Dynamic Server Allocation at Parallel Queues

We explore whether dynamically reassigning servers to parallel queues in response to queue imbalances can reduce average waiting time in those queues. We use approximate dynamic programming methods to determine when servers should be switched, and we compare the performance of such dynamic allocations to that of a pre-scheduled deterministic allocation. Testing our method on both synthetic data and data from airport security checkpoints at Boston Logan International Airport, we find that in situations where the uncertainty in customer arrival rates is significant, dynamically reallocating servers can substantially reduce waiting time. Moreover, we find that intuitive switching strategies that are optimal for queues with homogeneous entry rates are not optimal in this setting. Keywords: control of queues, fluid queues, approximate dynamic programming, dynamic server allocation, workforce management

How Effective Is Security Screening of Airline Passengers?

With a simple mathematical model, we explored the antiterrorist effectiveness of airport passenger prescreening systems. Supporters of these systems often emphasize the need to identify the most suspicious passengers, but they ignore the point that such identification does little good unless dangerous items can actually be detected. Critics often focus on terrorists\u27 ability to probe the system and thereby thwart it, but ignore the possibility that the very act of probing can deter attempts at sabotage that would have succeeded. Using the model to make some preliminary assessments about security policy, we find that an improved baseline level of screening for all passengers might lower the likelihood of attack more than would improved profiling of high-risk passengers

Procuring Pediatric Vaccines in a Two-Economy Duopoly

In this work, we aim to present an optimization model for vaccine pricing in a two-economy duopoly. This model observes the price dynamics between a high income country and a low income country that procure vaccinations through PAHO. This model is formulated to provide insights on optimal pricing strategy for PAHO to ultimately increase vaccine accessibility to low income countries. The objective is to satisfy the public demand at the lowest price possible, while providing enough profit for the vaccine manufacturers to stay in business. Using non-linear integer programming, the model results show that cross-subsidization occurs in PAHO vaccine procurement

Characteristics of Optimal Solutions to the Sensor Location Problem

In [Bianco, L., Giuseppe C., and P. Reverberi. 2001. "A network based model for traffic sensor location with implications on O/D matrix estimates". Transportation Science 35(1):50-60.], the authors present the Sensor Location Problem: that of locating the minimum number of traffic sensors at intersections of a road network such that the traffic flow on the entire network can be determined. They offer a necessary and sufficient condition on the set of monitored nodes in order for the flow everywhere to be determined. In this paper, we present a counterexample that demonstrates that the condition is not actually sufficient (though it is still necessary). We present a stronger necessary condition for flow calculability, and show that it is a sufficient condition in a large class of graphs in which a particular subgraph is a tree. Many typical road networks are included in this category, and we show how our condition can be used to inform traffic sensor placement.Comment: Submitted for peer review on October 3, 201

To Give or Not To Give: Pandemic Vaccine Donation Policy

The global SARS-CoV-2 (COVID-19) pandemic highlighted the challenge of equitable vaccine distribution between high- and low-income countries. Many high-income countries were reluctant or slow to distribute extra doses of the vaccine to lower-income countries via the COVID-19 Vaccines Global Access (COVAX) collaboration. In addition to moral objections to such vaccine nationalism, vaccine inequity during a pandemic could contribute to the evolution of new variants of the virus and possibly increase total deaths, including in the high-income countries. Using the COVID-19 pandemic as a case study, we use the epidemiological model of Holleran et al. that incorporates virus mutation. We identify realistic scenarios under which a donor country prefers to donate vaccines before distributing them locally in order to minimize local deaths during a pandemic. We demonstrate that a nondonor-first vaccination policy can delay, sometimes dramatically, the emergence of more-contagious variants. Even more surprising, donating all vaccines is sometimes better for the donor country than a sharing policy in which half of the vaccines are donated and half are retained because of the impact donation can have on delaying the emergence of a more contagious virus. Nondonor-first vaccine allocation is optimal in scenarios in which the local health impact of the vaccine is limited or when delaying emergence of a variant is especially valuable. In all cases, we find that vaccine distribution is not a zero-sum game between donor and nondonor countries. Thus, in addition to moral reasons to avoid vaccine nationalism, donor nations can also realize local health benefits from donating vaccines. The insights yielded by this framework can be used to guide equitable vaccine distribution in future pandemics.Comment: 21 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:2303.0591

A New Framework for Network Disruption

Traditional network disruption approaches focus on disconnecting or lengthening paths in the network. We present a new framework for network disruption that attempts to reroute flow through critical vertices via vertex deletion, under the assumption that this will render those vertices vulnerable to future attacks. We define the load on a critical vertex to be the number of paths in the network that must flow through the vertex. We present graph-theoretic and computational techniques to maximize this load, firstly by removing either a single vertex from the network, secondly by removing a subset of vertices.Comment: Submitted for peer review on September 13, 201

Multi-Year Optimization of Malaria Intervention: A Mathematical Model

Malaria is a mosquito-borne, lethal disease that affects millions and kills hundreds of thousands of people each year, mostly children. There is an increasing need for models of malaria control. In this paper, a model is developed for allocating malaria interventions across geographic regions and time, subject to budget constraints, with the aim of minimizing the number of person-days of malaria infection

Project-Based ORMS Education

Operations research and management science (ORMS) is not simply the rote application of formulas and algorithms but also an involved process of modeling ill-posed real-world problems. Students must therefore learn both the mathematical foundations of the field as well as the craft of the practice of ORMS. In this article, the author surveys different approaches to project-based education, which attempts to teach the practice of ORMS. The author also provides best practices for the specific example of student field projects with clients

Flight Delays at RegionEx

In this case about two fictitious airlines, RegionEx, a small regional airline, is a contracted regional carrier for Mississippi Delta Airlines (MDA), a major U.S. airline. In September, RegionEx exhibited a worse flight delay record than MDA, and is now at risk of losing its contract. The flight operations manager at RegionEx is tasked with analyzing the flight delay records and explaining RegionEx\u27s seemingly poor performance to RegionEx\u27s chief operations officer. Reflecting the recommendations of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) published by the American Statistical Association, this case emphasizes statistical literacy and conceptual understanding of data analysis rather than rote procedures. Undergraduate and MBA students will use basic data analysis techniques, such as graphical analysis, descriptive statistics, and two-sample hypothesis testing and correlation, to discover important paradoxes in the flight delay data. They will learn that subtle differences in the definition of business performance metrics can radically change their interpretation; graphical analysis of data can provide information about distributions that are masked by summary statistics; aggregating data across disparate sample sizes can skew means (Simpson\u27s paradox); and correlation does not imply causation