Dynamic Pickup and Delivery with Transfers

In the dynamic Pickup and Delivery Problem with Transfers (dPDPT), a set of transportation requests that arrive at arbitrary times must be assigned to a fleet of vehicles. We use two cost metrics that capture both the company’s and the customer’s viewpoints regarding the quality of an assignment. In most related problems, the rule of thumb is to apply a two-phase local search algorithm to heuristically determine a good requests-to-vehicles assignment. This work proposes a novel solution based on a graph-based formulation of the problem that treats each request independently. Briefly, in this conceptual graph, the goal is to find a shortest path from a node representing the pickup location to that of the delivery location. However, we show that efficient Bellman-Ford or Dijkstra-like algorithms cannot be applied. Still, our method is able to find dPDPT solutions significantly faster than a conventional two-phase local search algorithm, while the cost of the solution is only marginally increased.