Screening multi-dimensional heterogeneous populations for infectious diseases under scarce testing resources,with application to COVID-19

Testing provides essential information for managing infectious disease outbreaks, such as the COVID-19 pandemic. When testing resources are scarce, an important managerial decision is who to test. This decision is compounded by the fact that potential testing subjects are heterogeneous in multiple dimensions that are important to consider, including their likelihood of being disease-positive, and how much potential harm would be averted through testing and the subsequent interventions. To increase testing coverage, pooled testing can be utilized, but this comes at a cost of increased false-negatives when the test is imperfect. Then, the decision problem is to partition the heterogeneous testing population into three mutually exclusive sets: those to be individually tested, those to be pool tested, and those not to be tested. Additionally, the subjects to be pool tested must be further partitioned into testing pools, potentially containing different numbers of subjects. The objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. We develop data-driven optimization models and algorithms to design pooled testing strategies, and show, via a COVID-19 contact tracing case study, that the proposed testing strategies can substantially outperform the current practice used for COVID-19 contact tracing (individually testing those contacts with symptoms). Our results demonstrate the substantial benefits of optimizing the testing design, while considering the multiple dimensions of population heterogeneity and the limited testing capacity.     

An economic lot‐sizing problem with perishable inventory and economies of scale costs: Approximation solutions and worst case analysis

The costs of many economic activities such as production, purchasing, distribution, and inventory exhibit economies of scale under which the average unit cost decreases as the total volume of the activity increases. In this paper, we consider an economic lot‐sizing problem with general economies of scale cost functions. Our model is applicable to both nonperishable and perishable products. For perishable products, the deterioration rate and inventory carrying cost in each period depend on the age of the inventory. Realizing that the problem is NP‐hard, we analyze the effectiveness of easily implementable policies. We show that the cost of the best Consecutive‐Cover‐Ordering (CCO) policy, which can be found in polynomial time, is guaranteed to be no more than (4 + 5)/7 ≈ 1.52 times the optimal cost. In addition, if the ordering cost function does not change from period to period, the cost of the best CCO policy is no more than 1.5 times the optimal cost. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

公众聚集场所消防监督管理存在问题及对策

近年来 ,我国公众聚集场所群死群伤恶性火灾时有发生 ,原因固然是多方面的 ,但是 ,公众聚集场所在监督和管理两个层面上存在的突出问题和薄弱环节 ,不能不引起我们的高度重视。结合多年来开展消防监督工作的实践 ,从消防法律法规、消防安全管理体制、技术标准等方面分析了公众聚集场所消防安全监督管理存在的问题 ,并提出了相应对策措施。     

Revenue sharing contracts in a supply chain with uncontractible actions

We consider a supplier–customer relationship where the customer faces a typical Newsvendor problem of determining perishable capacity to meet uncertain demand. The customer outsources a critical, demand‐enhancing service to an outside supplier, who receives a fixed share of the revenue from the customer. Given such a linear sharing contract, the customer chooses capacity and the service supplier chooses service effort level before demand is realized. We consider the two cases when these decisions are made simultaneously (simultaneous game) or sequentially (sequential game). For each game, we analyze how the equilibrium solutions vary with the parameters of the problem. We show that in the equilibrium, it is possible that either the customer's capacity increases or the service supplier's effort level decreases when the supplier receives a larger share of the revenue. We also show that given the same sharing contract, the sequential game always induces a higher capacity and more effort. For the case of additive effort effect and uniform demand distribution, we consider the customer's problem of designing the optimal contract with or without a fixed payment in the contract, and obtain sensitivity results on how the optimal contract depends on the problem parameters. For the case of fixed payment, it is optimal to allocate more revenue to the supplier to induce more service effort when the profit margin is higher, the cost of effort is lower, effort is more effective in stimulating demand, the variability of demand is smaller or the supplier makes the first move in the sequential game. For the case of no fixed payment, however, it is optimal to allocate more revenue to the supplier when the variability of demand is larger or its mean is smaller. Numerical examples are analyzed to validate the sensitivity results for the case of normal demand distribution and to provide more managerial insights. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008     

Optimal source placement for point coverage in active multistatic sonar networks

The allocation of underwater sensors for tracking, localization, and surveillance purposes is a fundamental problem in anti-submarine warfare. Inexpensive passive receivers have been heavily utilized in recent years; however, modern submarines are increasingly quiet and difficult to detect with receivers alone. Recently, the idea of deploying noncollocated sources and receivers has emerged as a promising alternative to purely passive sensor fields and to traditional sonar fields composed of collocated sources and receivers. Such a multistatic sonar network carries a number of advantages, but it also brings increased system complexity resulting from its unusual coverage patterns. In this work, we study the problem of optimally positioning active multistatic sonar sources for a point coverage application where all receivers and points of interest are fixed and stationary. Using a definite range sensor model, we formulate exact methods and approximation algorithms for this problem and compare these algorithms via computational experiments. We also examine the performance of these algorithms on a discrete approximation of a continuous area coverage problem and find that they offer a significant improvement over two types of random sensor deployment.     

Clustered coverage orienteering problem of unmanned surface vehicles for water sampling

This study investigates a clustered coverage orienteering problem (CCOP), which is a generalization of the classical orienteering problem. The problem is widely motivated by the emerging unmanned techniques (eg, unmanned surface vehicles and drones) applied to environmental monitoring. Specifically, the unmanned surface vehicles (USVs) are used to monitor reservoir water quality by collecting samples. In the CCOP, the water sampling sites (ie, the nodes) are grouped into clusters, and a minimum number of nodes must be visited in each cluster. With each node representing a certain coverage area of the water, the objective of the CCOP is to monitor as much as possible the total coverage area in one tour of the USV, considering that overlapping areas provide no additional information. An integer programming model is first formulated through a linearization procedure that captures the overlapping feature. A two-stage exact algorithm is proposed to obtain an optimal solution to the problem. The efficiency and effectiveness of the two-stage exact algorithm are demonstrated through experiments on randomly generated instances. The algorithm can effectively solve instances with up to 60 sampling sites.     

数学名题与HPM研究

数学名题对于数学教育和HPM研究都具有重要的价值。法国数学教育家、数学史家史威兹提出,在数学问题配置与求解中可选择历史上不同时期、不同文化的一些数学名题。在此基础上,我们提出了HPM视角下的问题解决教学这一新课题。HPM视角下的问题解决教学侧重于对历史上所用各种数学思想方法进行比较分析,使学生了解不同文化背景中的数学思考方式,其目的在于培养学生数学洞察力,启发数学思想方法,提升数学思维能力,并可在社会历史文化与数学思维的双重醺陶下,获得数学认知活动的文化意义,在数学教育中实践多元文化关怀的理想。     

Scheduling and lot streaming in two‐machine open shops with no‐wait in process

We study the problem of minimizing the makespan in no‐wait two‐machine open shops producing multiple products using lot streaming. In no‐wait open shop scheduling, sublot sizes are necessarily consistent; i.e., they remain the same over all machines. This intractable problem requires finding sublot sizes, a product sequence for each machine, and a machine sequence for each product. We develop a dynamic programming algorithm to generate all the dominant schedule profiles for each product that are required to formulate the open shop problem as a generalized traveling salesman problem. This problem is equivalent to a classical traveling salesman problem with a pseudopolynomial number of cities. We develop and test a computationally efficient heuristic for the open shop problem. Our results indicate that solutions can quickly be found for two machine open shops with up to 50 products. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Flexibility and complexity in periodic distribution problems

In this paper, we explore trade‐offs between operational flexibility and operational complexity in periodic distribution problems. We consider the gains from operational flexibility in terms of vehicle routing costs and customer service benefits, as well as the costs of operational complexity in terms of modeling, solution methods, and implementation challenges for drivers and customers. The period vehicle routing problem (PVRP) is a variation of the classic vehicle routing problem in which delivery routes are constructed for a period of time; the PVRP with service choice (PVRP‐SC) extends the PVRP to allow service (visit) frequency to become a decision of the model. For the periodic distribution problems represented by PVRP and PVRP‐SC, we introduce operational flexibility levers and a set of quantitative measures to evaluate the trade‐offs between flexibility and complexity. We develop a Tabu Search heuristic to incorporate a range of operational flexibility options. We analyze the potential value and the increased operational complexity of the flexibility levers. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

The impact of manufacturer rebates on supply chain profits

Manufacturer rebates are commonly used as price discount tools for attracting end customers. In this study, we consider a two‐stage supply chain with a manufacturer and a retailer, where a single seasonal product faces uncertain and price‐sensitive demand. We characterize the impact of a manufacturer rebate on the expected profits of both the manufacturer and the retailer. We show that unless all of the customers claim the rebate, the rebate always benefits the manufacturer. Our results thus imply that “mail‐in rebates,” where some customers end up not claiming the rebate, particularly when the size of the rebate is relatively small, always benefit the manufacturer. On the other hand, an “instant rebate,” such as the one offered in the automotive industry where every customer redeems the rebate on the spot when he/she purchases a car, does not necessarily benefit the manufacturer. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007