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

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.