Balanced dynamic multiple travelling salesmen: algorithms and continuous approximations

TL;DR

This paper introduces heuristics and continuous models for the balanced dynamic multiple travelling salesmen problem, addressing real-time routing challenges with applications in taxi services and warehouse logistics.

Contribution

It proposes two new heuristics for dynamic routing and derives continuous approximation models as strategic tools, incorporating machine learning for predictive accuracy.

Findings

Heuristics effectively solve real-world dynamic routing scenarios.

Continuous models accurately approximate route lengths without running algorithms.

Machine learning models achieve below 3% mean absolute percentage error.

Abstract

Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are applied to a wide range of test instances. Taxi services and palette transfers in warehouses demonstrate how to use the BD-mTSP algorithms in real-world scenarios. Continuous approximation models for the BD-mTSP's are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers, and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean absolute percentage error of two of these models is below 3%.