Title: Allocating Resources to People with Preferences

Thesis advisor: Dr. Julie Swann

Committee members:

Dr. Ozlem Ergun (Mechanical & Industrial Engineering, Northeastern University)

Dr. Pinar Keskinocak

Dr. John Vande Vate

Dr. Santosh Vempala (School of Computer Science)

Date and Time: June 20th (Tuesday), 2017, at 11:00 AM

Location: Groseclose Room 226A

Summary:

Resource allocation can be viewed as the assignment of available resources to different people or tasks. Usually, resources can be allocated by markets (where people exchange goods or services based on price) or by central planning (a central planner or agency makes the decision). In many industrial applications such as assembling automobiles from parts or assigning time-constrained tasks to processors, central planning can often yield the optimal result with respect to the entire system. However, in other settings such as allocating healthcare services to patients, distributing vaccines to local providers, or assigning jobs to workers, preferences of the individuals are to be considered besides the welfare of the entire system.

Three practical and theoretical problems are presented that involve allocating resources to individuals with preferences or different needs:

1) using decentralized optimization to measure the access of patients to healthcare providers,

2) using agent-based simulation to quantify the benefit of allocating vaccines to local areas based on inventory information, and

3) designing heuristics and algorithms to analyze matching staff to jobs in a multi-period setting when both staff and jobs list preferences over members of the other group.

We use mathematical modeling approaches to analyze the three problems, in which choices of people are incorporated either using notions of equilibria and stability or in the design of the allocation policy.

The first part of this thesis presents an optimization framework for measuring healthcare spatial access, where we analytically demonstrate the advantages of using optimization approaches to quantify access to service providers and illustrate these advantages via a case study. The second part of this thesis addresses the value of inventory information in distributing vaccines in a flu pandemic, where we find that using policies that utilize inventory information of vaccine can improve the percentage of demand satisfied, reduce the disease incidence, and decrease inventory of wasted vaccine. The third part of this thesis introduces modeling for stable matching between workers and jobs in a multi-period setting, where we discuss new notions of stability and model the problem using integer programming with the preferences of people either staying the same or changing over time.  We obtain theoretical bounds on the objective function value, show that the problem is NP-hard under special preference lists, and develop heuristics to solve the problem with large number of workers and jobs and small number of periods. We provide insights on the sufficient and necessary conditions under which our algorithms and heuristics work well.