solving a stochastic multi-depot multi-objective vehicle routing problem by a simulated annealing

in this paper a stochastic multi depot multi objective vehicle routing problem (vrp) is studied. based on observations in real world problems we develop an aspect of the problem such as stochastic availability of routes. to solve the problem in this situation a two objective mathematical model is developed in which the related objective functions are: (1) minimizing transportation costs and (2) maximizing probability of delivery to customers. the second objective function which is nonlinear has performed to a linear function. since this problem is np hard to solve it we propose simulated annealing (sa) that is a well known meta heuristic algorithm. to show the performance of this algorithm we compare the related results in terms of run time and objective function values with the lower bound and lingo 8 software for different sizes of the given problem.