A product warranty is an agreement offered by a producer to a consumer to replace or repair a faulty item, or to partially or fully reimburse the consumer in the event of a failure. Warranties are very widespread and serve many purposes, including protection for producer, seller, and consumer. They are used as signals of quality and as elements of marketing strategies. In this study we review the notion of an online convex optimization algorithm and its variations, and apply it in warranty context. We introduce a class of profit functions, which are functions of warranty, and use it to formulate the problem of maximizing the company's profit over time as an online convex optimization problem. We use this formulation to present an approach to setting the warranty based on an online algorithm with low regret. Under a dynamic environment, this algorithm provides a warranty strategy for the company that maximises its profit over time.
The Operations Research Department at the Naval Postgraduate School educates experienced junior military officers in state-of-the-art operations research methods. As part of the educational program all officers go through a standard graduate course on network modeling. Within that course, students complete a class-long network modeling project of a real-world infrastructure system that solidifies their understanding of operations research concepts and moves the learning experience beyond the classroom. Through the project, students abstract their real-world problems into mathematics, repeatedly evaluate the connection between the mathematics and reality, and reason about the model results. The project has educational, re- search, and practical benefits. On occasion, students make discoveries of such significance that we have contacted the infrastructure system operators with briefings on the student analysis results. Some student projects have eventually influenced Department of Homeland Security and Department of Defense policy. We detail what makes the network modeling project work, and how to implement it in other universities.
Nedialko B. Dimitrov is with UT Austin, Sebastian Goll is with UT Austin, Nathaniel Hupert is with the CDC and Weill Cornell Medical College, Babak Pourbohloul is with British Columbia Centre for Disease Control, Lauren Ancel Meyers is with UT Austin and The Santa Fe Institute. ; In 2009, public health agencies across the globe worked to mitigate the impact of the swine-origin influenza A (pH1N1) virus. These efforts included intensified surveillance, social distancing, hygiene measures, and the targeted use of antiviral medications to prevent infection (prophylaxis). In addition, aggressive antiviral treatment was recommended for certain patient subgroups to reduce the severity and duration of symptoms. To assist States and other localities meet these needs, the U.S. Government distributed a quarter of the antiviral medications in the Strategic National Stockpile within weeks of the pandemic's start. However, there are no quantitative models guiding the geo-temporal distribution of the remainder of the Stockpile in relation to pandemic spread or severity. We present a tactical optimization model for distributing this stockpile for treatment of infected cases during the early stages of a pandemic like 2009 pH1N1, prior to the wide availability of a strain-specific vaccine. Our optimization method efficiently searches large sets of intervention strategies applied to a stochastic network model of pandemic influenza transmission within and among U.S. cities. The resulting optimized strategies depend on the transmissability of the virus and postulated rates of antiviral uptake and wastage (through misallocation or loss). Our results suggest that an aggressive community-based antiviral treatment strategy involving early, widespread, pro-rata distribution of antivirals to States can contribute to slowing the transmission of mildly transmissible strains, like pH1N1. For more highly transmissible strains, outcomes of antiviral use are more heavily impacted by choice of distribution intervals, quantities per shipment, and timing of shipments in relation to pandemic spread. This study supports previous modeling results suggesting that appropriate antiviral treatment may be an effective mitigation strategy during the early stages of future influenza pandemics, increasing the need for systematic efforts to optimize distribution strategies and provide tactical guidance for public health policy-makers. ; This work was supported by grants to LM from NIH Models of Infectious Disease Agent Study (MIDAS) (U01-GM087719-01), the James S. McDonnell Foundation, and NSF (DEB-0749097) and grants to BP from CIHR(PTL-97125 and PAP-93425) and the Michael Smith Foundation for Health Research. ; Biological Sciences, School of
The article of record as published may be found at: http://dx.doi.org:10.1371/journal.pone.0016094 ; In 2009, public health agencies across the globe worked to mitigate the impact of the swine-origin influenza, a (pH1N1) virus. There efforts included intensified surveillance, social distancing, hygiene measures, and the targeted use of antiviral medications to prevent infection (prophylaxis). In addition, aggressive antiviral treatment was recommended for certain patient subgroups to reduce the severity and duration of symptoms. To assist States and other localities meet these needs, the U.S. Government distributed a quarter of the anitviral medications in the Strategic National Stockpile within weeks of the pandemic's start. However, there are no quantitative models guiding the geo-temporal distribution of the remainder of the Stockpile in relation to pandemic spread or severity. We present a tactical optimization model for distributing this stockpile for treatment of infected cases during the early stages of a pandemic like 2009 pH1N1, prior to the wide availability of a strain-specific vaccine. Our optimization method efficiently searches large sets of intervention strategies applied to a stochastic network model of pandemic influneza transmission within and among U.S. cities. The resulting optimized strategies depend on the transmissability of the virus and postulated rates of antiviral uptake and wastage (through misallocation or loss). Our results suggest that an aggressive community-based antiviral treatment strategy involving early, widesprerad, pro-rata distribution of antivirals to States can contribute to slowing the transmission of mildly transmissible strains, like pH1N1. For more highly transmissible strains, outcomes of antiviral use are more heavily impacted by choice of distribution intervals, quantities per shipment, and timing of shipments in relation to pandemic spread. This study supports previous modeling results suggesting that appropriate antiviral treatment may be an effective mitigation strategy during the early stages of future influenze pandemics, increasing the need for systematic efforts to optimize distribution strategies and provide tactical guidance for public health policy-makers.
