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Many companies prefer to use third party logistics firms to deliver their goods and as such planning the return of the vehicles to the depot is not required. This is called open vehicle routing problem (OVRP). In literature, the OVRP is handled with minimum distance as objective function like vehicle routing problem. But in the real world, the objective function achieves minimum many costs like standard routing cost, stopping by cost and the deviation cost. The standard routes are previously defined under free market conditions by third party logistic firms. The deviation from the standard route is required to arrive cities which are not on the standard route. The stop by cost occurs on the delivery points. In this paper mentioned three costs are considered in the objective function while many papers consider only distance related costs in the literature. This paper proposes a new mathematical model for the OVRP. In the constraints, the last points of the routes are researched in detail. The standard route costs are determined by considering the last point of the route. Because of the NP-hard structure of the OVRP, the proposed mathematical model is solved with a hybrid metaheuristic called Civilized Genetic Algorithm (CGA). CGA is developed by hybridizing a modified genetic algorithm and a local search algorithm. The application of this study is implemented for the delivery routing of a combi boiler producer in Turkey. The third party logistic firms may use this proposed model and the solution approach for the real life applications. [ABSTRACT FROM AUTHOR]

In this study, stochastic vehicle routing problem (SVRP), which is one of the most important combinatorial optimization problems studied in the literature, is discussed. As it is known, the capacities of the vehicles and the demands of the customers are known in the classical vehicle routing problem, so the problem is deterministic. Since the problem parameters in real life problems vary according to the different situations, it is rare to know the exact values of the parameters. Therefore, there is a need to formulate the classical vehicle routing problem under uncertainty conditions. In this study, the vehicle routing problem is analyzed, and the demands are stochastically evaluated for the cases where customer demands are uncertain. In order to examine the variable demand conditions, the effects of these distributions on the solutions of the problem are investigated by using three different distributions, which are uniform, exponential, and Poisson. The GAMS software is used for computational results and the results of the stochastic and deterministic models of the problem are compared at the final part of the study. [ABSTRACT FROM AUTHOR]