机器不可靠且需求过程为k个泊松过程叠加的生产存贮系统

UNRELIABLE PRODUCTION-INVENTORY SYSTEM WITH SUPERPOSITION OF k POISSON DEMAND ARRIVAL PROCESSES

本文对机器不可靠的二阀值控制存贮水平的生产存贮系统进行了研究.一旦机器发生故障,会立即得到修理以使它重新工作;对产品的需求假设是k个复合泊松到达过程的叠加,需求量为独立同分布的随机变量.我们得到了存贮水平稳态分布存在的充分条件、分布函数的显性表达式,以及在稳态下系统运行的一些性能指标.

A production-inventory system is studied in which an unreliable machine is susceptible to failure following which they must be repaired to make it operative again and the demands for the product are superposition of k Poisson demand arrival processes, demand sizes are independent and identically distributed random variables. A two-critical-number policy is used to control a machine's setups and shutdowns. The sufficient conditions to ensure the existence of the stationary distribution of inventory level and explicit expression of this stationary distribution are obtained. Moreover, some performance measures of the system under steady-state condition are also obtained.