Incorporating Vehicle-Routing Problems into a Closed-Loop Supply Chain Network Using a Mixed-Integer Linear-Programming Model

In recent years, there has been a tremendous increase in environmental awareness, due to concerns about sustainability. Designing an efficient supply chain network that fulfills the expectation of both business owners and customers and, at the same time, pays attention to environmental protection is becoming a trend in the commercial world. This study proposes a theoretical model incorporating vehicle routing problems (VRPs) into the typical CLSC (closed-loop supply chain) network architecture. This combination assists all operators to act more efficiently in terms of environmental protection and profitability. A mixed-integer-linear-programming model for CLSC network design with fuzzy and random uncertain data is developed to achieve the goals. The parameters of the CLSC network are also programmed using hybrid fuzzy-stochastic mathematical programming. The model is for a single product and a single timeframe. Several numerical examples are provided to demonstrate the validity of the proposed mixed-integer-linear-programming (MILP) model. This study also investigated probabilistic possibilities for recourse variables with a trapezoidal fuzzy number using a problem size of four cases. The result indicates that the model performed well in the numerical test, suggesting it can help the operation to be more profitable if this model is implemented in their daily routines.