Coupled Learning Enabled Stochastic Programming with Endogenous Uncertainty

Predictive analytics, empowered by machine learning, is usually followed by decision-making problems in prescriptive analytics. We extend the previous sequential prediction-optimization paradigm to a coupled scheme such that the prediction model can guide the decision problem to produce coordinated decisions yielding higher levels of performance. Specifically, for stochastic programming (SP) models with latently decision-dependent uncertainty, without any parametric assumption of the latent dependency, we develop a coupled learning enabled optimization (CLEO) algorithm in which the learning step of predicting the local dependency and the optimization step of computing a candidate decision are conducted interactively. The CLEO algorithm automatically balances the exploration and exploitation via the trust region method with active sampling. Under certain assumptions, we show that the sequence of solutions provided by CLEO converges to a directional stationary point of the original nonconvex and nonsmooth SP problem with probability 1. In addition, we present preliminary experimental results which demonstrate the computational potential of this data-driven approach.

Multicomponent Maintenance Optimization: A Stochastic Programming Approach

Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems and are not applicable to complex systems consisting of multiple components, due to various interactions among the components. The multicomponent maintenance optimization problem, which joins the stochastic processes regarding the failures of components with the combinatorial problems regarding the grouping of maintenance activities, is challenging in both modeling and solution techniques, and has remained an open issue in the literature. In this paper, we study the multicomponent maintenance problem over a finite planning horizon and formulate the problem as a multistage stochastic integer program with decision-dependent uncertainty. There is a lack of general efficient methods to solve this type of problem. To address this challenge, we use an alternative approach to model the underlying failure process and develop a novel two-stage model without decision-dependent uncertainty. Structural properties of the two-stage problem are investigated, and a progressive-hedging-based heuristic is developed based on the structural properties. Our heuristic algorithm demonstrates a significantly improved capacity to handle large-size two-stage problems comparing to three conventional methods for stochastic integer programming, and solving the two-stage model by our heuristic in a rolling horizon provides a good approximation of the multistage problem. The heuristic is further benchmarked with a dynamic programming approach and a structural policy, which are two commonly adopted approaches in the literature. Numerical results show that our heuristic can lead to significant cost savings compared with the benchmark approaches.