<p>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 obtained by combining resilience through backup reassignment, agility through mobile facilities, and environmental considerations such as emission limits. Together, these elements help maintain demand satisfaction across both echelons and support long-term network performance. Two mixed-integer programming formulations are developed. The first formulation is a scenario-based formulation and the second is implicit formulation which both minimize expected fixed and service costs. To handle probabilistic service requirements, the implicit formulation integrates a machine learning–enhanced chance-constrained programming approach. In this framework,intractable capacity chance constraints are approximated by learned linear cuts that apply 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. The best-performing classifier is then selected as a surrogate model. To improve scalability, two fix-and-relax heuristics are developed for the implicit formulation, while a sample average approximation (SAA) method is used for the scenario-based formulation. Computational experiments demonstrate that the implicit formulation proposes a computationally efficient and high-quality alternative to the scenario-based formulation. Furthermore, the proposed heuristics and SAA approach effectively address medium- and large-scale instances, delivering high-quality solutions within acceptable computational times.</p>

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Viable supply chain network design: machine learning-derived chance-constrained programming

  • Mohammad Rohaninejad,
  • Behdin Vahedi-Nouri,
  • Elham Jelodari Mamaghani,
  • Mehdi Foumani,
  • Olga Battaia

摘要

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 obtained by combining resilience through backup reassignment, agility through mobile facilities, and environmental considerations such as emission limits. Together, these elements help maintain demand satisfaction across both echelons and support long-term network performance. Two mixed-integer programming formulations are developed. The first formulation is a scenario-based formulation and the second is implicit formulation which both minimize expected fixed and service costs. To handle probabilistic service requirements, the implicit formulation integrates a machine learning–enhanced chance-constrained programming approach. In this framework,intractable capacity chance constraints are approximated by learned linear cuts that apply 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. The best-performing classifier is then selected as a surrogate model. To improve scalability, two fix-and-relax heuristics are developed for the implicit formulation, while a sample average approximation (SAA) method is used for the scenario-based formulation. Computational experiments demonstrate that the implicit formulation proposes a computationally efficient and high-quality alternative to the scenario-based formulation. Furthermore, the proposed heuristics and SAA approach effectively address medium- and large-scale instances, delivering high-quality solutions within acceptable computational times.