ABSTRACT
Abstract Vaccination against infectious disease has been hailed as one of the great public health achievements of the twentieth century. However, the United States Recommended Childhood Immunization Schedule
is becoming increasingly complex, often requiring numerous separate injections to be administered during a single well-baby office visit. To address the issue of vaccine delivery complexity, vaccine manufacturers have developed combination vaccines that immunize against several diseases with a single injection. These combination vaccines are creating new challenges, such as how these vaccines should be administered to ensure that immunity is safely achieved. Furthermore, these vaccines are also creating a combinatorial explosion of alternatives and choices for public health policy-makers and administrators, pediatricians, and parents/guardians. This chapter presents two discrete optimization models that illuminate these alternatives and choices by selecting a vaccine formulary that minimizes the cost of fully immunizing a child and that limits the amount of extraimmunization (i.e., extra doses of vaccine) for any given childhood immunization schedule. The cost of vaccinating a child contributes to the underimmunization of children, and extraimmunization poses biological risks, amplifies philosophical concerns with vaccination, and creates an unnecessary economic burden on society. This chapter also discusses the computational complexity of these models, presents several optimization algorithms-both exact and heuristic-for solving these models, and provides a computational comparison of these algorithms using the 2006 Recommended Childhood Immunization Schedule as well as several randomly generated childhood immunization schedules that may be representative of future childhood immunization schedules.
