Robust Stable Cost Optimization in a Three Echelon Supply Chain Model
Robust Stable Cost Optimization in a Three Echelon Supply Chain Model
复制标题
三梯队供应链模型中鲁棒稳定的成本优化
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
M. Mönnigmann
中科院分区：
文献类型：
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作者：
Darya Kastsian;M. Mönnigmann
摘要将三级供应链建模为具有不确定参数的时不变离散系统，研究了三级供应链的优化问题。非线性规划方法的直接应用导致操作点确实是最优的，但不稳定。为了找到一个点的操作，这是最佳的和稳定的，我们增加了鲁棒动力学的约束，称为法向量约束的优化问题。实质上，法向量约束通过确保系统雅可比矩阵的所有特征值位于开单位圆内来保证系统的稳定性。法向量约束可以用来确保鲁棒稳定性，通过强制执行的特征值的位置，即使模型是受参数不确定性。通过将法向量方法应用于具有24个动力学方程和9个不确定参数的离散时间系统，我们证明了该方法适用于不能方便地处理的模型解析方法。
Abstract We optimize a supply chain with three echelons that is modeled as a time-invariant discrete-time system with uncertain parameters. A straight forward application of nonlinear programming methods results in a point of operation that indeed is optimal, but unstable. In order to find a point of operation that is both optimal and stable, we augment the optimization problem by constraints for robust dynamics known as normal vector constraints. Essentially, the normal vector constraints guarantee stability of the system by ensuring all eigenvalues of its Jacobian to lie in the open unit circle. The normal vector constraints can be used to ensure robust stability by enforcing the eigenvalue placement even if the model is subject to parametric uncertainty. By applying the normal vector method to a discrete-time system with 24 dynamical equations and nine uncertain parameters, we demonstrate that the method is appropriate for models that cannot conveniently be handled anymore by analytical methods.