Open Vehicle Routing Problem with Robust Optimization Approach

Abstract

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.