Modeling and optimization sustainable forest supply chain considering discount in transportation system and supplier selection under uncertainty

In recent decades, the forest industry has been growingly expanded due to economic conditions, climate changes, environmental and energy policies, and intense demand changes. Thus, appropriate planning is required to improve this industry. To achieve economic, social and environmental goals, a supply chain network is designed based on a multi-period and multi-product Mixed-Integer Non-Linear Programming (MINLP) model in which the objective is to maximize the profit, minimize detrimental environmental effects, improve social effects, and minimize the number of lost demands. In addition, to improve forest industry planning, strategic and tactical decisions have been implemented throughout the supply chain for all facilities, suppliers and machinery. These decisions significantly help to improve processes and product flows and to meet customers’ needs. In addition, because of the presence of uncertainty in some parameters, the proposed model was formulated and optimized under uncertainty using the hybrid robust possibilistic programming (HRPP-II) approach. The E-constraint technique was used to solve the multi-objective model, and the Lagrangian relaxation (LR) method was utilized to solve the model of more complex dimensions. A case study in Northern Iran was conducted to assess the efficiency of the suggested approach. Finally, a sensitivity analysis was performed to determine the impact of important parameters on objective functions. The results of this study show that increasing the working hours of machines instead of increasing their number, increasing the capacity of some facilities instead of establishing new facilities and expanding the transport fleet has a significant impact on achieving predetermined goals.