A flexible scheme for the bi-directional logistics

As the reverse logistics and the closed-loop supply chain networks have been adopted by enterprises, the bi-directional logistics have also drawn much attention in the literature in the past two decades. Three current main schemes of the bi-directional logistics had shortages and shortcomings. Therefore, a new scheme named the flexible delivery and pickup problem with time windows is addressed in this study. It conquers those shortages and shortcomings and remains good application properties of the three former schemes. The problem is then formulated into a mixed binary integer programming model. Since it is NP-hard, a coevolutionary genetic algorithm is proposed to get near optimal solutions of the problem. The computational results show that the developed method can provide better solutions in a comparatively shorter time.