a b s t r a c tMotivated by an industry example, we develop a mathematical framework to address the inventory replenishment and capacity planning problem for a closed-loop supply system with random returns. The provider needs to deliver new or refurbished products to a group of clients under a fixed cyclic schedule, and also collects back a random portion of the used products in the subsequent delivery cycle for refurbishment. We first address the product replenishment strategy, in which only a random portion of the delivered products will be returned for refurbishment and the supplier must regularly purchase new products to replace the lost units. We then analyze the capacity decision problem where the provider uses his facility to refurbish the returned products for reuse, and the provider could incur extra refurbishing cost to handle the returned product at the end of each cycle due to insufficient capacity. Our models provide a simple decision support tool for making effective replenishment and capacity decisions in managing such a closed-loop supply system.

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Policymakers often make decisions involving human-mortality risks and monetary outcomes that span across different time periods and horizons. Many projects or environmental-regulation policies involving risks to life, such as toxic exposures, are experienced over time. The preferences of individuals on lives lost or saved over time should be understood to implement effective policies. Using a within-subject survey design, we investigated our participants’ elicited preferences (in the form of ratings) for sequences of lives saved or lost over time at the participant level. The design of our study allowed us to directly observe the possible preference patterns of negative time discounting or a preference for spreading from the responses. Additionally, we embedded factors associated with three other prevalent anomalies of intertemporal choice (gain/loss asymmetry, short/long asymmetry, and the absolute magnitude effect) into our study for control. We find that our participants exhibit three of the anomalies: preference for spreading, absolute magnitude effect, and short/long-term asymmetry. Furthermore, fitting the data collected, Loewenstein and Prelec’s model for the valuation of sequences of outcomes allowed for a more thorough understanding of the factors influencing the individual participants’ preferences. Based on the results, the standard discounting model does not accurately reflect the value that some people place on sequences of mortality outcomes. Preferences for uniform sequences should be considered in policymaking rather than applying the standard discounting model.

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