Developing a Fuzzy Green Supply Chain Management Problem Considering Location Allocation Routing Problem: Hybrid Meta-Heuristic Approach

Nowadays, the internationalization of supply chains makes the management of operation affairs face a great challenge. On the other hand, vague parameters have challenged decision-makers to drive decision-making. To cope with these challenges, this study tries to model a green SCM (GSCM) model which considers fuzzy parameters. The objective function of our model is to minimize total fuzzy cost including fuzzy establishment costs of the plants and distribution centers, fuzzy transportation costs among the suppliers, facilities, and customers, fuzzy hiring cost of the transportation facilities, and miscellaneous fuzzy environmental impact costs. The developed model also includes facilities location constraints, material flow constraints, open transportation routing from plants to customers and from distribution centers to customers. Also, determining alternative products for customers has not been addressed in the literature.  Therefore, this paper tries to focus on the mentioned complex problem and develop a comprehensive model. Because of the level of complexity of the developed model, two empowered meta-heuristic approaches, named fuzzy hybrid genetic algorithm (FHGA) and fuzzy hybrid biogeography-based optimization algorithm (FHBBO), are implemented to solve the NP-hard developed problem. According to the best of our knowledge, the proposed FHGA is not addressed in the literature in this way. For instance, most of the fuzzy algorithms either are not hybrid or get out of the fuzzy environment in one of their complex evolution processes. However, our fuzzy hybrid algorithms follow a fuzzy environment from beginning test initialization to calculating the objective function and presenting the convergence plots and none of our parameters are defuzzied in all steps of these processes. Besides, miscellaneous Figures, illustrations, and tables support the explanations of results.