The Traveling Salesman Problem with Pickup and Delivery (TSPPD) describes the problem of finding a minimum cost path in which pickups precede their associated deliveries. The TSPPD is particularly important in the growing field of Dynamic Pickup and Delivery Problems (DPDP). These include the many-to-many Dial-A-Ride Problems (DARP) of companies such as Uber and Lyft, and the Meal Delivery Routing Problem (MDRP) of Grubhub. We examine exact methods for solving TSPPDs where orders from different pickup locations can be carried simultaneously. Our interest lies in solving such problems for real-time applications, in which finding high quality solutions quickly (often in less than a second) is more important that proving the optimality of such solutions.
We begin by considering enumeration, Constraint Programming (CP) with and without Assignment Problem (AP) inference duals, Mixed Integer Programming (MIP), and hybrid methods combining CP and MIP. Our CP formulations examine multiple techniques for ensuring pickup and delivery precedence relationships. We then propose a new MIP formulation for the Asymmetric Traveling Salesman Problem with Pickup and Delivery, along with valid inequalities for the Sarin-Sherali-Bhootra formulation. We study these models in their complete forms, relax complicating constraints of these models, and compare their performance. Finally, we examine the use of low-width Multivalued Decision Diagrams (MDDs) in a branch-and-bound with and without AP inference duals as a primal heuristic for finding high quality solutions to TSPPDs within strict time budgets.
In our results and conclusions, we attempt to provide guidance about which of these methods may be most appropriate for fast TSPPD solving given various time budgets and problem sizes. We present computational results showing the promise of our new MIP formulations when applied to pickup and delivery problems. Finally, we show that hybridized low-width MDDs can be more effective than similarly structured hybrid CP techniques for real-time combinatorial decision making.
|Commitee:||Brodsky, Alexander, Sofer, Ariela, Xu, Jie|
|School:||George Mason University|
|Department:||Systems Engineering and Operations Research|
|School Location:||United States -- Virginia|
|Source:||DAI-B 80/07/(E), Dissertation Abstracts International|
|Subjects:||Operations research, Computer science|
|Keywords:||Decision diagrams, Hybrid optimization, Pickup and delivery, Real-time optimization, Traveling salesman problem|
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