A Multi-Depot Dynamic Vehicle Routing Problem with Stochastic Road Capacity: An MDP Model and Dynamic Policy for Post-Decision State Rollout Algorithm in Reinforcement Learning

Abstract

In the event of a disaster, the road network is often compromised in terms of its capacity and usability conditions. This is a challenge for humanitarian operations in the context of delivering critical medical supplies. To optimise vehicle routing for such a problem, a Multi-Depot Dynamic Vehicle-Routing Problem with Stochastic Road Capacity (MDDVRPSRC) is formulated as a Markov Decision Processes (MDP) model. An Approximate Dynamic Programming (ADP) solution method is adopted where the Post-Decision State Rollout Algorithm (PDS-RA) is applied as the lookahead approach. To perform the rollout effectively for the problem, the PDS-RA is executed for all vehicles assigned for the problem. Then, at the end, a decision is made by the agent. Five types of constructive base heuristics are proposed for the PDS-RA. First, the Teach Base Insertion Heuristic (TBIH-1) is proposed to study the partial random construction approach for the non-obvious decision. The heuristic is extended by proposing TBIH-2 and TBIH-3 to show how Sequential Insertion Heuristic (SIH) (I1) as well as Clarke and Wright (CW) could be executed, respectively, in a dynamic setting as a modification to the TBIH-1. Additionally, another two heuristics: TBIH-4 and TBIH-5 (TBIH-1 with the addition of Dynamic Lookahead SIH (DLASIH) and Dynamic Lookahead CW (DLACW) respectively) are proposed to improve the on-the-go constructed decision rule (dynamic policy on the go) in the lookahead simulations. The results obtained are compared with the matheuristic approach from previous work based on PDS-RA.

Keywords

• reinforcement learning
• Markov decision processes
• approximate dynamic programming
• rollout algorithm
• constructive base heuristic
• vehicle routing problem