A novel stochastic programming approach for scheduling of batch processes with decision dependent time of uncertainty realization

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.