The purpose of this article is to review the literature on the topic of deterministic Vehicle Routing Problem (VRP) and to give a review on the exact and approximate solution techniques. More specifically the approximate (meta-heuristic) solution techniques are classified into: tabu search, simulated annealing, genetic algorithm, evolutionary algorithm, hybrid algorithm, and Ant Colony Optimization. Each of these solution techniques is briefly discussed and a case study from the literature is presented.

One of the challenging issues in today’s competitive world for servicing companies is uncertainty in some factors or parameters that they often derive from fluctuations of market price and other reasons. With regard to this subject, it would be essential to provide robust solutions in uncertain situations. This paper addresses an open Vehicle Routing Problem with demand uncertainty and cost of Vehicle uncertainty. Bertsimas and Sim’s method has been applied to deal with uncertainty in this paper. In addition, a deterministic model of open Vehicle Routing Problem is developed to present a robust counterpart model. The deterministic and the robust model is solved by GAMS software. Then, the mean and standard deviations of obtained solutions were compared in different uncertainty levels in numerous numerical examples to investigate the performance of the developed robust model and deterministic model. The computational results show that the robust model has a better performance than the solutions obtained by the deterministic model.

This article proposes a stochastic Vehicle Routing Problem within the frame-wok of chance constrained programming where one or more parameters are presumed to be random variables with known distribution function. The reality is that once we convert some special form of probabilistic constraint into their equivalent deterministic form then a nonlinear constraint generates. Knowing that reliable computer software for large scaled complex nonlinear programming Problem with 0-1 type decision variables for stochastic Vehicle Routing Problem is not easily available merely then the value of an approximation technique becomes imperative. In this article, theorems which build a foundation for moving toward the development of an approximate methodology for solving the stochastic Vehicle Routing Problem are stated and proved. Using these theorems one can easily convert a nonlinear type Vehicle Routing Problem of special type into an equivalently designed linear Problem that can be solved fast and easy.