[Paper Review] Balancing adaptability and predictability: K-revision multistage stochastic programming

Chengwenjian Wang, Alexander Estes+1 more|arXiv (Cornell University)|Jan 17, 2026

Risk and Portfolio Optimization0 citations

TL;DR

Introduces the K-revision approach to multistage stochastic programming, enforcing plan revisions limited to K per scenario, analyzes complexity, and develops MIP formulations with computational demonstrations.

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.

Motivation & Objective

• Motivates the need to balance fully adaptive MSP with predictable, commit-to plans.
• Proposes a framework where an initial plan is specified and can be revised at most K times per scenario.
• Aims to understand how K-revisions affect objective value versus solution consistency.
• Develops formulations and solution techniques to solve K-revision MSP.
• Demonstrates practicality through synthetic and real-world problem variants.

Proposed method

• Formally define K-revision constraints in MSP with plan and revision policies.
• Propose two mixed integer programming formulations for K-revision MSP.
• Provide a combinatorial characterization of the K-revision constraint to aid modeling.
• Analyze the complexity showing NP-hardness even in simple settings.
• Develop strengthening methods: variable-fixing, facet-defining cuts, and extended formulations.
• Demonstrate tractability and effectiveness via computational experiments on synthetic and SAGHP-like problems.

Experimental results

Research questions

• RQ1 How does limiting plan revisions to K affect the optimal objective relative to fully adaptive MSP?
• RQ2 What is the computational complexity of K-revision MSP and under what conditions can it be solved efficiently?
• RQ3 Can we formulate and strengthen practical MIP models that capture K-revision constraints effectively?
• RQ4 How do K-revision models perform on synthetic problems and practical applications like SAGHP and lot-sizing?

Key findings

• K-revision MSP is monotone in K; larger K never worsens the objective.
• Even in a simple hypercube setting, the K-revision problem is strongly NP-hard for 1 ≤ K ≤ T−2 when sizes are part of the input.
• There is a polynomial DP when T is fixed, enabling scalable solutions for fixed horizon with growing tree size.
• Two MIP formulations are developed, with tightness results and problem-specific strengthening techniques.
• A combinatorial ELBE-subtree based characterization helps connect plan revisions to strategic decisions.
• Computational experiments show K-revision approaches can achieve near-optimal performance with improved solution predictability compared to partially adaptive models.