Balancing adaptability and predictability: K-revision multistage stochastic programming

TL;DR

This paper introduces the K-revision multistage stochastic programming framework, allowing plans to be revised up to K times to balance adaptability with predictability, supported by theoretical analysis and computational experiments.

Contribution

It proposes a novel K-revision approach for multistage stochastic programming, including formulations, complexity analysis, and computational methods.

Findings

K-revision problems are NP-hard even in simple cases.

The approach achieves near-optimal solutions with increased predictability.

Computational experiments show the method is practical and effective.

Abstract

A standard assumption in multistage stochastic programming is that decisions are made after observing the uncertainty from the prior stage. The resulting solutions can be difficult to implement in practice, as they leave practitioners ill-prepared for future stages. To provide better foresight, we introduce the K-revision approach. This new framework requires plans to be specified in advance. To maintain flexibility, we allow plans to be revised a maximum of K times as new information becomes available. We analyze the complexity of K-revision problems, showing NP-hardness even in a simple setting. We examine, both theoretically and computationally, the impact of the K-revision approach on the objective compared with classical multistage stochastic programming models and the partially adaptive approach introduced in [1, 2]. We develop two MIP formulations, one directly from our definition and the other based on a combinatorial characterization. We analyze the tightness of these formulations and propose several methods to strengthen them. Computational experiments on synthetic problems and practical applications demonstrate that our approach is both computationally tractable and effective in reaching near-optimal performance while increasing the predictability of the solutions produced.