面向复杂生产系统设计与控制的仿真优化方法研究

The always increasing market competition is forcing companies to dedicate more and more attention to the configuration of their production and inventory systems and the way in which they are utilized. In this context, the design phase of either the configuration of the system or the policies controlling the system becomes relevant because affecting most of the future costs incurred during the system life cycle. In this phase, actual simulation-optimization methods do not satisfy the company needs, which have to design complex production and inventory systems. Complexity is due to the high number of possible alternatives, the randomness affecting dynamics, the non-linear behavior and the implicit relationships among variables. The common practice in companies is to use simulation to estimate the system performance (i.e., production rate, WIP, lead time, etc.) of a specific alternative, while the optimization phase is executed with simple rules of thumb. As a consequence, production and inventory systems are suboptimal and incur in higher costs than necessary.This project aims at developing a new framework for simulation-optimization of production and inventory systems. The framework is based on two main pillars: mathematical programming and time buffer. The first is innovatively used to make possible formulating and solving one mathematical model that simultaneously optimizes and simulates the production system. The time buffer is an approximation for simplifying the simulation-optimization problem when formulated as a mathematical model. More specifically all the synchronization mechanisms between parts in the production systems are translated into synchronization mechanisms between events. This translation is such that complex mathematical models with integer decision variables are easily commuted into linear mathematical models. This simplification allows simpler mathematical formulations to be quickly solved by optimization algorithms. Expected achievements are production systems with higher production rate, lower WIP, shorter order lead times and lower costs.

市场竞争越来越激烈，这使得企业越来越关注其生产和库存系统的配置及其使用方式。由于系统配置和控制系统的策略影响了大部分发生在生产周期中的成本，系统配置和控制系统策略的设计阶段相互关联。企业需要需要设计复杂生产系统和库存系统，然而实际仿真优化方法并不能满足公司的这个需求。由于具有大量的可选项、动态随机性、非线性特征、以及变量之间的隐性关系，企业通常使用仿真评估系统性能，然后基于经验进行优化。针对该问题，本项目拟研究基于数学规划和时间缓冲的仿真优化方法。首先构建能够同时优化和仿真生产系统的数学模型；然后基于时间缓冲近似，即将生产部件间的同步机制转化为事件之间的同步机制，以简化数学模型中的仿真优化问题；这种近似使得带有整数决策变量的复杂数学规划模型可以转化为便于优化算法快速求解的线性规划模型。项目所提出方案能够使得生产系统提高生产率，降低在制品水平，缩短订单提前期，降低成本。

离散事件仿真是复杂随机系统性能的主要评估工具之一。因此，仿真也越来越广泛的被应用于生产与库存系统设计和控制问题。本项目提出的离散事件优化（Discrete Event Optimization，DEO）方法是在一个数学规划模型中整合仿真和优化的建模和求解框架。离散事件优化方法表明仿真不仅可以作为随机系统的性能评估工具，还可以定义优化问题的可行域。DEO数学模型是仿真优化框架的核心，围绕这一核心，本项目同时研究了建模方法和求解算法，并将建立的方法应用于多个生产与库存系统设计和控制问题。. 本项目首先建立了基于事件的建模方法和近似求解算法。近似算法提出了时间缓存概念，即将两个相关事件发生的时间差作为近似线性约束的方法。这一近似方法即可以被用于直接求近似解，也可以在算法的初始阶段缩小可行域。拉式生产系统的库存控制问题和串联生产系统的缓存分配问题的数值实验表明，近似算法可以在合理时间内得到次优解。. 其次，本项目建立了基于图形的建模方法，简化了生产于库存系统设计和控制问题的建模和分析过程。图论建模方法可以被广泛应用于各种复杂系统，例如本项目建立了看板系统、闭环系统和装配系统的图论模型。. 最后，本项目建立了基于Benders分解的算法，有效的缩小了问题的规模。仿真过程中事件之间的触发关系被用来生成Benders约束，避免了使用求解器对数学规划模型进行求解，进一步提高了算法效率。通过分解，优化部分的求解更具灵活性，本项目的一个案例使用邻域搜索算法求解了有限库存下的缓存分配问题。分解算法也被用来求解串联系统的瓶颈检测问题，数值分析表明分解算法具备求解复杂问题的能力。