Publication database

We study sampling from a finite population without replacement when seeking an extreme (lowest or highest) value. An example is a buyer searching for the lowest price. Itis well known that there are decreasing returns to sampling from continuous populations: the expected minimum is a decreasing and discretely convex function of the sample size. We show that is true for sampling without replacement from a finite population. We also give a simple sufficient condition on population values for the properties to hold for other order statistics.

With permission of Elsevier

Problem definition: Vaccination campaigns often face significant operational challenges such as limited stockpiles, vaccine delivery delays, and constrained administration capacity. In such contexts fractional-dose vaccines have been described in the medical literature as a possible strategy because their efficacy reduction is typically not commensurate with the level of fractionation, allowing greater population coverage. We seek to determine the optimal use and potential benefits of a fractionated vaccine dose with lower and more uncertain efficacy, given the specific supply constraints faced by a country.
Methodology: We employ a Susceptible-Infected-Recovered (SIR) epidemic model integrating vaccination with full- and fractional-doses over time. We embed it within a deterministic optimal control model aimed at identifying vaccination policies that minimize total infections during an epidemic, given operational constraints restricting the stockpile, delivery rate and administration of vaccines. Using a statistical approach described in the clinical literature for estimating the uncertainty around fractional-dose efficacy, we conduct two application case-studies grounded in real-world scenarios.
Results: Our theoretical analysis provides an intuitive characterization of the optimal vaccination policy which, depending on the epidemic and operational parameters, may utilize a combination of full- and fractional-dose vaccines, either simultaneously or sequentially. We also examine simpler policies that employ a single vaccine dosage throughout the epidemic. We conclude that, while these single-dose policies can often be almost as effective as the optimal policy in averting infections, they are not as robust to the uncertainty affecting fractional-dose vaccine efficacy.
Managerial implications: Fractional-dose vaccines, used either alone or in conjunction with full-dose vaccines, present an opportunity to significantly reduce infections during an epidemic in resource-constrained settings. The proportion of fractional-dose vaccines relative to full-dose vaccines in a campaign should generally increase with the maximum vaccine administration rate and decrease with the total antigen stockpile available.

© 2025, INFORMS

We study the pricing of homogeneous products sold to customers who consider different sets of suppliers. We identify prices that are stable in the sense that no firm wishes to undercut a rival or to raise its price when rivals are able to respond by offering special deals. We derive predictionsforstable and disperse prices acrossseveral price-consideration specifications, and we contrast the implications with those of conventional approaches.

[This paper supersedes working papers Stable Price Dispersion (2024) and A Theory of Stable Price Dispersion (2019).]

© 1999-2026 John Wiley & Sons, Inc