We present solution methodologies for vehicle routing problems (VRPs) with stochastic demand, with a specific focus on the vehicle routing problem with stochastic demand (VRPSD) and the vehicle routing problem with stochastic demand and duration limits (VRPSDL). The VRPSD and the VRPSDL are fundamental problems underlying many operational challenges in the fields of logistics and supply chain management. We model the VRPSD and the VRPSDL as large-scale Markov decision processes. We develop cyclic-order neighborhoods, a general methodology for solving a broad class of VRPs, and use this technique to obtain static, fixed route policies for the VRPSD. We develop pre-decision, post-decision, and hybrid rollout policies for approximate dynamic programming (ADP). We provide analytical results that position these policies within the rollout literature and identify conditions under which our proposed rollout methods are equivalent to the traditional form. Our rollout policies lay a methodological foundation for solving large-scale sequential decision problems and provide a framework for developing dynamic routing policies. Our dynamic rollout policies for the VRPSDL significantly improve upon benchmark fixed route policies frequently implemented in practice. We also identify circumstances in which our rollout policies appear to offer little or no benefit compared to this benchmark. These observations can guide managerial decision making regarding when the use of our procedures is justifiable. We also demonstrate that our vii TABLE OF CONTENTS LIST OF TABLES .
