A hybrid metaheuristic for a sustainable supply chain network design with carbon emission consideration

Abstract

Designing and optimising supply chain networks, including location decisions and sustainable transport, are essential to operational efficiency. Research on supply chain network design with multiple echelons has predominantly focused on one type of location problem, the discrete location problem, while lacking a significant type of facility location problem in continuous space. Unlike discrete models, which restrict facility location to predefined candidate locations, continuous location problems offer greater flexibility, allowing facilities to be located anywhere on the plane. Existing studies on facility location in continuous space, specifically the capacitated continuous facility location problem (CCFP), are confined to two-echelon contexts and do not extend to a comprehensive supply chain network design with multiple echelons. The CCFP also incorporates facility capacity constraints, making it particularly relevant for addressing real-world supply chain challenges, where capacity limits and cost-efficiency must be balanced across increasingly complex networks. Addressing multi-echelon supply chain networks in continuous space is vital due to their increasing complexity in modern logistics, where interconnected echelons of suppliers, distribution centres, and customers require integrated and cost-efficient solutions. In location problems, it is possible to find different facility fixed (opening) costs, which is essential in operations and supply chain design. In CCFP, the aim is to identify the number of facilities that minimise the sum of the fixed and transportation costs. One critical aspect of designing sustainable supply chains is selecting the most eco-friendly transportation mode that reduces carbon emission costs. More importantly, incorporating transportation mode selection within the CCFP framework in supply chain design represents another significant gap in the existing literature, emphasising the need for a comprehensive study. This research studies the design of a three-echelon supply chain within the CCFP framework with fixed facilities costs and integrates transportation mode selection. The objective is to minimise the supply chain's total cost, including transportation, fixed, and carbon emission costs. Three mathematical models are presented to formulate this problem. This study hybrids two approximation methods, a Greedy Randomised Adaptive Search Procedure metaheuristic (GRASP) and a Variable Neighbourhood Search metaheuristic (VNS), to solve the CCFP problem. To deal with fixed costs, a continuous fixed cost function approach has been implemented. For the transportation mode selection problem, a greedy heuristic put forward to select the mode with the lowest emission cost. The performance of each proposed model and the hybridised metaheuristics is evaluated using benchmark data sets from the literature. The results are validated and compared with those produced by the mathematical programming problems solver, CPLEX, using the same data. The results show that the proposed methods in this research significantly outperform CPLEX for medium and larger-scale instances in terms of computation time and solution quality. A brief on future research avenues is also provided.