Pickup and delivery problem with hard time windows considering stochastic and time-dependent travel times

Due to the uncertain nature of the traffic system, it is not trivial for delivery companies to reliably satisfy customers' time windows. To guarantee the reliability of the pickup and delivery service under stochastic and time-dependent travel times, we consider a pickup and delivery problem with hard time windows considering stochastic and time-dependent travel times. We propose a chance-constrained model where the operational cost and the service's reliability are considered. To quantify the service reliability, every node is associated with a desired node service level, and there exists a global service level, both measured by success probabilities. We present an estimation method for arrival times and success probabilities under stochastic travel and service times. We propose an exact solution approach based on a branch-price-and-cut framework, where a labeling algorithm generates columns. Computational experiments are conducted to assess the effectiveness of the solution framework, and Monte Carlo simulations are used to show that the proposed method can generate routes that satisfy both node and global service levels.