Solving reverse logistics vehicle routing problems with time windows

A vehicle routing problem with simultaneous pick-up and delivery in closed-loop logistics network optimization is studied in this paper. Since, in practice, material pick-up and delivery are only allowed to take place on certain time periods, we consider the reverse logistics vehicle routing problem with time windows. A mixed integer programming model is proposed to formulate the considered problem. A heuristic solution approach for solving the model is developed due to the NP-hard nature of solving the model. The heuristic solution is then used as an initial solution of a simulated annealing procedure for improved solutions. The proposed heuristic method and the simulated annealing procedure yield very promising solutions in much less computational time when compared with optimal solutions generated by exact solution procedures. Numerical examples are presented to illustrate the developed model and solution methods.