A hybrid method for solving multi-depot VRP with simultaneous pickup and delivery incorporated with Weber basis saving heuristic

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Under growing concerns with sustainability in global and changing market, establishing a cooperative and competitive logistic is becoming a keen issue to provide manufacturing systems amenable to sales and operations planning. As a deployment for such practice, we have engaged in the various studies on logistics optimization. Especially, noticing that transportation cost and/or CO2 emission actually depend not only on distance but also loading weight (Weber basis), we have recently developed a few hybrid meta-heuristic methods for vehicle routing problems (VRP) and shown their effectiveness through numerical experiments. To the best of our knowledge, however, there exist no studies that take the Weber basis into account on VRP except for ours. As a hot interest in this area, we pay our attention on VRP with simultaneous pickup and delivery (VRPSPD). Then, this study attempts to extend the foregoing Weber basis study under single depot to multi-depot problem and intends to reveal some properties of VRPSPD. To work with such concerns, we have developed a novel hierarchical method comprised of a modified tabu search, a graph algorithm for the minimum cost flow problem and a Weber basis saving method. The proposed method is possible to solve various real world applications practically even with large problem sizes. Finally, the effectiveness of the proposed method is validated through numerical experiments taken place from various viewpoints to discuss about some peculiar features of VRPSPD.

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