Dependent-Chance Goal Programming for Sustainable Supply Chain Design: A Reinforcement Learning-Enhanced Salp Swarm Approach

Yassine Boutmir (), Rachid Bannari, Achraf Touil, Mouhsene Fri and Othmane Benmoussa
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Yassine Boutmir: Laboratory of Engineering Sciences, Informatics, Logistics and Mathematics Department, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco
Rachid Bannari: Laboratory of Engineering Sciences, Informatics, Logistics and Mathematics Department, National School of Applied Sciences, Ibn Tofail University, Kenitra 14000, Morocco
Achraf Touil: Laboratory of Engineering, Industrial Management and Innovation, Faculty of Sciences and Techniques, Hassan 1st University, Settat 26000, Morocco
Mouhsene Fri: Euromed University of Fes, UEMF, Fes 30000, Morocco
Othmane Benmoussa: Euromed University of Fes, UEMF, Fes 30000, Morocco

Sustainability, 2025, vol. 17, issue 13, 1-41

Abstract: The Sustainable Supply Chain Network Design Problem (SSCNDP) is to determine the optimal network configuration and resource allocation that achieve the trade-off among economic, environmental, social, and resilience objectives. The Sustainable Supply Chain Network Design Problem (SSCNDP) involves determining the optimal network configuration and resource allocation that allows trade-off among economic, environmental, social, and resilience objectives. This paper addresses the SSCNDP under hybrid uncertainty, which combines objective randomness got from historical data, and subjective beliefs induced by expert judgment. Building on chance theory, we formulate a dependent-chance goal programming model that specifies target probability levels for achieving sustainability objectives and minimizes deviations from these targets using a lexicographic approach. To solve this complex optimization problem, we develop a hybrid intelligent algorithm that combines uncertain random simulation with Reinforcement Learning-enhanced Salp Swarm Optimization (RL-SSO). The proposed RL-SSO algorithm is benchmarked against standard metaheuristics—Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), and standard SSO, across diverse problem instances. Results show that our method consistently outperforms these techniques in both solution quality and computational efficiency. The paper concludes with managerial insights and discusses limitations and future research directions.

Keywords: dependent-chance goal programming; sustainable supply chain; hybrid uncertainty; hybrid intelligent algorithm; reinforcement learning; salp swarm optimization (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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