Optimal Production Control of Hybrid Manufacturing/Remanufacturing Failure-Prone Systems under Diffusion-Type Demand
Optimal Production Control of Hybrid Manufacturing/Remanufacturing Failure-Prone Systems under Diffusion-Type Demand
复制标题
扩散型需求下混合制造/再制造易失效系统的优化生产控制
DOI：
10.4236/am.2013.43079
复制
发表时间：
2013
影响因子：
1
通讯作者：
A. Gharbi
中科院分区：
文献类型：
--
作者：
Samir Ouaret;V. Polotski;J. Kenné;A. Gharbi
分析了不确定条件下制造/再制造混合系统的生产控制问题。考虑了两个不确定性来源：机器随机故障和维修，需求水平被建模为扩散型随机过程。与大多数研究认为需求水平是恒定的且结果较少的情况相反，需求被建模为泊松过程，具有较少的离散水平和指数分布的切换时间，而这里的需求被建模为扩散类型的过程。特别分析了累积需求下的Wiener过程和Ornstein-Uhlenbeck过程。我们用Hamilton-Jacobi-Bellman(HJB)偏微分方程组的形式描述了随机控制问题，并给出了它的最优性条件。我们证明了HJB方程是二阶的，这与恒定需求率(对应于我们案例中的平均需求)的情况相反，其中HJB方程是线性偏微分方程组。我们应用Kushner型有限差分格式和策略改进程序数值求解HJB方程，证明了对于我们所介绍的两种需求模型，最优生产策略都是套期保值点型的，类似于已知的恒定需求情况。所得结果可以数值计算考虑需求变化的混合制造/再制造系统的最优生产策略，并表明库什纳型离散格式可以成功地应用于求解基本的二阶HJB方程。
The problem of production control for a hybrid manufacturing/remanufacturing system under uncertainty is analyzed. Two sources of uncertainty are considered: machines are subject to random breakdowns and repairs, and demand level is modeled as a diffusion type stochastic process. Contrary to most of studies where the demand level is considered constant and fewer results where the demand is modeled as a Poisson process with few discrete levels and exponentially distributed switching time, the demand is modeled here as a diffusion type process. In particular Wiener and Ornstein-Uhlenbeck processes for cumulative demands are analyzed. We formulate the stochastic control problem and develop optimality conditions for it in the form of Hamilton-Jacobi-Bellman (HJB) partial differential equations (PDEs). We demonstrate that HJB equations are of the second order contrary to the case of constant demand rate (corresponding to the average demand in our case), where HJB equations are linear PDEs. We apply the Kushner-type finite difference scheme and the policy improvement procedure to solve HJB equations numerically and show that the optimal production policy is of hedging-point type for both demand models we have introduced, similarly to the known case of a constant demand. Obtained results allow to compute numerically the optimal production policy in hybrid manufacturing/ remanufacturing systems taking into account the demand variability, and also show that Kushner-type discrete scheme can be successfully applied for solving underlying second order HJB equations.