关于易腐产品的$M/M/1$生产服务库存模型的最优控制

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．

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

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.