Supporting Document for (revised)
Solving Reverse Logistics Vehicle Routing Problems with Time Windows
Sally Kassem and Mingyuan Chen
(presented in the Cover Letter in submitting the first version of the same paper)
In this paper, the vehicle routing problems with simultaneous pickup and delivery and time windows are studied. Research work shown in the literature in this area is limited. In addition, the problem presented in this paper differs from others in several key aspects. The assumptions and constraints considered in solving our problem are more practical and realistic. The considered problem was formulated as a mixed integer linear programming model. A new heuristic method was developed to solve thevehicle routing problem and tested by a substantial number of testing instances of various problem sizes. These testing instances are adopted from benchmark problems from the literature. Results of the developed heuristic method are very promising and encouraging. In addition, we used a simulated annealing approach to further improve the quality of the solutions obtained by the proposed heuristic. To our knowledge, this paper is the first work to use simulated annealing to solve vehicle routing problems with simultaneous pickup and delivery and time windows. The results show that the proposed solution approach combined with simulated annealing search was able to reach optimal solutions, with much less computational time, for all the tested problems of which optimal solutions were verified by exact optimization. In todays manufacturing practice, many manufacturers are required or consider taking back their end-of-life products in addition to the distribution of their new products. The study presented in this paper has strong potential of applications for such manufacturing companies as it focuses on simultaneous forward and reverse logistics with consideration of many practical aspects. The likely industries to benefit from this work are manufacturing and distribution companies specializing in food processing, electronics, compliances, photocopying equipment, to name a few.