Title: On the Misclassification Cost Problem and Dynamic Resource Allocation Models for EMS
Description: The first chapter of this thesis is centered around a simple problem: to do or not to do something. As in life, every decision has an unknown outcome and planning agents try to balance the trade offs of such decision based on some relevant information. After processing the relevant information a decision is reached. In this chapter, the problem is formalized and parameterized in two frameworks: In the first framework discrete decision models known as decision trees are studied, where we design an optimization algorithm to solve the misclassification cost problem in this family of representations; The second framework studies continuously differentiable models (such as logistic regression and Deep Neural Networks) where we propose a two-step optimization procedure of the misclassification cost problem, as well as characterizing the statistical estimation problem relative to the sample size used for training. We illustrate the methodology by developing a computerized scheme to administer (or not) a preventive intervention to patients arriving to the hospital with the objective of minimizing their risk of acquiring a Hospital Acquired Infection (HAI).

The second chapter expands on the idea of the first one to a sequential setting. The problem is framed as a Markov Decision Process algorithm using a state aggregation strategy based on Decision Trees. These incremental state aggregations are solved using a Linear Programming (LP) approach to obtain a compact policy that converges to the optimal one asymptotically, as well as showing that the computational complexity of our algorithm depends on the tree structure of the optimal policy rather than the cardinality of the state space. We illustrate the advantages of our approach using the widely known cartpole balancing environment against a Deep Neural Network based approach showing that with a similar computational complexity our algorithm performs better in certain instances of MDP. In the last two chapters we deal with modeling Emergency Medical Service (EMS) optimization such that the demand for medical services is met with the best possible supply allocation in the face of uncertainty of the demand in space and time.

In the third chapter we develop a short-term prediction model for call volume at a 911 call center. The rationale of the model is to use the recent call volume to update a historically calibrated model of the call volume that in periods when the call volume distribution drastically changes, can be arbitrarily distant from its expected value. The model is casted as a linear correction of the historical estimation, calculating both the mean and variance of the correction. We justify the formulation using a regime switching doubly stochastic process framework to illustrate the type of distribution changes our model captures. We also propose a staffing model to preemptively staff a call center using our volume prediction as input for the call center demand such that the waiting times of the customers are minimized. This formulation can be casted as a Second Order Cone Program (SOCP) or a Linear Program (LP) with integrality constraints. We illustrate the methodology to predict the call volume during the Covid-19 pandemic to a 911 call center in New York City.

In the fourth chapter we modify a well known set covering formulation to perform ambulance scheduling such that the supply of ambulances matches the demand in space and time. We enhance this model using a high resolution simulation model to correct an unknown steady-state service rate of the system (dependent on many exogenous and endogenous factors such as the ambulance dispatch policy and time-varying traffic patterns) as a constraint in the scheduling formulation. We show that this formulation effectively makes the system faster by maximizing the minimum slack between supply and demand during a 24-hour period. We present an algorithm to iteratively solve the scheduling formulation while correcting the implied location and time dependent service rate of the ambulance system using the simulation generated ambulance waiting times of patients in the city. We illustrate our algorithm to schedule municipally managed ambulances in New York City as a case study.