Antibiotic resistance, an alarming health care issue, can be “reversed” if a set of antibiotics are applied in the “right” order (hence, the name “antibiotics time machines”). To be more precise, suppose we have a population of bacteria and for each bacterium of a given genotype, an antibiotic alters it to another type with some probability. Our aim is to apply a set of antibiotics (K in number) with a specified precedence (in N steps) so as to maximize the fraction of bacteria (with d number of distinct genotypes) becoming a certain type. We will assume that intermediary observations regarding the effect of antibiotics are observable at some certain (but not all) decision points. Instead of the straightforward and computationally expensive approach of enumeration, we propose to use a multi-stage stochastic mixed-integer program and dynamic programming to model and solve this challenging problem.
Junior IE students with a strong background in operations research (IE 312 is required) and computing will be preferred.