Dynamic programming approaches for the traveling salesman problem with drone

TLDR

The emerging truck‑drone delivery model introduces the traveling salesman problem with drone (TSP‑D), a new planning challenge. The paper aims to develop exact solution approaches for the TSP‑D using dynamic programming and to compare these methods experimentally. The authors employ dynamic programming techniques to formulate exact solutions for the TSP‑D and conduct experimental comparisons of these methods. Experiments demonstrate that the dynamic programming approaches solve larger TSP‑D instances than prior mathematical programming methods, and that limiting truck visits during drone operations markedly reduces solution times with minimal loss in solution quality.

Abstract

Abstract A promising new delivery model involves the use of a delivery truck that collaborates with a drone to make deliveries. Effectively combining a truck and a drone gives rise to a new planning problem that is known as the traveling salesman problem with drone (TSP‐D). This paper presents exact solution approaches for the TSP‐D based on dynamic programming and provides an experimental comparison of these approaches. Our numerical experiments show that our approach can solve larger problems than the mathematical programming approaches that have been presented in the literature thus far. Moreover, we show that restrictions on the number of locations the truck can visit while the drone is away can help significantly reduce the solution times while having relatively little impact on the overall solution quality.