Edward C. Sewell

An integer programming model for vaccine procurement and delivery for childhood immunization: a pilot study.

The National Immunization Program of the Centers for Disease Control and Prevention has identified several challenges that must be faced in childhood immunization programs to deliver and procure vaccines to protect against the common preventable diseases. The biomedical challenge is how to combine and formulate products to take advantage of new vaccines without requiring additional injections. A programmatic challenge is to incorporate them into already crowded immunization schedules. The economic challenge is to make wise procurement choices from among a growing number of competing products. This paper reports the results of a pilot study using operations research methodologies to address the third of these challenges. The pilot is an integer programming model for procuring vaccines for a set of childhood diseases. The model is studied under various scenarios (minimum total cost, next lowest total cost, maximum total cost, minimum total cost with all manufacturers represented). The results of this pilot study demonstrate how a practical set of operations research tools can be developed to guide vaccine selection and procurement, which might stimulate the development of innovations in new vaccines to meet the challenges of disease control through immunization.

A Branch, Bound, and Remember Algorithm for the Simple Assembly Line Balancing Problem

We present a new exact algorithm for the assembly line balancing problem. The algorithm finds and verifies the optimal solution for every problem in the combined benchmarks of Hoffmann, Talbot, and Scholl in less than one-half second per problem, on average, including one problem that has remained open for over 10 years. The previous best-known algorithm is able to solve 257 of the 269 benchmarks. The new algorithm is based on a branch-and-bound method that uses memory to eliminate redundant subproblems.

A Branch and Bound Algorithm for the Stability Number of a Sparse Graph

We present a branch and bound algorithm for finding a maximum stable set in a graph. The algorithm uses properties of the stable set polytope to construct strong upper bounds. Specifically, it uses cliques, odd cycles, and a maximum matching on the remaining nodes. The cliques are generated via standard coloring heuristics, and the odd cycles are generated from blossoms found by a matching algorithm. We report computational experience on two classes of randomly generated graphs and on the DIMACS Challenge Benchmark graphs. These experiments indicate that the algorithm is quite effective, particularly for sparse graphs.

An application of the branch, bound, and remember algorithm to a new simple assembly line balancing dataset

The simple assembly line balancing problem (SALBP) is a well-studied NP-complete problem for which a new problem database of generated instances was published in 2013. This paper describes the application of a branch, bound, and remember (BB&R) algorithm using the cyclic best-first search strategy to this new database to produce provably exact solutions for 86% of the unsolved problems in this database. A new backtracking rule to save memory is employed to allow the BB&R algorithm to solve many of the largest problems in the database.

Using an Integer Programming Model to Determine the Price of Combination Vaccines for Childhood Immunization

The Recommended Childhood Immunization Schedule has become sufficiently crowded that the prospect of adding additional vaccines to this schedule may not be well received by either health-care providers or parents/guardians. This has encouraged vaccine manufacturers to develop combination vaccines that can permit new vaccines to be added to the schedule without requiring children to be exposed to an unacceptable number of injections during a single clinic visit. This paper develops an integer programming model to assess the economic premium that exists in having combination vaccines available. The results of this study suggest that combination vaccines provide a cost effective alternative to individual vaccines and that further developments and innovations in this area by vaccine manufacturers can provide significant economic and societal benefits.

Using Monte Carlo Simulation to Determine Combination Vaccine Price Distributions for Childhood Diseases

The Recommended Childhood Immunization Schedule provides guidelines that allow pediatricians to administer childhood vaccines in an efficient and effective manner. Research by vaccine manufacturers has resulted in the development of new vaccines that protect against a growing number of diseases. This has created a dilemma for how to insert such new vaccines into an already crowded immunization schedule, and prompted vaccine manufacturers to develop vaccine products that combine several individual vaccines into a single injection. Such combination vaccines permit new vaccines to be inserted into the immunization schedule without requiring children to be exposed to an unacceptable number of injections during a single clinic visit. Given this advantage, combination vaccines merit an economic premium. The purpose of this paper is to describe how Monte Carlo simulation can be used to assess and quantify this premium by studying four combination vaccines that may become available for distribution within the United States. Each combination vaccine is added to twelve licensed vaccine products for six childhood diseases (diphtheria, tetanus, pertussis, haemophilus influenzae type B, hepatitis B, and polio). Monte Carlo simulation with an integer programming model is used to determine the (maximal) inclusion price distribution of four combination vaccines, by randomizing the cost of an injection. The results of this study suggest that combination vaccines warrant price premiums based on the cost assigned to administering an injection, and that further developments and innovations in this area by vaccine manufacturers may provide significant economic and societal benefits.

Maximum-weight stable sets and safe lower bounds for graph coloring

The best method known for determining lower bounds on the vertex coloring number of a graph is the linear-programming column-generation technique, where variables correspond to stable sets, first employed by Mehrotra and Trick in 1996. We present an implementation of the method that provides numerically-safe results, independent of the floating-point accuracy of linear-programming software. Our work includes an improved branch-and-bound algorithm for maximum-weight stable sets and a parallel branch-and-price framework for graph coloring. Computational results are presented on a collection of standard test instances, including the unsolved challenge problems created by David S. Johnson in 1989.

Solving the shortest route cut and fill problem using simulated annealing.

Abstract This paper introduces the shortest route cut and fill problem (SRCFP). The SRCFP is a NP-hard discrete optimization problem for leveling a construction project site, where the objective is to find a vehicle route that minimizes the total distance traveled by a single earthmoving vehicle between cut and fill locations. An optimal vehicle route is a route that minimizes the total haul distance that a single earthmoving vehicle travels. Simulated annealing algorithms are formulated to address the SRCFP. To assess the effectiveness of simulated annealing on the SRCFP, a greedy algorithm is constructed to compute an upper bound and the Held–Karp 1-tree lower bound is used to compute a lower bound. Extensive computational results are reported using several randomly generated instances of the SRCFP.

Designing pediatric vaccine formularies and pricing pediatric combination vaccines using operations research models and algorithms.

The National Immunization Program, housed within the Centers for Disease Control and Prevention in the USA, has identified several challenges that must be faced in childhood immunization programs to deliver and procure vaccines that immunize children from the plethora of childhood diseases. The biomedical issues cited include how drug manufacturers can combine and formulate vaccines, how such vaccines are scheduled and administered and how economically sound vaccine procurement can be achieved. This review discusses how operations research models can be used to address the economics of pediatric vaccine formulary design and pricing, as well as how such models can be used to address a new set of pediatric formulary problems that will surface with the introduction of pediatric combination vaccines into the US pediatric immunization market.

Branch-and-bound algorithms

The branch-and-bound (B&B) algorithmic framework has been used successfully to find exact solutions for a wide array of optimization problems. B&B uses a tree search strategy to implicitly enumerate all possible solutions to a given problem, applying pruning rules to eliminate regions of the search space that cannot lead to a better solution. There are three algorithmic components in B&B that can be specified by the user to fine-tune the behavior of the algorithm. These components are the search strategy, the branching strategy, and the pruning rules. This survey presents a description of recent research advances in the design of B&B algorithms, particularly with regards to these three components. Moreover, three future research directions are provided in order to motivate further exploration in these areas.