Vehicle Routing Problems that Minimize the Completion Time: Heuristics, Worst-Case Analyses, and Computational Results

In the standard Vehicle Routing Problem (VRP), we route a fleet of vehicles to deliver the demands of all customers such that the total distance traveled by the fleet is minimized. In this dissertation, we study variants of the VRP that minimize the completion time, i.e., we minimize the distance of the longest route. We call it the min-max objective function. In applications such as disaster relief efforts and military operations, the objective is often to finish the delivery or the task as soon as possible, not to plan routes with the minimum total distance. Even in commercial package delivery nowadays, companies are investing in new technologies to speed up delivery instead of focusing merely on the min-sum objective. In this dissertation, we compare the min-max and the standard (min-sum) objective functions in a worst-case analysis to show that the optimal solution with respect to one objective function can be very poor with respect to the other. The results motivate the design of algorithms specifically for the min-max objective. We study variants of min-max VRPs including one problem from the literature (the min-max Multi-Depot VRP) and two new problems (the min-max Split Delivery Multi-Depot VRP with Minimum Service Requirement and the min-max Close-Enough VRP). We develop heuristics to solve these three problems. We compare the results produced by our heuristics to the best-known solutions in the literature and find that our algorithms are effective. In the case where benchmark instances are not available, we generate instances whose near-optimal solutions can be estimated based on geometry. We formulate the Vehicle Routing Problem with Drones and carry out a theoretical analysis to show the maximum benefit from using drones in addition to trucks to reduce delivery time. The speed-up ratio depends on the number of drones loaded onto one truck and the speed of the drone relative to the speed of the truck.

Does therapeutic writing help people with long-term conditions? Systematic review, realist synthesis and economic considerations

Background Writing therapy to improve physical or mental health can take many forms. The most researched model of therapeutic writing (TW) is unfacilitated, individual expressive writing (written emotional disclosure). Facilitated writing activities are less widely researched. Data sources Databases including: MEDLINE, EMBASE, PsychINFO, Linguistics and Language Behavior Abstracts, AMED, and CINHAL were searched from inception to March 2013. Review methods Four TW practitioners provided expert advice. Study procedures were conducted by one reviewer and checked by a second. Randomised controlled trials (RCTs) and non-randomised comparative studies were included. Quality was appraised using the Cochrane risk of bias tool. Unfacilitated and facilitated TW studies were analysed separately under ICD-10 chapter headings. Meta-analyses were performed where possible using Revman 5.2. Costs were estimated from an NHS perspective and three cost-consequence case studies were prepared. Realist synthesis followed RAMESES guidelines. Objectives To review the clinical and cost-effectiveness of TW for people with long-term health conditions (LTCs) compared to no writing, or other controls, reporting any relevant clinical outcomes. To conduct a realist synthesis to understand how TW might work, and for whom. Results From 14,658 unique citations, 284 full text papers were reviewed and 64 studies (58 RCTs) were included in the final effectiveness reviews. Five studies examined facilitated TW, these were extremely heterogeneous with unclear or high risk of bias, but suggested that facilitated TW interventions may be beneficial in individual LTCs. Unfacilitated expressive writing was examined in 59 studies of variable, or unreported, quality. Overall there was very little or no evidence of any benefit reported in the following conditions (number of studies): HIV (six); breast cancer (eight); gynaecological and genitourinary cancers (five); mental health (five); asthma (four); psoriasis (three); chronic pain (four). In inflammatory arthropathies (six) there was a reduction in disease severity (n= 191, standardised mean difference (SMD) - 0.61 [95% confidence intervals (95% CI) -0.96, -0.26]) in the short term on meta-analysis of four studies. For all other LTCs there was either no, or sparse, data with no, or inconsistent, evidence of benefit. Meta-analyses conducted across all the LTCs provided no evidence that unfacilitated EW had any effect on depression at short term (n= 1,563, SMD -0.06, 95% CI -0.29 to 0.17, substantial heterogeneity), or long term (n= 778, SMD-0.04 95% CI -0.18 to 0.10, little heterogeneity) follow up, or on anxiety, physiological or biomarker-based outcomes. One study reported costs, none reported cost-effectiveness, twelve reported resource use; meta-analysis suggested reduced medication use but no impact on health centre visits. Estimated costs of intervention were low, but there was insufficient evidence to judge cost-effectiveness. Realist review findings suggested that facilitated TW is a complex intervention and group interaction contributes to the perception of benefit. It was unclear from the available data who might benefit most from facilitated TW. Limitations Difficulties with developing realist review programme theory meant that mechanisms operating during TW remain obscure. Conclusions Overall there is little evidence to support the effectiveness or cost-effectiveness of unfacilitated expressive writing interventions in people with LTCs. Further research focussed on facilitated TW in people with LTCs could be informative.

MULTI-UNIT ACCIDENT CONTRIBUTIONS TO U.S. NUCLEAR REGULATORY COMMISSION QUANTITATIVE HEALTH OBJECTIVES: A SAFETY GOAL POLICY ANALYSIS USING MODELS FROM STATE-OF-THE-ART REACTOR CONSEQUENCE ANALYSES

The U.S. Nuclear Regulatory Commission implemented a safety goal policy in response to the 1979 Three Mile Island accident. This policy addresses the question “How safe is safe enough?” by specifying quantitative health objectives (QHOs) for comparison with results from nuclear power plant (NPP) probabilistic risk analyses (PRAs) to determine whether proposed regulatory actions are justified based on potential safety benefit. Lessons learned from recent operating experience—including the 2011 Fukushima accident—indicate that accidents involving multiple units at a shared site can occur with non-negligible frequency. Yet risk contributions from such scenarios are excluded by policy from safety goal evaluations—even for the nearly 60% of U.S. NPP sites that include multiple units. This research develops and applies methods for estimating risk metrics for comparison with safety goal QHOs using models from state-of-the-art consequence analyses to evaluate the effect of including multi-unit accident risk contributions in safety goal evaluations.

Broad-scale mapping of seafloor habitats in the north-east Atlantic using existing environmental data

If marine management policies and actions are to achieve long-term sustainable use and management of the marine environment and its resources, they need to be informed by data giving the spatial distribution of seafloor habitats over large areas. Broad-scale seafloor habitat mapping is an approachwhich has the benefit of producing maps covering large extents at a reasonable cost. This approach was first investigated by Roff et al. (2003), who, acknowledging that benthic communities are strongly influenced by the physical characteristics of the seafloor, proposed overlaying mapped physical variables using a geographic information system (GIS) to produce an integrated map of the physical characteristics of the seafloor. In Europe the method was adapted to the marine section of the EUNIS (European Nature Information System) classification of habitat types under the MESH project, andwas applied at an operational level in 2011 under the EUSeaMap project. The present study compiled GIS layers for fundamental physical parameters in the northeast Atlantic, including (i) bathymetry, (ii) substrate type, (iii) light penetration depth and (iv) exposure to near-seafloor currents andwave action. Based on analyses of biological occurrences, significant thresholds were fine-tuned for each of the abiotic layers and later used in multi-criteria raster algebra for the integration of the layers into a seafloor habitat map. The final result was a harmonised broad-scale seafloor habitat map with a 250 m pixel size covering four extensive areas, i.e. Ireland, the Bay of Biscay, the Iberian Peninsula and the Azores. The map provided the first comprehensive perception of habitat spatial distribution for the Iberian Peninsula and the Azores, and fed into the initiative for a pan- European map initiated by the EUSeaMap project for Baltic, North, Celtic and Mediterranean seas.

The role of heart rate as a risk marker for predicting adverse outcomes

Cardiovascular disease is one of the leading causes of death around the world. Resting heart rate has been shown to be a strong and independent risk marker for adverse cardiovascular events and mortality, and yet its role as a predictor of risk is somewhat overlooked in clinical practice. With the aim of highlighting its prognostic value, the role of resting heart rate as a risk marker for death and other adverse outcomes was further examined in a number of different patient populations. A systematic review of studies that previously assessed the prognostic value of resting heart rate for mortality and other adverse cardiovascular outcomes was presented. New analyses of nine clinical trials were carried out. Both the original and extended Cox model that allows for analysis of time-dependent covariates were used to evaluate and compare the predictive value of baseline and time-updated heart rate measurements for adverse outcomes in the CAPRICORN, EUROPA, PROSPER, PERFORM, BEAUTIFUL and SHIFT populations. Pooled individual patient meta-analyses of the CAPRICORN, EPHESUS, OPTIMAAL and VALIANT trials, and the BEAUTIFUL and SHIFT trials, were also performed. The discrimination and calibration of the models applied were evaluated using Harrell’s C-statistic and likelihood ratio tests, respectively. Finally, following on from the systematic review, meta-analyses of the relation between baseline and time-updated heart rate, and the risk of death from any cause and from cardiovascular causes, were conducted. Both elevated baseline and time-updated resting heart rates were found to be associated with an increase in the risk of mortality and other adverse cardiovascular events in all of the populations analysed. In some cases, elevated time-updated heart rate was associated with risk of events where baseline heart rate was not. Time-updated heart rate also contributed additional information about the risk of certain events despite knowledge of baseline heart rate or previous heart rate measurements. The addition of resting heart rate to the models where resting heart rate was found to be associated with risk of outcome improved both discrimination and calibration, and in general, the models including time-updated heart rate along with baseline or the previous heart rate measurement had the highest and similar C-statistics, and thus the greatest discriminative ability. The meta-analyses demonstrated that a 5bpm higher baseline heart rate was associated with a 7.9% and an 8.0% increase in the risk of all-cause and cardiovascular death, respectively (both p less than 0.001). Additionally, a 5bpm higher time-updated heart rate (adjusted for baseline heart rate in eight of the ten studies included in the analyses) was associated with a 12.8% (p less than 0.001) and a 10.9% (p less than 0.001) increase in the risk of all-cause and cardiovascular death, respectively. These findings may motivate health care professionals to routinely assess resting heart rate in order to identify individuals at a higher risk of adverse events. The fact that the addition of time-updated resting heart rate improved the discrimination and calibration of models for certain outcomes, even if only modestly, strengthens the case that it be added to traditional risk models. The findings, however, are of particular importance, and have greater implications for the clinical management of patients with pre-existing disease. An elevated, or increasing heart rate over time could be used as a tool, potentially alongside other established risk scores, to help doctors identify patient deterioration or those at higher risk, who might benefit from more intensive monitoring or treatment re-evaluation. Further exploration of the role of continuous recording of resting heart rate, say, when patients are at home, would be informative. In addition, investigation into the cost-effectiveness and optimal frequency of resting heart rate measurement is required. One of the most vital areas for future research is the definition of an objective cut-off value for the definition of a high resting heart rate.

Reducing the global burden of depression : population level analysis of intervention cost-effectiveness in 14 world regions

International evidence on the cost and effects of interventions for reducing the global burden of depression remain scarce. Aims: To estimate the population-level cost-effectiveness of evidence-based depression interventions and their contribution towards reducing current burden. Method: Primary-care-based depression interventions were modelled at the level of whole populations in 14 epidemiological subregions of the world. Total population-level costs (in international dollars or I$) and effectiveness (disability adjusted life years (DALYs) averted) were combined to form average and incremental cost-effectiveness ratios. Results: Evaluated interventions have the potential to reduce the current burden of depression by 10–30%. Pharmacotherapy with older antidepressant drugs, with or without proactive collaborative care, are currently more cost-effective strategies than those using newer antidepressants, particularly in lower-income subregions. Conclusions: Even in resource-poor regions, each DALYaverted by efficient depression treatments in primary care costs less than 1 year of average per capita income, making such interventions a cost-effective use of health resources. However, current levels of burden can only be reduced significantlyif there is a substantialincrease substantial increase intreatment coverage.

Correcting for bias when estimating the cost of hospital-acquired infection : an analysis of lower respiratory tract infections in non-surgical patients

Hospital acquired infections (HAI) are costly but many are avoidable. Evaluating prevention programmes requires data on their costs and benefits. Estimating the actual costs of HAI (a measure of the cost savings due to prevention) is difficult as HAI changes cost by extending patient length of stay, yet, length of stay is a major risk factor for HAI. This endogeneity bias can confound attempts to measure accurately the cost of HAI. We propose a two-stage instrumental variables estimation strategy that explicitly controls for the endogeneity between risk of HAI and length of stay. We find that a 10% reduction in ex ante risk of HAI results in an expected savings of £693 ($US 984).