A robust approach for a green periodic competitive VRP under uncertainty: DE and PSO algorithms

The purpose of this paper is to examine and evaluate a new mathematical model of vehicle routing problem in order to optimize fuel consumption and maximize commercial profitability under the conditions of uncertainty of distributor service to customers using robust approach under scenario. According to the real world, distribution companies are interested in minimizing consumption of fuel in the distribution of goods for two reasons: the first reason is that reducing the consumption of fuel will reduce the current costs of distribution companies and ultimately increase their profits. The second reason is that reducing fuel consumption will reduce the harmful effects of greenhouse gases and air pollution. Other words, distribution companies operate in a competitive environment that has more than one distributor in the distribution network, and start time for serving customers has a significant impact on the profitability of the distributors. To calculate the efficiency of the proposed model, we used differential evolution (DE) algorithm and Particle swarm optimization (PSO), and the results were compared in small and medium scales with the results of the exact solution method. To verify proceeds of proposed algorithms in large scales, a number of sample problems were created in large scales and the figures were evaluated. The computational results indicate that DE algorithm has a better computational function, but the PSO algorithm has better computational time.