Resource Allocation Models in Healthcare Decision Making

Abstract

We present models for allocating limited healthcare resources efficiently among target populations in order to maximize society's welfare and/or minimize the expected costs. In general, this thesis is composed of two major parts.

Firstly, we formulate a novel uncapacitated fixed-charge location problem which considers the preferences of customers and the reliability of facilities simultaneously. A central planner selects facility locations from a set of candidate sites to minimize the total cost of opening facilities and providing service. Each customer has a strict preference order over a subset of the candidate sites, and uses her most preferred available facility. If that facility fails due to a disruptive event, the customer attends her next preferred available facility. This model bridges the gap between the location models that consider the preferences of customers and the ones that consider the reliability of facilities. It applies to many healthcare settings, such as preventive care clinics, senior centers, and disaster response centers. In such situations, patient (or customer) preferences vary significantly. Therefore, there could be a large number of subgroups within the population depending on their preferences of potential facility sites. In practice, solving problems with large numbers of population subgroups is very important to increase granularity when considering diverse preferences of several different customer types. We develop a Lagrangian branch-and-bound algorithm and a branch-and-cut algorithm. We also propose valid inequalities to tighten the LP relaxation of the model. Our numerical experiments show that the proposed solution algorithms are efficient, and can be applied to problems with extremely large numbers of customers.

Secondly, we study the allocation of colorectal cancer (CRC) screening resources among individuals in a population. CRC can be early-detected, and even prevented, by undergoing periodic cancer screenings via colonoscopy. Current guidelines are based on existing medical evidence, and do not explicitly consider (i) all possible alternative screening policies, and (ii) the effect of limited capacity of colonoscopy screening on the economic feasibility of the screening program. We consider the problem of allocating limited colonoscopy capacity for CRC screening and surveillance to a population composed of patients of different risk groups based on risk factors including age, CRC history, etc. We develop a mixed integer program that maximizes the quality-adjusted life years for a given patient population considering the population's demographics, CRC progression dynamics, and relevant constraints on the system capacity and the screening program effectiveness. We show that the current guidelines are not always optimal. In general, when screening capacity is high, the optimal screening programs recommend higher screening rates than the current guidelines, and the optimal screening policies change with age and gender. This shows the significance of incorporating screening capacity into the decisions of optimal screening policies.