Today’s leaders are increasingly aware that monolithic organizations are slow to adapt to the rapidly changing needs and perspectives of their constituencies or customers. Systems of systems are an alternative paradigm, where independent and frequently specialized subsidiaries are enabled to act autonomously while operating in an interconnected context. A logistics network where last mile delivery is handled autonomously. A supply network that eschews traditional depots for wide distribution of resources. A crisis response where evacuation, supply, and treatment are handled in tandem by modular and specialized units. These new paradigms require new mathematical modeling tools for planning and analysis.
For instance, the distribution of supplies through a logistics network is frequently modeled so that the capabilities of the network can be assessed linearly. However, if the units that comprise the network can operate autonomously and negotiate when and where they will interact with each other, linear flow becomes coupled with non-linear variation in the parameters that describe the network. Likewise, if new capabilities or interactions are realized amongst disparate units, the underlying structure of the network itself will change.
GDA brings together world-class expertise in a variety of mathematical optimization and modeling domains to address new problems where no single perspective is sufficient to capture the problem’s full complexity. We have integrated tools in linear programming, non-linear optimization, and network exploration to provide planning capabilities that seek resilient and efficient configurations of assets.
GDA brings expertise in algebraic topology to bear in modeling complicated scheduling problems. GDA’s shape analytics tools and mathematical expertise can help questions such as:
- How can effort be committed to de-risk failures?
- How can uncertainty be incorporated into models to create resilient plans?
- How can plans be minimally perturbed during execution to meet unforeseen needs?
GDA was presented with a highly integrated medical logistics problem, asking how specialized assets could respond to a multi-faceted crisis that included the treatment and evacuation of patients along with supply of perishable resources. We utilized linear programming, network theory, and nonlinear optimization to configure plausible plans that accounted for bidirectional resource flow, in situ patient treatment, modular and emergent asset capabilities, the positioning of fixed platforms, and time constraints on patient evacuation and resource delivery. We then used these plans to bootstrap reinforcement learning of policies that could effectively respond to uncertainty in a modeled dynamic environment.
Our methodology incorporated an extremely flexible API based on context free grammars that enabled our customer to specify, in a well-structured manner, asset capabilities and how those capabilities compose as assets interact.