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 same time, pays attention protection is becoming trend commercial world. This study proposes theoretical model incorporating vehicle routing problems (VRPs) into typical CLSC (closed-loop chain) architecture. combination assists all operators act more efficiently terms profitability. A mixed-integer-linear-programming for design with fuzzy random uncertain data developed achieve goals. The parameters are also programmed using hybrid fuzzy-stochastic mathematical programming. single product timeframe. Several numerical examples provided demonstrate validity proposed (MILP) model. investigated probabilistic possibilities recourse variables trapezoidal number problem size four cases. result indicates performed well test, suggesting it can help operation be profitable if this implemented their daily routines.