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<p>We propose a novel bi-objective two-stage stochastic formulation for the problem of designing a resilient and agile supply chain network with suppliers, potential locations for facilities and customers. As suppliers and facilities are vulnerable to disruption risks, preparedness and reactive measures are considered. These include conditional backup sourcing, facility fortification and deferral of customer demand. This flexibility enhances the supply chain’s responsiveness to disruptions and to uncertainty in demand and costs. First-stage decisions define a schedule for facility deployment, the choice of fortification levels for unreliable facilities, and the selection of primary and backup suppliers. Once uncertainty is disclosed, second-stage decisions determine the activation of backup suppliers and the material flows across the network. Flows may include delayed deliveries to customers, bounded by a maximum lateness threshold. Two conflicting objectives are considered: minimising total expected cost and total expected unmet demand. We develop a tailored two-phase heuristic procedure that is embedded in the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-constraint method. Computational experiments on randomly generated instances demonstrate the effectiveness of the proposed methodology, especially for large-scale instances where a state-of-the-art solver fails to find a feasible solution within a given time limit. Moreover, we provide a comparative analysis of a representative subset of Pareto-optimal solutions that highlights cost-resilience-responsiveness trade-offs to support decision-making.</p>

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Bi-objective stochastic supply chain network design under supplier and facility disruption risks

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月16日

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  • Angelo Aliano Filho,
  • Isabel Correia,
  • Teresa Melo

摘要

We propose a novel bi-objective two-stage stochastic formulation for the problem of designing a resilient and agile supply chain network with suppliers, potential locations for facilities and customers. As suppliers and facilities are vulnerable to disruption risks, preparedness and reactive measures are considered. These include conditional backup sourcing, facility fortification and deferral of customer demand. This flexibility enhances the supply chain’s responsiveness to disruptions and to uncertainty in demand and costs. First-stage decisions define a schedule for facility deployment, the choice of fortification levels for unreliable facilities, and the selection of primary and backup suppliers. Once uncertainty is disclosed, second-stage decisions determine the activation of backup suppliers and the material flows across the network. Flows may include delayed deliveries to customers, bounded by a maximum lateness threshold. Two conflicting objectives are considered: minimising total expected cost and total expected unmet demand. We develop a tailored two-phase heuristic procedure that is embedded in the \(\varepsilon \) ε -constraint method. Computational experiments on randomly generated instances demonstrate the effectiveness of the proposed methodology, especially for large-scale instances where a state-of-the-art solver fails to find a feasible solution within a given time limit. Moreover, we provide a comparative analysis of a representative subset of Pareto-optimal solutions that highlights cost-resilience-responsiveness trade-offs to support decision-making.