A new bi-objective green medicine supply chain network design under fuzzy environment: Hybrid metaheuristic algorithms

This paper studies the design of the green medicine supply chain network under uncertainty, which integrates allocation, location, production, distribution, routing, inventory, and purchasing problems. The main contribution of the current paper is to design a fuzzy bi-objective Mixed-Integer Linear Programming (MILP) model for a multi-period, three-echelon, multi-product, and multi-modal transportation green medicine supply chain network (GMSCN). Additionally, the main aim of this network is to consider the environmental impacts related to the establishment of pharmacies and hospitals, by focusing on the reduction of greenhouse gases and the control of environmental pollutants. Therefore, to cope with uncertain parameters, fuzzy programming is utilized to examine uncertainty parameters. To solve the GMSCN model, meta-heuristic algorithms are used, including social engineering optimization, improved kill herd, improved social spider optimization, and hybrid whale optimization and simulated annealing. In this regard, two new hybrid algorithms called hybrid Firefly Algorithm and Simulated Annealing (HFFA-SA) and Hybrid Firefly Algorithm and Social Engineering Optimization (HFFA-SEO) to solve the proposed model for the first time are developed. In order to show the applicability of our paper and the lack of benchmark functions in the literature, a set of simulated data in two sizes including small- and large-sized problems is provided. Finally, the results of the analysis and the designed problems indicate that the GMSCN model and developed solution approaches are promising.