A shortest path algorithm for the departure time and speed optimization problem

We present a shortest-path algorithm for the departure time and speed optimization problem under traffic congestion. The objective of the problem is to determine an optimal schedule for a vehicle visiting a fixed sequence of customer locations to minimize a total cost function encompassing emissions cost and labor cost.We account for the presence of traffic congestion, which limits the vehicle speed during peak hours.We show how to cast this problem as a shortest-path problem by exploiting some structural results of the optimal solution. We illustrate the solution method and discuss some properties of the problem.