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This paper presents a new approach for formulating the delivery problem by drones with general energy consumption models where the drones visit a set of places to deliver parcels to customers. Drones can perform multiple trips that start and end at a central depot while visiting several customers along their paths. The problem determines the routing and scheduling decisions of the drones in order to minimize the total transportation cost of serving customers. For the first time, the new formulation approach enables us to use the best available energy consumption model without the need of any extra approximations. Though the approach works in a very general setting including non-convex energy consumption models, it is also computationally efficient as the resulting optimization model has a linear relaxation. A numerical study on 255 benchmark instances with up to 50 customers and a specific energy function indicate that all the instances can be solved 20 times faster on average using the new formulation when compared to the best existing branch-and-cut algorithm. All the 15 benchmark instances with 50 customers are solved exactly, whereas none of them has been solved optimally before. Moreover, new instances with up to 150 customers are solved with small error bounds within a few hours. The new approach can be simply applied to consider the extra energy required when a drone needs to continue hovering until opening the delivery time window. It can also be applied to the case where the flight time is dependent on the drone's payload weight. Owing to the flexibility of the new approach, these challenging extensions are formulated as linear optimization models for the first time.

The COVID-19 disease spreads swiftly, and nearly three months after the first positive case was confirmed in China, Coronavirus started to spread all over the United States. Some states and counties reported high number of positive cases and deaths, while some reported lower COVID-19 related cases and mortality. In this paper, the factors that could affect the risk of COVID-19 infection and mortality were analyzed in county level. An innovative method by using K-means clustering and several classification models is utilized to determine the most critical factors. Results showed that mean temperature, percent of people below poverty, percent of adults with obesity, air pressure, population density, wind speed, longitude, and percent of uninsured people were the most significant attributes, Comment: 15 pages, 8 figures, 5 tables

This paper studies a stochastic congested location problem in the network of a service system that consists of facilities to be established in a finite number of candidate locations. Population zones allocated to each open service facility together creates a stream of demand that follows a Poisson process and may cause congestion at the facility. The service time at each facility is stochastic and depends on the service capacity and follows a general distribution that can differ for each facility. The service capacity is selected from a given (bounded or unbounded) interval. The objective of our problem is to optimize a balanced performance measure that compromises between facility-induced and customer-related costs. Service times are represented by a flexible location-scale stochastic model. The problem is formulated using quadratic conic optimization. Valid inequalities and a cut-generation procedure are developed to increase computational efficiency. A comprehensive numerical study is carried out to show the efficiency and effectiveness of the solution procedure. Moreover, our numerical experiments using real data of a preventive healthcare system in Toronto show that the optimal service network configuration is highly sensitive to the service-time distribution. Our method for convexifying the waiting-time formulas of M/G/1 queues is general and extends the existing convexity results in queueing theory such that they can be used in optimization problems where the service rates are continuous.

There is a considerable amount of ongoing research on the use of Bayesian control charts for detecting a shift from a good quality distribution to a bad quality distribution in univariate and multivariate processes. It is widely claimed that Bayesian control charts are economically optimal; see, for example, Calabrese (1995) [Bayesian process control for attributes. Management Science, DOI: 10.1287/mnsc.41.4.637] and Makis (2008) [Multivariate Bayesian control chart. Operations Research, DOI: 10.1287/opre.1070.0495]. Some researchers also generalize the optimality of controls defined based on posterior probabilities to the class of partially observable Markov decision processes. This note points out that the existing Bayesian control charts cannot generally be optimal because many years ago an analytical counterexample was provided by Taylor (1965) [Markovian sequential replacement processes. The Annals of Mathematical Statistics, DOI: 10.1214/aoms/1177699796].

Mixed-Integer Second-Order Cone Programs (MISOCPs) form a nice class of mixed-inter convex programs, which can be solved very efficiently due to the recent advances in optimization solvers. Our paper bridges the gap between modeling a class of optimization problems and using MISOCP solvers. It is shown how various performance metrics of M/G/1 queues can be molded by different MISOCPs. To motivate our method practically, it is first applied to a challenging stochastic location problem with congestion, which is broadly used to design socially optimal service networks. Four different MISOCPs are developed and compared on sets of benchmark test problems. The new formulations efficiently solve large-size test problems, which cannot be solved by the best existing method. Then, the general applicability of our method is shown for similar optimization problems that use queue-theoretic performance measures to address customer satisfaction and service quality.

The memory-type control charts, such as EWMA and CUSUM, are powerful tools for detecting small quality changes in univariate and multivariate processes. Many papers on economic design of these control charts use the formula proposed by Lorenzen and Vance (1986) [Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics, 28(1), 3-10, DOI: 10.2307/1269598]. This paper shows that this formula is not correct for memory-type control charts and its values can significantly deviate from the original values even if the ARL values used in this formula are accurately computed. Consequently, the use of this formula can result in charts that are not economically optimal. The formula is corrected for memory-type control charts, but unfortunately the modified formula is not a helpful tool from a computational perspective. We show that simulation-based optimization is a possible alternative method., Comment: Computational Statistics, 2020

The entropic value-at-risk (EVaR) is a new coherent risk measure, which is an upper bound for both the value-at-risk (VaR) and conditional value-at-risk (CVaR). As important properties, the EVaR is strongly monotone over its domain and strictly monotone over a broad sub-domain including all continuous distributions, while well-known monotone risk measures, such as VaR and CVaR lack these properties. A key feature for a risk measure, besides its financial properties, is its applicability in large-scale sample-based portfolio optimization. If the negative return of an investment portfolio is a differentiable convex function, the portfolio optimization with the EVaR results in a differentiable convex program whose number of variables and constraints is independent of the sample size, which is not the case for the VaR and CVaR. This enables us to design an efficient algorithm using differentiable convex optimization. Our extensive numerical study shows the high efficiency of the algorithm in large scales, compared to the existing convex optimization software packages. The computational efficiency of the EVaR portfolio optimization approach is also compared with that of CVaR-based portfolio optimization. This comparison shows that the EVaR approach generally performs similarly, and it outperforms as the sample size increases. Moreover, the comparison of the portfolios obtained for a real case by the EVaR and CVaR approaches shows that the EVaR approach can find portfolios with better expectations and VaR values at high confidence levels.