This paper introduces a multistage stochastic mixed-integer programming model designed for a goal-based investing (GBI) problem, incorporating the option of goal postponement. Our model allows individuals to defer the...
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This paper introduces a multistage stochastic mixed-integer programming model designed for a goal-based investing (GBI) problem, incorporating the option of goal postponement. Our model allows individuals to defer the fulfillment of their goals within a predefined timeframe. We emphasize the advantages of incorporating goal postponement into the GBI framework, including its ability to accommodate stage-preference ambiguity, address mistiming issues, and enhance utility for individuals. Theoretical results of a GBI problem with goal postponement are presented, and to tackle large-scale multistage GBI problems, we employ a decomposition algorithm known as stochastic dual dynamic integerprogramming (SDDiP). Numerical results demonstrate that the option to postpone a goal proves especially advantageous when goals are exposed to high inflation rates, and SDDiP emerges as a computationally efficient approach for handling large-scale GBI problems.
Influenza (flu) is a serious public health concern. The first line of defense is the flu shot, whose composition is updated annually to adjust for frequent mutations of the circulating viruses. The World Health Organi...
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Influenza (flu) is a serious public health concern. The first line of defense is the flu shot, whose composition is updated annually to adjust for frequent mutations of the circulating viruses. The World Health Organization recommends which strains to include in the flu shot based on global surveillance. Vaccine manufacturers produce trivalent and quadrivalent flu shots. The design of the flu shot, however, affects the manufacturers' capacity and profit. In return, production decisions of the manufacturers affect the societal vaccination benefit by determining coverage and timely availability. We model this two-level hierarchy using a bilevel multistagestochasticmixed-integer program. Calibrated with publicly available data, our model integrates the flu shot composition and manufacturing in a stochastic and dynamic environment. We derive a branch-and-price algorithm to find the global optimal solution. We also propose an effective heuristic to provide the public health planners with a decision aid tool. Finally, we perform numerical experiments to answer important public health policy questions and to quantify the impact of the proposed modeling extensions. A major conclusion of our work is that the vaccine strain of a category that is not expected to be very prevalent and/or that is unlikely to drift in the upcoming season should be selected as early as possible, especially when the selections for other strain categories have to be postponed to improve the flu shot design.
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