Symmetric Policy Design for Multi-Agent Dispatch Coordination in Supply Chains

TL;DR

Coordinating dispatches among $N$ warehouses that share a limited resource is prone to collisions or idle slots without coordination. The paper proposes a symmetric, decentralized control framework based on a common-information dynamic programming (DP) approach, with a central coordinator issuing prescriptions and agents updating beliefs about others’ urgency. It formalizes a symmetric team decision problem, derives an optimal symmetric policy through DP, and demonstrates substantial performance gains over belief-based heuristics and always-dispatch baselines across multiple load scenarios. The approach offers scalable, fair coordination for shared-capacity supply chains and lays groundwork for extensions to larger networks, evolving urgencies, and heterogeneous resources.

Abstract

We study a decentralized dispatch coordination problem in a multi-agent supply chain setting with shared logistics capacity. We propose symmetric (identical) dispatch strategies for all agents, enabling efficient coordination without centralized control. Using a common information approach, we derive a dynamic programming solution that computes optimal symmetric dispatch strategies by transforming the multi-agent problem into a tractable dynamic program on the agents common information state. Simulation results demonstrate that our method significantly reduces coordination cost compared to baseline heuristics, including belief-based strategies and an always-dispatch policy. These findings highlight the benefits of combining symmetric strategy design with a common information-based dynamic programming framework for improving multi-agent coordination performance.

Figures (3)

• Figure 1: Optimal symmetric dispatch policy probabilities as a function of agent urgency and the belief that other agents are high urgency. The color represents the probability of dispatching under the optimal policy (yellow = 1.0, dark blue = 0.0). High-urgency agents dispatch more often when they believe others are unlikely to dispatch (left side), but reduce probability as their belief in others' high urgency increases (right side). Low-urgency agents are less likely to dispatch if they believe another agent is certainly high urgency (right side), but will dispatch with moderate probability when they suspect others will not dispatch (left side).
• Figure 2: Belief evolution for Agent A about Agent B's urgency in two scenarios. In Scenario A (yellow), a collision at $t=1$ (both dispatched) makes A's belief that B is High rise to 1.0 by $t=2$. In Scenario B (red), an idle slot at $t=1$ causes A’s belief in B being High to drop near 0, but a successful dispatch at $t=2$ slightly raises it.
• Figure 3: Cumulative dispatch coordination cost (lower is better) under different strategies across load scenarios. Light Load: most slots have no urgent agents. Moderate Load: roughly one urgent agent at a time. Heavy Load: often multiple urgent agents competing. The optimal symmetric strategy achieves the lowest cost in all scenarios. The threshold-based heuristic improves over a naive “always dispatch” strategy, but still incurs higher costs (more collisions in heavy load, more idle in light load) compared to the proposed method.