Solving contextual chance-constrained programming under decision-dependent uncertainty

TL;DR

This paper introduces a nonparametric approximation method called CCW for solving decision-dependent chance-constrained programming problems, improving tractability and solution quality in complex, real-world scenarios.

Contribution

The paper proposes a novel CCW approach that constructs local neighborhoods of historical data to handle decision-dependent uncertainty, enabling convex reformulations and efficient solutions.

Findings

CCW improves solution feasibility and quality.

The method outperforms benchmarks in runtime and reliability.

Experiments demonstrate practical effectiveness in real-world case studies.

Abstract

We study contextual chance-constrained programming under decision-dependent uncertainty. In this setting, a decision not only needs to satisfy constraints but also alters the distribution of uncertain outcomes. This dependency makes the problem particularly difficult: because feasibility probabilities vary with decisions, it creates both statistical endogeneity and computational intractability. To address this, we propose a nonparametric approximation method based on Contextual Cluster Weights (CCW). For any given decision and context, CCW constructs a local neighborhood (cluster) of ``similar" historical observations and assigns them equal weight. This approach successfully renders both the objective and chance constraints tractable, while providing uniform-in-decision consistency guarantees. Furthermore, we develop reformulations that use pre-calculated clusters. We show that under a specific nestedness condition, these reformulations yield a convex feasible region, which allows for efficient solving. Experiments, including a case study with JD.com, demonstrate that our method outperforms benchmarks in solution quality, feasibility reliability, and runtime. This framework offers a scalable and data-driven approach for firms to make reliable operational decisions when their actions influence uncertainty. It effectively balances performance, risk, and robustness, while remaining interpretable and implementable in practice.