A Benders decomposition approach for a new sustainable pharmaceutical supply chain network: a case study in France

Recently, sustainable supply chains have emerged to emphasize the importance of social and environmental concerns along with economic factors in supply chain management. In this context, there is a necessity for mathematical models that indicate environmental aspects and the social effects of the supply chain network. In the present study, a new multi-product production, distribution, and transportation, in which the economic, environmental, and social effects under CO2 emission to fill this gap are presented. Additionally, service technology under various criteria in the social aspects and time window for the earliest and latest arrival time of products to main distribution centers are provided. Also, other novelties of this paper, the environmental effects to open main and local distribution centers, warehouses, and pharmacies are considered as environmental effects. So, the main contributions of this paper are to develop a multi objective, dynamic production and distribution planning using time windows in service technology of sustainable pharmaceutical supply Chain Network. In this regard, the mathematical model is formulated as a mixed-integer linear programming model. Moreover, a Benders decomposition approach is appropriately extended to solve the presented model. In the proposed approach, the problem is decomposed into two models of sub-problem and a master. The master problem is developed by means of preprocessing and valid inequalities. The general and relative efficiency of the model and approach is experimentally assessed. The pharmaceutical production and distribution system of France is considered as a real case study in this paper. Eventually, the results indicate that the proposed approach considerably outperforms, and the efficiency of the developed model is verified through a set of sensitivity analyses.