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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 ›› 2020, Vol. 37 ›› Issue (6): 685-698.doi: 10.3969/j.issn.1005-3085.2020.06.004

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关于易腐产品的$M/M/1$生产服务库存模型的最优控制

王  赛,   岳德权,   张媛媛,   田瑞玲   

  1. 燕山大学理学院，秦皇岛  066004
  • 收稿日期:2018-05-17 接受日期:2018-10-29 出版日期:2020-12-15 发布日期:2021-02-15
  • 通讯作者: 岳德权 E-mail: ydq@ysu.edu.cn
  • 基金资助:
    国家自然科学基金 ,(11601469)；河北省自然科学基金 ,(A2017203078)；河北省高等学校科技计划重点项目 (ZD2018042).

Optimal Control of $M/M/1$ Production Inventory System with Positive Service Time and Perishable Items

WANG Sai,   YUE De-quan,   ZHANG Yuan-yuan,   TIAN Rui-ling   

  1. School of Science, Yanshan University, Qinhuangdao 066004
  • Received:2018-05-17 Accepted:2018-10-29 Online:2020-12-15 Published:2021-02-15
  • Contact: D. Yue. E-mail address: ydq@ysu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (11601469); the Natural Science Foundation of Hebei Province (A2017203078); the Key Project of Science and Technology Program of Higher Education Institutions of Hebei Province (ZD2018042).

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摘要： 本文研究了易腐产品的$M/M/1$生产服务库存模型．假设易腐产品的寿命、产品的生产时间和服务时间均服从指数分布．首先，利用拟生灭过程理论，求出了模型稳态平衡条件．其次，给出了稳态概率向量的矩阵几何解，进一步得到了与本模型相关的性能指标和成本函数的计算公式．最后，利用遗传算法分析了模型的最优生产库存策略和系统参数对性能指标的敏感性．本文的结果可以为生产型企业的库存管理者提供一些理论依据．

关键词: 易腐产品, $({s,S})$策略, 生产库存系统, 遗传算法, 矩阵几何解

Abstract: The $M/M/1$ production-service-inventory model with perishable products is studied. The life time of the perishable product, the production time and the service time are all assumed to be exponentially distributed. Firstly, the steady-state equilibrium condition of the model is obtained by using the quasi-birth-and-death process theory. Secondly, the matrix geometric solution of the steady-state probability vector is obtained, and the calculation formulas of the performance index and cost function are obtained. Finally, the genetic algorithm is used to analyze the sensitivity of the model's optimal production inventory strategy and the effect of system parameters on performance indexes. The results of this paper can provide some theoretical basis for inventory managers of production companies.

Key words: perishable items, $(s,S)$ strategy,  , production-inventory system, generic algorithm, matrix-geometric solution

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