Assessing Customer Service Reliability in Route Planning with Self-Imposed Time Windows and Stochastic Travel Times

Abstract

This paper presents mathematical models and solution methods for assigning time windows to customers in vehicle routing problems with stochastic travel times. The goal is to design minimum-cost routes in terms of traveling distance and to simultaneously minimize the expected penalty costs associated with the assignment of time windows. Focus is given on how to evaluate the flexibility of time windows and to incorporate service reliability into the routing plans. Two mathematical models are proposed for the stochastic time window assignment problem that treat the travel times as continuous and discrete random variables, and take into account lateness and earliness penalties, penalties for the time window widths, and chance constraints to model the probability of serving each customer within the assigned time window so as to meet service reliability requirements. A hierarchical solution approach is proposed. At the first level, the master vehicle routing problem is solved via an adaptive large neighborhood search metaheuristic to optimize the routing cost, while at the second level the subordinate time window assignment subproblems are solved optimally. Various computational experiments are conducted to assess the performance of the proposed algorithmic framework, to understand time window flexibility, to study the trade-off between service reliability and routing costs, and to demonstrate the effectiveness and applicability of optimal time window assignment policies in an urban transportation environment with uncertain travel times.