Variability scaling and capacity planning in Covid-19 pandemic

Capacity planning is a very important global challenge in the face of Covid-19 pandemic.In order to hedge against the fluctuations in the random demand and to take advantage of risk pooling effect,one needs to have a good understanding of the variabilities in the demand of resources.However,Covid-19 predictive models that are widely used in capacity planning typically often predict the mean values of the demands(often through the predictions of the mean values of the confirmed cases and deaths)in both the temporal and spatial dimensions.They seldom provide trustworthy prediction or estimation of demand variabilities,and therefore,are insufficient for proper capacity planning.Motivated by the literature on variability scaling in the areas of physics and biology,we discovered that in the Covid-19 pandemic,both the confirmed cases and deaths exhibit a common variability scaling law between the average of the demand μ and its standard deviationσ,that is,σ ∝ μ^(β),where the scaling parameterμis typically in the range of 0.65 to 1,and the scaling law exists in both the temporal and spatial dimensions.Based on the mechanism of contagious diseases,we further build a stylized network model to explain the variability scaling phenomena.We finally provide simple models that may be used for capacity planning in both temporal and spatial dimensions,with only the predicted mean demand values from typical Covid-19 predictive models and the standard deviations of the demands derived from the variability scaling law.

Review on ranking and selection: A new perspective

In this paper,we briefly review the development of ranking and selection(R&S)in the past 70 years,especially the theoretical achievements and practical applications in the past 20 years.Different from the frequentist and Bayesian classifications adopted by Kim and Nelson(2006b)and Chick(2006)in their review articles,we categorize existing R&S procedures into fixed-precision and fixed-budget procedures,as in Hunter and Nelson(2017).We show that these two categories of procedures essentially differ in the underlying methodological formulations,i.e.,they are built on hypothesis testing and dynamic programming,respectively.In light of this variation,we review in detail some well-known procedures in the literature and show how they fit into these two formulations.In addition,we discuss the use of R&S procedures in solving various practical problems and propose what we think are the important research questions in the field.

Gradient and Hessian of Joint Probability Function with Applications on Chance-Constrained Programs

Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them.We then design a Monte Carlo algorithm,based on these estimators,to solve chance-constrained programs.Our numerical study shows that the algorithm works well,especially only with the gradient estimators.