当前位置: 首页>博士论文>资源详情
不确定环境下生产控制与能力规划的综合优化
中文摘要

制造系统的生产控制问题与能力规划问题往往被分开单独研究。然而,当生产能力不足时,即使采用最优生产控制依然不能满足需求;另一方面,由于生产控制的目的是将生产能力发挥到极致,因此如果生产能力规划不考虑生产控制,那么规划后得到的生产能力往往会偏高,从而浪费设备成本。尤其是在不确定环境下(例如:机器随机故障、产品更新迭代引起的工艺路线不确定等),这两个问题更需要综合考虑,以使得制造系统能以最小的投资成本获得最好的生产性能,同时抵御不确定因素带来的负面影响。因此,本文分别研究了四种典型制造系统在不确定环境下生产控制与能力规划的综合优化问题。 一、考虑机器随机故障时单品种多并行机多阶段串行生产线的综合优化问题。 这一问题的目标是最小化设备成本,同时保证平均生产成本小于允许值。而分析系统状态的稳态概率分布是评估平均生产成本的关键。首先我们从简单的单阶段多并行机制造系统着手,分析了它的稳态概率分布计算方法。然后基于单阶段系统的稳态概率分布,提出了两阶段串行生产线的近似稳态概率分布的计算方法以及两阶段串行生产线的分解方法。进一步地,将两阶段系统的稳态概率分布计算方法以及分解方法推广至多阶段生产线,从而计算多阶段生产线各缓冲区库存水平的稳态概率分布以及平均生产成本。最后采用基于梯度的算法来优化生产控制参数,再采用整数规划算法来求解能力规划问题。数值仿真实验表明所提出的稳态概率分布的计算方法是准确的,同时,生产控制和生产能力综合优化所得到的解在投资成本和生产性能上优于单独考虑生产控制与能力规划的解。 二、考虑机器随机故障时多品种多并行机多阶段制造系统综合优化问题。 这一问题的目标是最小化设备成本,同时保证平均生产成本小于允许值。同样地,获取它的稳态的概率分布是关键。因为两品种多并行机单阶段不考虑欠产情形的制造系统可以被认为是多品种多并行机多阶段系统的基本模块。我们首先分析这个基本模块在优先级安全库存点控制策略下的稳态概率分布。虽然这个基本模块的库存水平所构成的状态分布区域的形状会影响稳态概率平衡方程,但是我们仍然建立了各种产品的统一边缘概率平衡方程,通过这个统一边缘概率平衡方程,我们可以计算出各种产品的边缘稳态概率分布。我们进一步将这个结果扩展到多品种多并行机单阶段系统;并基于串行生产线的分解方法计算出多品种多并行机多阶段系统状态的边缘稳态概率分布。最后采用基于梯度的算法求解优化生产控制参数,再采用整数规划算法来求解能力规划问题。数值仿真表明所提出的边缘稳态概率分布的计算方法是准确的,并且综合优化所得到的解在投资成本和生产性能上优于单独考虑生产控制与能力规划的解。 三、考虑机器随机故障时多阶段装配型制造系统综合优化问题。 这一问题的目标是最小化设备成本,同时保证平均生产成本小于允许值。同样地,获取这一系统的稳态概率分布是关键。首先我们分析了该类型装配系统的近似最优生产控制策略,以确定系统状态的分布域。进一步对分布域中的各个状态建立概率平衡方程。随后我们提出了一种分析方法以获得该系统稳态边缘概率分布,从而进一步获得平均生产成本。由于最优控制参数受到生产能力的约束,我们采用混合整数优化来优化机器数量,从而解决装配系统的综合优化问题。数值仿真实验表明所提出的稳态概率分布的计算方法是准确的,并且综合优化所得到的解在投资成本和生产性能上优于单独考虑生产控制与能力规划的解。 四、产品品种及工艺路线多变时半导体晶圆制造系统综合优化问题。 半导体晶圆制造系统属于可重入类型的制造系统。由于产品的数量和种类各不相同,当产品不断更新或者需求量不断变化时,晶圆的加工工艺路线就有很强的不确定性。为了描述和刻画这种不确定因素,我们定义了晶圆转移概率。基于开环排队网络模型,建立了系统在制品水平与晶圆转移概率的关系。由于存在不确定的晶圆转移概率影响,平均在制品水平会波动,有时候甚至会超出一个允许的上界。因此我们建立了一个鲁棒生产能力规划模型,该模型分为两层:下层是在给定小车数量之下找出最大在制品波动;上层是优化小车数量使得在制品最大波动和平均在制品水平超过给定阈值的概率最小。最后通过分析目标函数的单调性来解决这一鲁棒生产能力规划问题。数值仿真实验表明,基于所提出的鲁棒能力规划模型获得的小车数量对于不确定晶圆转移概率有很好的鲁棒性。 本文的主要理论贡献如下:(1)对单品种多并行机多阶段串行生产线提出了综合优化模型,为了解决综合优化中生产成本评估问题,提出了新的分解方法以及系统状态的稳态概率分布的计算方法:(2)对多品种多并行机多阶段制造系统提出了综合优化模型,首先对两品种多并行机单阶段制造系统归纳出统一的稳态边缘概率分布,并推广至多品种多并行机多阶段制造系统以评估其生产成本;(3)对多阶段装配系统提出了综合优化模型,并通过对状态空间的归并提出了广义两维状态空间的概念,基于广义两维状态空间提出了系统状态的稳态边缘概率分布的计算方法,并应用于评估生产成本;(4)针对半导体制造系统,提出了不确定晶圆转移概率用于刻画晶圆工艺路线的变化,并提出了基于开环排队网络的鲁棒能力规划模型用于优化小车数量。 本文针对四类典型的制造系统的生产控制及能力规划的综合优化问题提供了数学模型、分析方法和解决办法,实现了以较小的设备投资成本发挥优良的生产性能,并能够抵御不确定因素对系统的影响,本文的研究结果对实际的制造系统节约设备成本和降低生产成本具有良好的指导意义。 关键词:生产控制;能力规划;概率平衡方程;稳态概率分布;开环排队网络;

英文摘要

For a manufacturing system, its capacity planning problem and production control problem are usually solved separately. However, production capacity cannot exert its maximum productivity without employing optimal production control; and optimal production control may not satisfy the demand without sufficient production capacity. Specially, in order to make the manufacturing system exert the maximum production performance with minimum investment on devices under uncertainties, e.g., random machine failure and uncertain process route, it is more important to jointly optimize capacity planning and production control to resist the negative effects of uncertain factors. Therefore, in this paper, we study the Integrated Production Control and Capacity Planning (IPCCP) problem under uncertainties for four types typical manufacturing systems. 1.The IPCCP problem of single-product-type, multi-parallel-machine and multi-stage serial production line with random machine failure The objective of the IPCCP problem for a single-product-type, multi-parallel-machine and multi-stage serial production line with random machine failure is to minimize the investment on machines while keeping the average production cost below a desired level. Moreover, the key point for evaluating the average production cost is also the calculation of the steady-state probability distribution of the state variables. Firstly, we start with single-stage and multi-parallel-machine manufacturing system, and develop the method of calculating its steady state probability distribution. Based on the steady state probability distribution of single-stage and multi-parallel-machine manufacturing system, we propose a method of calculating the steady state probability distribution of a two-stage and multi-parallel-machine system by using a decomposition-based method. Furthermore, the method of calculating the probability distribution of a two-stage and multi-parallel-machine system is extended to a multi-stage production line. Thus, the average production cost of multi-stage production line can also be acquired. Finally, we employ a gradient-based algorithm to optimize the production control parameters and an integer programming technique to optimize the production capacity. Numerical experiments are conducted to verify the correctness of the method of evaluating steady-state probability distribution, and indicate that the solution of PI-PCCP has better performance. 2.The IPCCP problem of multi-product-type, multi-parallel-machine and multi-stage manufacturing system with random machine failure The objective of the IPCCP problem for a multi-product-type, multi-parallel-machine and multi-stage manufacturing system with random machine failure is to minimize the investment on machines while keeping the average production cost below a desired level. Moreover, the key point for evaluating the average production cost is also the calculation of the steady-state probability distribution of the state variables. Because the two-product-type, multi-parallel-machine and single-stage manufacturing system where no demand backlog is allowed can be considered as a building-block of a multi-product-type, multi-parallel-machine and multi-stage manufacturing system, we firstly analyze its steady state probability distribution under the prioritized hedging point policy. Although the shape of the domains of the work-in-process (WIP) levels influences the steady state probability balance equations, we still have developed a unified form of the marginal probability balance equations for all the possible shapes of WIP domains, which can be used to calculate the marginal probability distribution for each product type for the two-product-type and multi-parallel-machine system. Furthermore, we extend this analysis method to the multiple-product-type, multi-parallel-machine, and single-stage system. Based on the decomposition method of a production line, we can calculate the marginal probability distribution of a multiple-product-type, multi-parallel-machine, and multi-stage system and its average production cost. Finally, we employ a gradient-based algorithm to optimize the production control parameters and an integer programming technique to optimize the production capacity. Numerical experiments are conducted to verify the correctness of the method of evaluating steady-state probability distribution, and indicate that the solution of the IPCCP problem has better performance. 3.The IPCCP problem of multi-stage assembly system with random machine failure The objective of the IPCCP problem for a multi-stage assembly system with random machine failure is to minimize its investment on machines while keeping the average production cost below a desired level. Moreover, the key point for evaluating the average production cost is also the calculation of steady-state probability distribution of the state variables. Firstly, we analyze the approximate control policy of the multi-stage assembly system to determine state distribution domain. Furthermore, the probability balance equations of all the states in the state distribution domain are constructed. Then, we propose a method to obtain the marginal probability distribution of the multi-stage assembly system. Thus, the average production cost can be obtained. Because the optimal control policy parameter is impacted by production capacity, we employ the mixed integer programming technique to obtain the optimal machine number. Numerical experiments are conducted to verify the correctness of the method of evaluating steady-state probability distribution, and indicate that the solution of the IPCCP problem has better performance. 4.The IPCCP problem of semiconductor manufacturing system with uncertain wafer lots transfer probability For a semiconductor manufacturing system, wafer lots transfer probability (WLTP) is introduced to capture the flowing rate of wafer lots among production tools, which is uncertain due to various wafer types and quantities. We study a new production capacity planning problem for wafer fabrication systems with uncertain WLTP. Based on an open queueing network model, the average work-in-process (WIP) level of the system is evaluated. Because of the uncertain WLTP, the average WIP level fluctuates significantly and sometimes exceeds its desired upper bound. Therefore, we develop a robust production capacity planning model with two layers: the bottom layer is for finding the maximum WIP fluctuation under a given vehicle quantity, and the upper layer is for determining the vehicle quantities to minimize the WIP fluctuation and the probability of the average WIP exceeding its upper bound. A method based on the monotonicity of the objective functions is developed to solve such a bi-objective optimization problem. Numerical experiments indicate that the solution of robust capacity planning has stronger robustness against uncertain WLTP. The main contributions of this research include: (1) An IPCCP model is proposed for a single-product-type, multi-parallel-machine and multi-stage serial production line. In order to evaluate the average production cost, we developed a new decomposition-based method for such a system based on the method of calculating its steady state probability distribution. (2) An IPCCP model is proposed for a multi-product-type, multi-parallel-machine and multi-stage manufacturing system. Firstly, we develop an uniform steady state marginal probability distribution of the two-product-type, multi-parallel-machine and one-stage manufacturing system, and extend this marginal probability distribution to a multi-product-type, multi-parallel -machine and multi-stage manufacturing system so as to evaluate its production cost; (3) An IPCCP model is proposed for a multi-stage assembly system. By aggregating the state space, we propose a concept of generalized two-dimensional state space. Furthermore, the method of calculating marginal steady state probability distribution of the multi-stage assembly system is proposed based on the concept of generalized two-dimensional state space, which can be used to evaluate the production cost. (4) For a semiconductor manufacturing system, we propose the uncertain WLTP to describe the change of the wafer processing routes, also develop the robust capacity planning model based on open queuing network so as to optimize the vehicle quantities. The mathematical model, analysis method and algorithm are developed for the IPCCP problems of four typical manufacturing systems, which are helpful for them to achieve their best production performance at a minimum investment on machines, and to resist the negative impact of uncertainties. The results of this research provide a good guidance to reducing the investment on machines and decreasing the production cost for real-world manufacturing systems. Key words: production control; capacity planning; probability balance equation; steady state probability distribution; open queueing network.

作者相关
主题相关
看过该书的人还在看哪些书