The data-driven time-dependent traveling salesperson problem

In this paper, we study a single-vehicle routing problem with stochastic service times, stochastic time-dependent travel times, and soft time windows, where the travel times may be interdependent. The objective is to minimize the expected route duration plus penalties for late arrivals. The stochasticity is modeled using a set of scenarios based on historical data. This approach enables the spatial and temporal interdependencies in the road network to be captured. We introduce a specialized branch-and-bound algorithm and a successful adaptive large neighborhood search heuristic for the problem. In a numerical experiment based on real historical travel time data, we demonstrate the applicability of both methods to problem instances of up to 40 customers and 40 scenarios. These dimensions are safe upper bounds for instances originating from the field service operation domain. The resulting routes are tested on realistic scenarios that were not included in the problem input (the training set) to demonstrate the merits of using historical data. Compared with solutions that ignore the time dependency and/or stochasticity of the parameters, our solutions are consistently superior.