基于离散-连续约束的医药供应链混合建模与优化

The main scientific objective of the proposed research cooperation is the modeling and optimization of complex systems arising in the pharmaceutical supply chain. Due to highly interconnected medical flows, it allows to include easily additional modeling aspects as discrete decisions and stochastic effects. In applications to pharmaceutical supply chain, we therefore aim to analyse the resilience of supply chain and derive a hybrid model including discrete decisions as well as a continous description for the production flow on this kind of complex networks. First we aim on coupling the discrete and continuous level by presenting a suitable mathematical model with well–defined transitions. Besides the modeling of observed phenomena, we also include control measures at discrete and continuous level. In the case of pharmaceutical supply chain, this corresponds for example to short–term adjustments and long–term planning goals, respectively. The arising systems will be analyzed both theoretically and numerically. The mid-range goal to be achieved within the duration of the project is the extension of novel modeling approach of supply chain dynamics by description of local controls. Further, we plan to establish the link to averaged macroscopic models and controls. The long term goal of the research is the possibility to treat complex transport processes as well as to include different further areas. We plan the development of providing a theoretical as well as a numerical insights via variational inequalities. This will be accompanied by the development of efficient numerical algorithms for solving the problems of pharmaceutical supply chain in China.

本项目主要研究在医药供应链体系中复杂系统的模型建立与优化问题。在医药流通过程中，供应链内部多种因素互相影响，导致离散化决策和随机效应的产生。首先将对医药供应链体系进行弹性分析，建立一个混合模型，引进短期决策（如当前库存管理）和长期决策（如医院长期订单），在模型中分别表现为离散和连续约束。其次，我们将联立该模型中离散和连续约束，根据守恒定律，使之转化成为一个合理的混合优化模型。最后，我们将对所得到的模型进行理论上的分析，并采用多种技巧将其转化成为一个混合整数模型或线性规划模型，利用变分不等式进行求解。本项目的实行一方面有助于丰富具有多尺度时效性需求的医药供应链建模方法，为揭示供应链内在复杂性提供新的手段，有利于医药供应链优化算法的建立；另一方面，可以拓展医药供应链的应用领域，解决医药供应链运营中急需解决的实际问题，为医药供应链服务水平的提高和运行成本的控制提供可行的应用方法。

针对医药供应链和一般复杂性系统，本项目系统讨论了定价策略、生产库存控制策略和绩效管理的集成问题，建立了几类供应链系统库存控制联合决策模型，运用理论分析与数值实例等方法研究了这类问题的稳定性、解的存在性和最优策略的结构性质和求解。具体成果主要体现在研究了（1）供应链建模与系统分析研究；（2）不确定性情况下复杂系统的稳定性研究（3）供应链系统的联合决策问题；（4）供应链模型的应用和推广。

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