On the optimization of pit stop strategies via dynamic programming

Pit stops are a key element of racing strategy in several motor sports. Typically, these stops involve decisions such as in which laps to stop, and which type of tire, of three possible compounds, to set at each of these stops. There are several factors that increase the complexity of the task: the impact of lap times depending on the tire compound, the wear of the tires, unexpected events on the track such as safety cars and the weather, among others. This work presents a Dynamic Programming formulation that addresses the pit-stop strategy problem in order to optimize the laps in which to stop, and the tire changes that minimize the total race time. We show the relative performance of the optimal strategies for starting with tires of different compounds with different yellow-flag scenarios. Then, we extend the Dynamic Program (DP) to a Stochastic Dynamic Programming (SDP) formulation that incorporates random events such as yellow flags or rainy weather. We are able to visualize and compare these optimal pit-stop strategies obtained with these models in different scenarios. We show that the SDP solution, compared to the DP solution, tends to delay pit stops in order to benefit from a possible yellow flag. Finally, we show that the SDP outperforms the DP, especially in races in which yellow flags are likely to be waved more frequently.