Major application areas of the process systems engineering, such as hybrid control, scheduling and synthesis can be formulated as mixed integer linear programming (MILP) problems and are naturally susceptible to uncertainty. Multi-parametric programming theory forms an active field of research and has proven to provide invaluable tools for decision making under uncertainty. While uncertainty in the right-hand side (RHS) and in the objective function’s coefficients (OFC) have been thoroughly studied in the literature, the case of left-hand side (LHS) uncertainty has attracted significantly less attention mainly because of the computational implications that arise in such a problem. In the present work, we propose a novel algorithm for the analytical solution of multi-parametric MILP (mp-MILP) problems under global uncertainty, i.e. RHS, OFC and LHS. The exact explicit solutions and the corresponding regions of the parametric space are computed while a number of case studies illustrates the merits of the proposed algorithm.

过程系统工程的主要应用领域，例如混合控制，调度和综合，可以表述为混合整数线性规划（MILP）问题，并且自然容易受到不确定性的影响。多参数编程理论构成了一个活跃的研究领域，并已被证明可以为不确定性条件下的决策提供宝贵的工具。尽管文献中已经对右侧不确定性（RHS）和目标函数系数（OFC）进行了深入研究，但是左侧不确定性（LHS）的情况却引起了人们的广泛关注，这主要是由于计算的影响在这样的问题中出现。在目前的工作中，我们提出了一种新的算法，用于求解全局不确定性下的多参数MILP（mp-MILP）问题，即RHS，OFC和LHS。