了一个由生产中心和分销中心组成的两阶段生产–库存排队系统，针对生产中心提出了一个新的生产策略---$(rQ+m,KQ)$生产策略，分销中心采取$(s,Q)$库存补货策略。顾客到达过程为泊松过程，补货时间、服务时间和生产时间均服从指数分布。首先，建立连续时间Markov模型，利用拟生灭过程理论，求出了系统稳态平衡条件。其次，通过求解修正系统模型的稳态概率分布，获得了系统的稳态概率分布的乘积解，进而给出了系统的稳态性能指标的计算公式。最后，以系统平均费用最小为目标，利用遗传算法计算系统的最优库存策略和平均费用。通过数值算例对系统采取的4种生产库存策略进行了比较分析，结果显示：在一定的条件下，生产中心采取$(m,KQ)$策略时，系统的平均费用更小。

关键词: 生产库存系统, 排队系统, $(s,Q)$策略, 拟生灭过程, 损失销售, 库存控制

Abstract:

This paper studies a two-stage production-service inventory system which is composed of a  production center and a distribution center. A new production strategy, $(rQ+m,KQ)$ production strategy, is proposed for the production center. The distribution center adopts $(s,Q)$ inventory replenishment strategy. Customers arrive according to a Poisson process, and the lead time, the service time and the production time are assumed to be exponentially distributed. Firstly, the continuous-time Markov model is established, and the steady-state condition of the system is obtained by using the theory of quasi-birth-and-death process. Secondly, by solving the steady-state probability distribution of the modified system model, some steady-state probability distribution of the system is obtained. Then formula of computing of the steady-state performance indexes of the system are given. Finally, by using genetic algorithm, the optimal inventory strategies and average cost of the system that aim to minimize the average cost of the system are calculated. The four production inventory strategies of the system are compared by numerical examples. The results show that under certain conditions, the average cost of the system is the lowest when the production center adopts the $(m,KQ)$ strategy.

Key words: production inventory system, queueing system, $(s, Q)$ strategy, quasi-birth-and-death process, lost sales, inventory control

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