In large-scale emergency, the vehicle routing problem focuses on finding the best routes for vehicles. The equitable distribution has a vital role in this problem to decrease the number of death and save people's lives. In addition to this, air pollution is a threat to people’s life and it can be considered to omit other kinds of disasters happens because of it. So, a new MINLP model presented is going to face a real situation by considering real world assumptions such as fuzzy demands and travel time, multi depots and items, vehicle capacity and split delivery. The first objective function is to minimize the sum of unsatisfied demand which follows a piecewise function and the second one is to minimize the cost which depends on the fuel consumption. In order to solve the multi-objective problem with fuzzy parameters, nonlinear function has been linearized by convex combination and a new crisp model is presented by defusing fuzzy parameters. Finally, NSGA-П algorithm is applied to solve this problem and the numerical results gained by this procedure demonstrate its convergence and its efficiency in this problem.

Keywords: Vehicle routing problem, Equity, Air pollution, Uncertainty, Split delivery, NSGA-П

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