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There are two major ways of selling impressions in display advertising. They are either sold in spot through auction mechanisms or in advance via guaranteed contracts. The former has achieved a significant automation via real-time bidding (RTB); however, the latter is still mainly done over the counter through direct sales. This paper proposes a mathematical model that allocates and prices the future impressions between real-time auctions and guaranteed contracts. Under conventional economic assumptions, our model shows that the two ways can be seamless combined programmatically and the publisher's revenue can be maximized via price discrimination and optimal allocation. We consider advertisers are risk-averse, and they would be willing to purchase guaranteed impressions if the total costs are less than their private values. We also consider that an advertiser's purchase behavior can be affected by both the guaranteed price and the time interval between the purchase time and the impression delivery date. Our solution suggests an optimal percentage of future impressions to sell in advance and provides an explicit formula to calculate at what prices to sell. We find that the optimal guaranteed prices are dynamic and are non-decreasing over time. We evaluate our method with RTB datasets and find that the model adopts different strategies in allocation and pricing according to the level of competition. From the experiments we find that, in a less competitive market, lower prices of the guaranteed contracts will encourage the purchase in advance and the revenue gain is mainly contributed by the increased competition in future RTB. In a highly competitive market, advertisers are more willing to purchase the guaranteed contracts and thus higher prices are expected. The revenue gain is largely contributed by the guaranteed selling.

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One trend in the recent healthcare transformations is people are encouraged to monitor and manage their health based on their daily diets and physical activity habits. However, much attention of the use of operational research and analytical models in healthcare has been paid to the systematic level such as country or regional policy making or organisational issues. This paper proposes a model concerned with healthcare analytics at the individual level, which can predict human physical activity status from sequential lifelogging data collected from wearable sensors. The model has a two-stage hybrid structure (in short, MOGP-HMM) -a multi-objective genetic programming (MOGP) algorithm in the first stage to reduce the dimensions of lifelogging data and a hidden Markov model (HMM) in the second stage for activity status prediction over time. It can be used as a decision support tool to provide real-time monitoring, statistical analysis and personalized advice to individuals, encouraging positive attitudes towards healthy lifestyles. We validate the model with the real data collected from a group of participants in the UK, and compare it with other popular two-stage hybrid models. Our experimental results show that the MOGP-HMM can achieve comparable performance. To the best of our knowledge, this is the very first study that uses the MOGP in the hybrid two-stage structure for individuals' activity status prediction. It fits seamlessly with the current trend in the UK healthcare transformation of patient empowerment as well as contributing to a strategic development for more efficient and cost-effective provision of healthcare.

In sponsored search, advertisement (abbreviated ad) slots are usually sold by a search engine to an advertiser through an auction mechanism in which advertisers bid on keywords. In theory, auction mechanisms have many desirable economic properties. However, keyword auctions have a number of limitations including: the uncertainty in payment prices for advertisers; the volatility in the search engine's revenue; and the weak loyalty between advertiser and search engine. In this paper we propose a special ad option that alleviates these problems. In our proposal, an advertiser can purchase an option from a search engine in advance by paying an upfront fee, known as the option price. He then has the right, but no obligation, to purchase among the pre-specified set of keywords at the fixed cost-per-clicks (CPCs) for a specified number of clicks in a specified period of time. The proposed option is closely related to a special exotic option in finance that contains multiple underlying assets (multi-keyword) and is also multi-exercisable (multi-click). This novel structure has many benefits: advertisers can have reduced uncertainty in advertising; the search engine can improve the advertisers' loyalty as well as obtain a stable and increased expected revenue over time. Since the proposed ad option can be implemented in conjunction with the existing keyword auctions, the option price and corresponding fixed CPCs must be set such that there is no arbitrage between the two markets. Option pricing methods are discussed and our experimental results validate the development. Compared to keyword auctions, a search engine can have an increased expected revenue by selling an ad option.