Exploiting Graphical Optimization Models to Solve Discrete Decision Problems in Healthcare and Supply Chain Logistics

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Despite a tremendous increase in the performance of mixed integer programming (MIP) and constraint programming (CP) solvers during the past few decades, many discrete decision problems in supply chain and healthcare logistics (SCHL) remain challenging. The focus of this research program will be on the development of graphical optimization models (GOMs) to yield faster solutions for discrete decision problems in SCHL. The term “graphical model” traditionally refers to a probabilistic graphical model that expresses the conditional dependence structure between random variables. However, in the context of discrete optimization, we use the term GOM to represent a broad class of graph-based models that describe a system with states and action variables and a set of linking equations. In the literature, such GOMs are used to build dynamic programs (DP), MIP formulations with network flow components, decomposition approaches that rely on column or row generation, and global constraints in CP. The main advantage of GOMs is their increased precision in representing discrete decisions compared to methods that rely solely on continuous (linear or nonlinear) relaxations. These models, which require considerable memory to build and manipulate, are becoming increasingly useful as the availability and cost of memory improve. In this proposal, we will focus on GOMs derived from hypergraphs (HG) and decision diagrams (DDs), which have been successfully used in the context of optimization. The four main objectives of my research program are to use GOMs: 1) to build a new generation of discrete solvers; 2) to better model uncertainty in SCHL problems; 3) to support deep reinforcement learning (DRL) for combinatorial optimization; and 4) to solve industrial SCHL problems in real time. We aim to have both a methodological and a practical impact. The research will a) provide our Canadian startup partners with new tools that will allow them to compete and succeed on a global scale, and b) help our Canadian public service and healthcare partners to be more efficient in caring for the population. The 12 highly qualified personnel (HQP) that will be trained by this program are expected to join academia or industry as scientists or domain experts.