Rollout Policies for Dynamic Solutions to the Multivehicle Routing Problem with Stochastic Demand and Duration Limits

Abstract

We develop a family of rollout policies based on fixed routes to obtain dynamic solutions to the vehicle routing problem with stochastic demand and duration limits (VRPSDL). In addition to a traditional one-step rollout policy, we leverage the notions of the pre-and post-decision state to distinguish two additional rollout variants. We tailor our rollout policies by developing a dynamic decomposition scheme that achieves high quality solutions to large problem instances with reasonable computational effort. Computational experiments demonstrate that our rollout policies improve upon the performance of a rolling horizon procedure and commonly employed fixed-route policies, with improvement over the latter being more substantial.

A priori policy evaluation and cyclic-order-based simulated annealing for the multi-compartment vehicle routing problem with stochastic demands

“…The procedures of Section 4 build on Appendix A of Goodson et al (2013), which develops a priori policy evaluation methods for a single-compartment VRPSD with route duration constraints where the objective is to maximize expected demand served. We extend the methods of Goodson et al (2013) to the multi-compartment case and to the objective of minimizing expected route costs.…”

“…The method we propose to calculate the exact expected cost of an a priori MCVRPSD policy builds on Goodson, Ohlmann, and Thomas (2013) and applies to problem instances where customer demands follow discrete probability distributions with finite support. The method requires exponential time to execute and is not practical for use in optimization procedures.…”

An Adaptive Memory Programming Framework for the Robust Capacitated Vehicle Routing Problem

“…Problems with stochastic travel times are studied in Kenyon and Morton (2003), while Adelman (2004) and Kleywegt et al (2004) combine the vehicle routing problem with aspects of stochastic inventory control. Bent and Hentenryck (2004), Goodson et al (2013), Hvattum et al (2006) and Smith et al (2010) study dynamic problems where customer requests arrive over time and the very presence of customers is subject to uncertainty. For reviews of the stochastic vehicle routing literature, we refer to Cordeau et al (2007), Gendreau et al (1996) and Toth and Vigo (2002).…”

Variable neighborhood search for the stochastic and dynamic vehicle routing problem

“…A DVRP with stochastic customers and time windows (VRPTW) has been solved (Bent and Hentenryck 2004), and a real world case study suggests the need to extend the VRPTW to deal with dynamic and stochastic customer information (Hvattum et al 2006). More recently, and in the field of approximate dynamic programming (ADP), methods to dynamically modify the routing plan have been proposed for the VRPSD with route duration constraints (Goodson et al 2013). Also in the field of ADP, a DVRP that aims at maximizing the number of accepted customers was solved by modeling customer locations as random variables (Ulmer et al 2013).…”