Viable Supply Chain Network Design: Machine Learning-Derived Chance-Constrained Programming

Abstract

This paper investigates a viable two-echelon supply chain network design problem with unreliable facilities subject to disruptions. Unlike existing studies that consider supply chain echelons in isolation, the proposed models explicitly capture cross-echelon disruptions and quantify the value of incorporating such interdependencies. Network viability is achieved by jointly integrating resilience (via backup reassignment), agility (via mobile facilities), and environmental impact (via emissions caps) to ensure demand satisfaction across both echelons and support long-term network survival. Two mixed-integer programming formulations are developed: a scenario-based formulation and an implicit formulation, both minimizing expected fixed and service costs. To handle probabilistic service requirements, the implicit formulation incorporates a machine learning-enhanced chance-constrained programming approach, in which intractable capacity chance constraints are replaced by learned linear cuts enforcing a 95% service confidence level. These cuts are trained using several classification methods, including logistic regression, L1-regularized logistic regression, stochastic gradient descent, the perceptron algorithm, and logistic regression with a regularization parameter of 0.1, with the best-performing classifier selected as a surrogate. To further enhance scalability, two fix-and-relax heuristics are developed for the implicit formulation, while a sample average approximation (SAA) method is applied to the scenario-based formulation. Computational experiments demonstrate that the implicit formulation offers a computationally efficient and high-quality alternative to the scenario-based formulation. Moreover, the proposed heuristics and SAA approach effectively address medium- and large-scale instances, delivering high-quality solutions within acceptable computational times.