Douglas R. Bish

Planning for a bus-based evacuation

Planning for a bus-based regional evacuation is essential for emergency preparedness, especially for regions threatened by hurricanes that have large numbers of transit-dependent people. While this difficult planning problem is a variant of the vehicle routing problem, it differs in some key aspects, including the objective and the network structure (e.g., capacitated shelters). This problem is not well studied. In this paper we introduce a model specifically designed for bus-based evacuation planning, along with two mathematical programming formulations, which are used to develop a heuristic algorithm. Using these models, we analyze the differences in the structural properties of optimal solutions between this problem and traditional vehicle routing problems.

Aggregate-level demand management in evacuation planning

Without successful large-scale regional evacuations, threats such as hurricanes and wild-fires can cause a large loss of life. In this context, automobiles are oftentimes an essential transportation mode for evacuations, but the ensuing traffic typically overwhelms the roadway capacity and causes congestion on a massive scale. Congestion leads to many problems including longer, costlier, and more stressful evacuations, lower compliance rates, and increased risk to the population. Supply-based strategies have traditionally been used in evacuation planning, but they have been proven to be insufficient to reduce congestion to acceptable levels. In this paper, we study the demand-based strategies of aggregate-level staging and routing to structure the evacuation demand, both with and without congestion. We provide a novel modeling framework that offers strategic flexibility and utilizes a lexicographic objective function that represents a hierarchy of relevant evacuation-based goals. We also provide insights into the nature and effect of network bottlenecks. We compare our model with and without congestion in relation to tractability, normative optimality, and robustness under demand uncertainty. We also show the effectiveness of using demand-based strategies as opposed to using the status quo that involves a non-staged or simultaneous evacuation process. Effective solution procedures are developed and tested using hypothetical problem instances as well as using a larger study based on a portion of coastal Virginia, USA.

Decision support for hospital evacuation and emergency response

Evacuation planning is an important part of a hospital’s emergency management plan. In an evacuation the safety and health of patients is the fundamental success parameter. Thus, in this paper we introduce an evacuation model, appropriate for planning and operations, that has the objective of minimizing expected risk, both the threat risk that is forcing the evacuation, and the risk inherent in transporting patients, some in critical condition. Specifically, we study the allocation of patients, categorized by criticality and care requirements, to a limited fleet of vehicles of various capacities and medical capabilities, to be transported to appropriate receiving hospitals considering the current available space in each hospital for each category of patient. The model is an integer program, where the non-linear expected risks are calculated a-priori. This model has a structure that has excellent solution characteristics that permit us to solve large problems in a reasonable time, enabling the model to potentially be used for both planning and operations. To illustrate the solvability of this model and demonstrate its characteristics, we apply it to a realistic case study based on the evacuation of a large regional hospital.

Cost-effectiveness of Babesia microti antibody and nucleic acid blood donation screening using results from prospective investigational studies.

Babesia microti causes transfusion‐transmitted babesiosis (TTB); currently, blood donor screening assays are unlicensed but used investigationally.

Optimal evacuation planning using staging and routing

Evacuation is an important disaster management tool. Evacuating a large region by automobile (the most commonly used mode) is a difficult task, especially as high levels of traffic congestion often form. This paper studies the use of demand-based strategies, specifically, the staging and routing of evacuees. These strategies attempt to manage demand in order to reduce or eliminate congestion. A strategic mixed-integer programming planning model that accounts for evacuation dynamics and congestion is used to study these strategies. The strategies adopted incorporate different evacuee types based on destination requirements and shelter capacity restrictions. The main objective studied is to minimize the network clearance time. We examine the structure of optimal strategies, yielding insights into the use of staging and routing in evacuation management. These insights are then used to develop effective solution procedures. To demonstrate the efficacy of the proposed solution technique, we provide computational experience using a large realistic example based on Virginia Beach.

Modeling the Capacity Drop Phenomenon at Freeway Bottlenecks using the INTEGRATION Software

Abstract Empirical studies have demonstrated that the discharge flow rate at a bottleneck is reduced following the onset of congestion. These flow reductions, also known as capacity drops, are typically measured by comparing the queue discharge flowrate to the maximum pre-queue discharge flow rate. This research demonstrates, through the use of the INTEGRATION microscopic traffic simulation software, that these empirically observed capacity drops can be simulated without enforcing a discontinuity in the steady-state car-following or fundamental diagram. Instead, these capacity drops may be captured by constraining and varying vehicle acceleration levels, which in turn produces the desired macroscopic behavior by introducing gaps between vehicles. The study demonstrates that the INTEGRATION software produces capacity drops at the same level of magnitude as empirically observed. The study then uses the INTEGRATION software to demonstrate the empirically observed stochastic capacity and demonstrates how it is impacted by the level of acceleration that drivers are willing to exert, the lane changing behavior, and the percentage of heavy vehicles in the traffic stream.

Optimal selection of screening assays for infectious agents in donated blood

Blood products are an essential component of any health system, and their safety, in terms of being free of “transfusion-transmitted infections” (TTIs), i.e., diseases that include Human Immunodeficiency Virus, Hepatitis Viruses, Human T-cell Lymphotropic Virus, Syphilis, West Nile Virus, and Chagas’ Disease, is crucial. However, blood screening tests are imperfectly reliable, with the possibility of false-negatives and false-positives. The budget-constrained decision-maker needs to (i) select a set of screening tests to administer to each unit of donated blood, and (ii) construct a “decision rule” with which to classify each blood unit as infection-free versus infected. The objective is to minimize the TTI risk for blood classified as infection-free, which depends on the efficacies of the entire set of tests selected and the decision rule adopted. This risk structure leads to a nonlinear optimization problem. Our analysis provides efficient optimal algorithms for a special case where only mono-infections are possible, and an effective heuristic and lower bounds for the general case with co-infection possibility. Our case study for the sub-Saharan Africa, Ghana, Thailand, and the United States illustrates the value of our optimization-based approach, which generates region-specific test composition by explicitly considering the regional TTI prevalence rates, and provides insights.

Comparative Statics Analysis of Multiproduct Newsvendor Networks Under Responsive Pricing

We propose a novel analytic approach for the comparative statics analysis of multiproduct multiresource newsvendor networks under responsive pricing. Our approach involves exploiting the properties of the primal mathematical programming formulation and of the dual variables and linking those properties to the concept of convex orders and to properties of the underlying demand function. The use of convex orders allows us to establish our main results without restriction to a specific demand distribution. A major strength of our approach is that it is “scalable,” i.e., it applies to newsvendor networks with any number of “nonindependent” i.e., demand or resource sharing products and resources, without an exponential increase in effort as problem size increases. This is unlike the current approaches commonly used in the operations management literature, which typically involve a parametric analysis of the recourse problem, followed by the use of Jacobians and the implicit function theorem. Providing a rigorous framework for comparative statics analysis, which can be applied to other problems that are not amenable to traditional parametric analysis, is our main contribution. We demonstrate this approach on the optimal capacity decision problem in multiproduct newsvendor networks under responsive pricing, formulated as a two-stage stochastic programming problem with recourse: The firm determines the resource capacities ex ante, in the first stage, when demand intercepts are uncertain, and makes the pricing and production decisions ex post, in the second stage, when demand intercepts e.g., market conditions are fully observed. This particular problem and its variants are well studied in the operations management literature. A comparative statics analysis is integral to the study of the capacity investment decision, as it allows answers to important questions such as the following: “Does the firm acquire more or less of the different resources available as demand uncertainty increases? Does the firm benefit from an increase in demand uncertainty?” Using our proposed approach, we establish comparative statics results on how the newsvendors expected profit and optimal capacity decision change with demand risk in multiproduct multiresource newsvendor networks. We also extend our analysis to the study of demand dependence in two-product networks.

Optimal service order for mass-casualty incident response

In the aftermath of a mass-casualty incident, one of the first steps in the response is to triage the casualties. Triage systems categorize the casualties based on criticality, and then prioritize casualties for transfer to hospitals for further treatment. The prioritization is usually based on simply ordering the casualty types without considering the available resources to transport them and the scale of the disaster. These factors can significantly affect the outcome of the rescue efforts. In this research we study a mathematical model to incorporate the above mentioned factors in the triage process. We assume a disaster location with a set of casualties, categorized by criticality and care requirements, that must be transported to hospitals in the region using a fleet of available ambulances. The goal is to maximize the expected number of survivors. We analyze the structure of the optimal solution to this problem, and compare the performance of the model with the current practice and other related models in the literature.

Residual risk and waste in donated blood with pooled nucleic acid testing

An accurate estimation of the residual risk of transfusion-transmittable infections (TTIs), which includes the human immunodeficiency virus (HIV), hepatitis B and C viruses (HBV, HCV), among others, is essential, as it provides the basis for blood screening assay selection. While the highly sensitive nucleic acid testing (NAT) technology has recently become available, it is highly costly. As a result, in most countries, including the United States, the current practice for human immunodeficiency virus, hepatitis B virus, hepatitis C virus screening in donated blood is to use pooled NAT. Pooling substantially reduces the number of tests required, especially for TTIs with low prevalence rates. However, pooling also reduces the tests sensitivity, because the viral load of an infected sample might be diluted by the other samples in the pool to the point that it is not detectable by NAT, leading to potential TTIs. Infection-free blood may also be falsely discarded, resulting in wasted blood. We derive expressions for the residual risk, expected number of tests, and expected amount of blood wasted for various two-stage pooled testing schemes, including Dorfman-type and array-based testing, considering infection progression, infectivity of the blood unit, and imperfect tests under the dilution effect and measurement errors. We then calibrate our model using published data and perform a case study. Our study offers key insights on how pooled NAT, used within different testing schemes, contributes to the safety and cost of blood. Copyright