Batch Process Scheduling under Uncertainty using Data-Driven Multistage Adaptive Robust Optimization

Abstract

This paper proposes a novel data-driven batch process scheduling approach based on multistage adaptive robust optimization coupled with robust kernel density estimation (RKDE). The kernelized iteratively re-weighted lease squares (KIRWLS) algorithm combined with kernel tricks are adopted to learn the probability density function from outlier-corrupted uncertain processing time data. We then propose a data-driven outlier-resilient uncertainty set for scheduling problem using the extracted distributional information. The proposed framework exhibits robustness to contamination of uncertainty data by integrating robust optimization with robust statistics. The batch process scheduling is then formulated as a data-driven multistage decision-making problem. By introducing affine decision rules for recourse variables, the resulting data-driven multistage adaptive robust optimization problem can be solved efficiently. We apply the proposed data-driven multistage adaptive robust optimization to a multipurpose batch process scheduling problem using a dataset to demonstrate the superiority of the proposed method. Our proposed approach generates $13,851 more profits than those of multistage adaptive robust optimization with box set. Compared with the multistage adaptive robust optimization using kernel density estimation (KDE), the result returned from the proposed method generates $4,064 more profits.