designing a mathematical model for two-echelon allocation-routing problem by applying the route and transportation fleet conditions

A novel mixed integer non-linear mathematical model is presented in this paper for the two-echelon allocation-routing problem by applying the conditions of the route and transportation fleet under uncertainty. the cost of allocating drivers to non-homogeneous vehicles is calculated in this model based on the type of the vehicle, the lifecycle of the car, the experience of the driver, and different degrees of hardness that are defined for various routes. the cost of passing the route is defined based on an initial fixed cost and the degree of hardness of the route. also, the reliability of the routes in each section is defined as an objective in the second echelon of the model aimed at enhancing the reliability rate. two metaheuristic algorithms, nsgaii and mopso, are utilized to solve the model. then, their performance rates in problems with different sizes are statistically evaluated and compared by different indices, following the adjustment of their parameters by taguchi’s method, through which results indicated the high efficiency of the model. a sensitivity analysis is ultimately performed on the results obtained from the solution, and some suggestions are made for the development of the model.