A Stochastic Programming Approach to the Antibiotics Time Machine Problem

Burak Kocuk, Sabancı University

Abstract

Antibiotics Time Machine is an important problem to understand the antibiotic resistance, an alarming global healthcare issue, and how it can be reversed. Mathematically, it can be modelled as follows: Consider a set of genotypes, each of which contain a set of mutated and unmutated genes. Suppose that a set of growth rate measurements of each genotype under a set of antibiotics are given. The transition probabilities of a ‘realization’ of a Markov chain associated with each arc under each antibiotic are computable via a predefined function given the growth rate realizations. The aim is to maximize the expected probability of reaching to the genotype with all unmutated genes given the initial genotype in a predetermined number of transitions, considering the following two sources of uncertainties: i) the randomness in growth rates, ii) the transition probabilities, which are functions of growth rates. We develop stochastic mixed-integer linear programming and dynamic programming approaches to solve static and dynamic versions of the Antibiotics Time Machine Problem under the aforementioned uncertainties. We adapt a Sample Average Approximation approach that exploits the special structure of the problem and provide accurate solutions that perform very well in an out-of-sample analysis.

Short Bio

Burak Kocuk is an assistant professor at the Industrial Engineering Program, Sabancı University. He obtained his BS degrees in Industrial Engineering and Mathematics, and MS degree in Industrial Engineering from Boğaziçi University. He obtained his PhD degree of Operations Research at the School of Industrial and Systems Engineering, Georgia Institute of Technology. Before joining Sabancı University, he was a postdoctoral fellow at the Tepper School of Business, Carnegie Mellon University. His current research focuses on mixed-integer nonlinear programming and stochastic optimization problems, from both theoretical and methodological aspects.

Venue

Friday, May 13, 2022, 4.00 pm - Zoom Meeting