A rollout algorithm framework for heuristic solutions to finite-horizon stochastic dynamic programs

Same‐day delivery with heterogeneous fleets of drones and vehicles

“…RAs use heuristic policies to approximate the cost‐to‐go in a Bellman equation. For an overview of RAs, the interested reader is referred to Goodson et al . Here and in the remainder of the section, we focus our analysis only on results from instances using the generated geography.…”

Consolidation & coordination in urban freight transport

“…The idea behind π roll is that we generate a number of sample arrival paths and heuristically solve the decision problems for these paths, thereby obtaining an estimate for the downstream costs. This benchmark policy is comparable to the rollout procedures as presented in, e.g., Goodson et al (2013) and Goodson et al (2017). More precisely, our benchmark policy may be viewed as a version of the postdecision rollout that is described in Goodson et al (2017), in which we look ahead for multiple time steps.…”

“…This benchmark policy is comparable to the rollout procedures as presented in, e.g., Goodson et al (2013) and Goodson et al (2017). More precisely, our benchmark policy may be viewed as a version of the postdecision rollout that is described in Goodson et al (2017), in which we look ahead for multiple time steps. To apply π roll at a given decision moment, we first generate a set Ω m , which contains m random arrival paths of length τ roll , i.e., ω m = {ω m t+1 , ... , ω m t+τ roll }.…”

“…However, these instances do not capture all the dynamics embedded in the problem, whereas medium-sized instances cannot be solved exactly. To evaluate the online performance of ADP, we compare with three consolidation policies without lookahead, as well as a rollout policy that incorporates a downstream cost estimate based on randomly generated future orders (Goodson et al, 2017). Under the first myopic policy π direct , we always ship orders as soon as possible, as long as primary vehicle capacity is available.…”

Multi-period dynamic technician routing and scheduling problems with experience-based service times and stochastic customers

“…First, by not considering the cost-to-go in the Bellman equation, we solve a daily routing problem that is a deterministic problem. Second, in the fashion of rolling horizon or rollout methods (for discussion, see (Goodson et al, 2015)), rather than solving for every state as is necessary in traditional backward dynamic programming, we can step forward in time and solve for only the observed demand realizations. A sketch of our solution approach can be found in Algorithm 2.1.…”