# Distributionally Robust Facility Location Problem under Decision-dependent Stochastic Demand

arXiv: https://arxiv.org/abs/1912.05577 · HTML: https://mlsanity.com/paper/1912.05577/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Dec 2019.

## Built on by (most cited first, 4 of 4)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [Decision-Dependent Stochastic Optimization: The Role of Distribution Dynamics](https://mlsanity.com/paper/2503.07324/) (2025)
- [Decision-Dependent Distributionally Robust Markov Decision Process Method in Dynamic Epidemic Control](https://mlsanity.com/paper/2306.14051/) (2023)
- [Learning-Based Surrogate Method for Stochastic Optimization under Decision-Dependent Uncertainty with Adaptive Random Designs](https://mlsanity.com/paper/2505.07298/) (2025)

## Abstract (arXiv)

Facility location decisions significantly impact customer behavior and consequently the resulting demand in a wide range of businesses. Furthermore, sequentially realized uncertain demand enforces strategically determining locations under partial information. To address these issues, we study a facility location problem where the distribution of customer demand is dependent on location decisions. We represent moment information of stochastic demand as a piecewise linear function of facility-location decisions. Then, we propose a decision-dependent distributionally robust optimization model, and develop its exact mixed-integer linear programming reformulation. We further derive valid inequalities to strengthen the formulation. We conduct an extensive computational study, in which we compare our model with the existing (decision-independent) stochastic and robust models. Our results demonstrate superior performance of the proposed approach with remarkable improvement in profit and quality of service by extensively testing problem characteristics, in addition to computational speed-ups due to the formulation enhancements. These results draw attention to the need of considering the impact of location decisions on customer demand within this strategic-level planning problem.