Dynamic and robust network resource allocation

Abstract

Networks are essential modeling tools in engineering, business, and public policy research. They can represent physical connections, such as manufacturing processes. They can be relationships among people, such as patient treatment in healthcare. They can also represent abstract interactions, such as the biological reaction between a certain vaccine and a certain virus. In this work, we bring several seemingly disparate problems under the same modeling framework, and show their thematic coherence via the angle of dynamic optimization on networks. Our research problems are drawn from business risk management, public health security, and public policy on vaccine selection. A common theme is the integrative design of (1) strategic resource placement on a network, and (2) operational deployment of such resources. We outline the research questions, challenges, and contributions as follows.

Modern automotive manufacturing networks are complex and global, comprising tens of thousands of parts and thousands of plants and suppliers. Such interconnection leaves the network vulnerable to disruptive events. A good risk mitigation decision support system should be data-driven, interpretable, and computational efficient. We devise such a tool via a linear optimization model, and integrate the model into the native information technology system at Ford Motor Company. In public security, policymakers face decisions regarding the placement of medical resources and training of healthcare personnel, to minimize the social and economic impact of potential large scale bio-terrorism attacks. Such decisions have to integrate the strategic positioning of medical inventories, understanding of adversary's behavior, and operational decisions that involve the deployment and dispensing of medicines.

We formulate a dynamic robust optimization model that addresses this decision question, apply a tractable solution heuristic, and prove theoretical guarantees of the heuristic's performance. Our model is calibrated with publicly available data to generate insights on how the policymakers should balance investment between medical inventory and personnel training. The World Health Organization and regional public health authorities decide on the influenza (flu) vaccine type ahead of flu season every year. Vaccine effectiveness has been limited by the long lead time of vaccine production - during the production period, flu viruses may evolve and vaccines may become less effective. New vaccine technologies, with much shorter production lead times, have gone through clinical trials in recent years. We analyze the question of optimal vaccine selection under both fast and slow production technologies. We formulate the problem as a dynamic distributionally robust optimization model.

Exploiting the network structure and using tools from discrete convex analysis, we prove some structural properties, which leads to informative comparative statics and tractable solution methods. With publicly available data, we quantify the societal benefit of current and future vaccine production technologies. We also explore the reduction in disease burden if WHO expand vaccine portfolio to include more than one vaccine strain per virus subtype. In each of the applications, our main contributions are four-fold. First, we develop mathematical models that capture the decision process. Second, we provide computational technology that can efficiently process these models and generate solutions. Third, we develop theoretical tools that guarantee the performance of these computational technology. Last, we calibrate our models with real data to generate quantitative and implementable insights.