Probabilistic Traveling Salesman Problem with Deadlines

Time-constrained deliveries are one of the fastest growing segments of the delivery business, and yet, there is surprisingly little literature that addresses time constraints in the context of stochastic customer presence. We begin to fill that void by introducing the probabilistic traveling salesman problem with deadlines (PTSPD). The PTSPD is an extension of the well-known probabilistic traveling salesman problem in which, in addition to stochastic presence, customers must also be visited before a known deadline. We present two recourse models and a chance constrained model for the PTSPD. Special cases are discussed for each model, and computational experiments are used to illustrate under what conditions stochastic and deterministic models lead to different solutions.