Drone-Delivery Network for Opioid Overdose -- Nonlinear Integer Queueing-Optimization Models and Methods

We propose a new stochastic emergency network design model that uses a fleet of drones to quickly deliver naxolone in response to opioid overdoses. The network is represented as a collection of M/G/K queuing systems in which the capacity K of each system is a decision variable and the service time is modelled as a decision-dependent random variable. The model is an optimization-based queuing problem which locates fixed (drone bases) and mobile (drones) servers and determines the drone dispatching decisions, and takes the form of a nonlinear integer problem, which is intractable in its original form. We develop an efficient reformulation and algorithmic framework. Our approach reformulates the multiple nonlinearities (fractional, polynomial, exponential, factorial terms) to give a mixed-integer linear programming (MILP) formulation. We demonstrate its generalizablity and show that the problem of minimizing the average response time of a network of M/G/K queuing systems with unknown capacity K is always MILP-representable. We design two algorithms and demonstrate that the outer approximation branch-and-cut method is the most efficient and scales well. The analysis based on real-life overdose data reveals that drones can in Virginia Beach: 1) decrease the response time by 78%, 2) increase the survival chance by 432%, 3) save up to 34 additional lives per year, and 4) provide annually up to 287 additional quality-adjusted life years

Multi-Objective Probabilistically Constrained Programming with Variable Risk: New Models and Applications

We consider a class of multi-objective probabilistically constrained problems MOPCP with a joint chance constraint, a multi-row random technology matrix, and a risk parameter (i.e., the reliability level) defined as a decision variable. We propose a Boolean modeling framework and derive a series of new equivalent mixed-integer programming formulations. We demonstrate the computational efficiency of the formulations that contain a small number of binary variables. We provide modeling insights pertaining to the most suitable reformulation, to the trade-off between the conflicting cost/revenue and reliability objectives, and to the scalarization parameter determining the relative importance of the objectives. Finally, we propose several MOPCP variants of multi-portfolio financial optimization models that implement a downside risk measure and can be used in a centralized or decentralized investment context. We study the impact of the model parameters on the portfolios, show, via a cross-validation study, the robustness of the proposed models, and perform a comparative analysis of the optimal investment decisions

An Integer L-shaped Method for Dynamic Order Dispatching in Autonomous Last-Mile Delivery with Demand Uncertainty

Given the potential to significantly reduce the cost and time in last-mile delivery, autonomous delivery solutions via delivery robots or unmanned aerial vehicles have received increasing attention. This paper studies the dynamic order dispatching problem in an autonomous last-mile delivery system with intrinsic demand uncertainty. We consider a rolling order-fulfilment context and formulate a two-stage stochastic programming to take into account both existing unfulfilled orders and future incoming requests to minimize the total expected delays in package delivery. The considered uncertainty includes the stochastic arrival of delivery requests, their types, locations/delivery distances, and associated penalties for late delivery. Due to the constrained service capacity, the size of the problem grows exponentially as the number of simulated scenarios increases. In this study, we propose a modified integer L-shaped method, which (i) significantly reduces the number of nodes in the branching tree, and (ii) simplifies the computation of optimality cuts. The computational results show that these two modifications improve the average running time by roughly 10 times and 1,000 times compared to the non-customized L-shaped method and the classic branch-and-bound method, respectively. The linearly growing computational speed in response to the number of scenarios enables it as a viable solution for large-sized problems in reality

Multi-Agent Search for a Moving and Camouflaging Target

In multi-agent search planning for a randomly moving and camouflaging target, we examine heterogeneous searchers that differ in terms of their endurance level, travel speed, and detection ability. This leads to a convex mixed-integer nonlinear program, which we reformulate using three linearization techniques. We develop preprocessing steps, outer approximations via lazy constraints, and bundle-based cutting plane methods to address large-scale instances. Further specializations emerge when the target moves according to a Markov chain. We carry out an extensive numerical study to show the computational efficiency of our methods and to derive insights regarding which approach should be favored for which type of problem instance

Recent advances in the theory and practice of logical analysis of data

Logical Analysis of Data (LAD) is a data analysis methodology introduced by Peter L. Hammer in 1986. LAD distinguishes itself from other classification and machine learning methods by the fact that it analyzes a significant subset of combinations of variables to describe the positive or negative nature of an observation and uses combinatorial techniques to extract models defined in terms of patterns. In recent years, the methodology has tremendously advanced through numerous theoretical developments and practical applications. In the present paper, we review the methodology and its recent advances, describe novel applications in engineering, finance, health care, and algorithmic techniques for some stochastic optimization problems, and provide a comparative description of LAD with well-known classification methods

Threshold boolean form for joint probabilistic constraints with random technology matrix.

We develop a new modeling and exact solution method for stochastic programming problems that include a joint probabilistic constraint in which the multirow random technology matrix is discretely distributed. We binarize the probability distribution of the random variables in such a way that we can extract a threshold partially defined Boolean function (pdBf) representing the probabilistic constraint. We then construct a tight threshold Boolean minorant for the pdBf. Any separating structure of the tight threshold Boolean minorant defines sufficient conditions for the satisfaction of the probabilistic constraint and takes the form of a system of linear constraints. We use the separating structure to derive three new deterministic formulations equivalent to the studied stochastic problem. We derive a set of strengthening valid inequalities for the reformulated problems. A crucial feature of the new integer formulations is that the number of integer variables does not depend on the number of scenarios used to represent uncertainty. The computational study, based on instances of the stochastic capital rationing problem, shows that the MIP reformulations are orders of magnitude faster to solve than the MINLP formulation. The method integrating the derived valid inequalities in a branch-andbound algorithm has the best performance

Desempenho do modelo estocástico de média-variância para o mercado brasileiro de ações

Os modelos de média-variância de otimização de carteira apresentam questionamentos em relação ao seu efetivo desempenho devido ao chamado erro de estimação. Em conseqüência, a otimização estocástica vêm aumentando sua importância devido à possibilidade da inclusão da incerteza na estimativa dos parâmetros. Neste estudo foi avaliado o desempenho do modelo de otimização de carteira proposto por Bonami e Lejeune (2009) e reformulado por Filomena e Lejeune (2011a) no mercado brasileiro de ações. Ambos os modelos podem ser caracterizados como versões probabilísticas do modelo clássico de média-variância proposto por Markowitz (1952). O modelo de Filomena e Lejeune (2011a) apresentou desempenho médio superior aos benchmarks IBRX-50 e IBOVESPA. No entanto, o mesmo apresentou resultados viáveis em apenas 12,5% dos 64 cenários de teste. Embora isto possa ser considerada inicialmente uma limitação do modelo (o qual poderia ser melhorada com uma reavaliação de alguns parâmetros), também pode ser analisada como um benefício para os investidores, pois oferece pontos de entrada e saída do mercado de ações

Desempenho do modelo estocástico na média-variância para o mercado brasileiro de ações

Os modelos de média-variância deotimização de carteira apresentam questionamentos em relação ao seu efetivo desempenho devido ao chamado erro de estimação.Em consequência, a otimização estocástica vem aumentando sua importância pois permite à possibilidade da inclusão da incerteza na estimativa dos parâmetros. Neste estudo foi avaliado o desempenho do modelo de otimização de carteira proposto por Bonami e Lejeune (2009), e reformulado por Filomena e Lejeune (2012), no mercado brasileiro de ações. Ambos os modelos podem ser caracterizados como versões probabilísticas do modelo clássico de média-variância proposto por Markowitz (1952). O modelo de Filomena e Lejeune (2012) apresentou desempenho médio superior aos benchmarks IBRX-50 e IBOVESPA. No entanto, o mesmo apresentou resultados viáveis em apenas 12,5% dos 64 cenários de teste. Embora isto possa ser considerado uma limitação do modelo,também pode ser analisado como um benefício para os investidores, pois oferece pontos de entrada e saída do mercado de ações.The estimation error is a well-documented problem of the mean-variance optimization models. Therefore, stochastic optimization has increased its importance on portfolio optimization given its ability to include uncertainty as a parameter. In this study, the performance of the model proposed by Filomenaand Lejeune (2012), a reformulated version of a previous model developed by Bonami and Lejeune (2009), was evaluated for the Brazilian stock market. Both models can be characterized as probabilistic versions of the classical model developed by Markowitz (1952). The performance of the model was superior when compared to the market benchmarks IBRX-50 and IBOVESPA. However, it presented feasibility in just 12,5% of the 64 test cases. Although this can initially be seen as a strong limitation for the practical use of the model, this can be considered as a very important pragmatic information for investors, since the model provides possible entry and exit points on the stock market

Different Oxidative Stress Response in Keratinocytes and Fibroblasts of Reconstructed Skin Exposed to Non Extreme Daily-Ultraviolet Radiation

Experiments characterizing the biological effects of sun exposure have usually involved solar simulators. However, they addressed the worst case scenario i.e. zenithal sun, rarely found in common outdoor activities. A non-extreme ultraviolet radiation (UV) spectrum referred as “daily UV radiation” (DUVR) with a higher UVA (320–400 nm) to UVB (280–320 nm) irradiance ratio has therefore been defined. In this study, the biological impact of an acute exposure to low physiological doses of DUVR (corresponding to 10 and 20% of the dose received per day in Paris mid-April) on a 3 dimensional reconstructed skin model, was analysed. In such conditions, epidermal and dermal morphological alterations could only be detected after the highest dose of DUVR. We then focused on oxidative stress response induced by DUVR, by analyzing the modulation of mRNA level of 24 markers in parallel in fibroblasts and keratinocytes. DUVR significantly modulated mRNA levels of these markers in both cell types. A cell type differential response was noticed: it was faster in fibroblasts, with a majority of inductions and high levels of modulation in contrast to keratinocyte response. Our results thus revealed a higher sensitivity in response to oxidative stress of dermal fibroblasts although located deeper in the skin, giving new insights into the skin biological events occurring in everyday UV exposure