Uncertainty modelling is key to obtain a realistically feasible solution for large-scale optimization problems. In this study, we consider two-stage stochastic programming to model discrete-time batch process operations with a type II endogenous (decision dependent) uncertainty, where time of uncertainty realizations are dependent on the model decisions. We propose an integer programming model to solve the problem, whose key feature is that it does not require auxiliary binary variables or explicit non-anticipativity constraints to ensure non-anticipativity. To the best of our knowledge this is the first model dealing with such type II uncertainties that has these characteristics, which makes it a much more computationally attractive model. We present a proof that non-anticipativity is enforced implicitly as well as computational results using a large-scale scientific services industrial plant. The computational results from the case study depicts significant benefits in using the proposed stochastic programming approach.

不确定性建模是获得大规模优化问题现实可行解决方案的关键。在这项研究中，我们考虑使用两阶段随机规划来模拟具有 II 类内生（决策相关）不确定性的离散时间批处理操作，其中不确定性实现的时间取决于模型决策。我们提出了一个整数规划模型来解决这个问题，其主要特点是不需要辅助二元变量或显式非预期约束来确保非预期性。据我们所知，这是第一个处理具有这些特征的 II 类不确定性的模型，这使其成为一个在计算上更具吸引力的模型。我们提供了一个证明，即使用大型科学服务工业工厂隐式强制执行非预期性以及计算结果。案例研究的计算结果描述了使用建议的随机编程方法的显着优势。