Staffing under Taylor's Law: A Unifying Framework for Bridging Square-root and Linear Safety Rules

Staffing rules serve as an essential management tool in service industries to attain target service levels. Traditionally, the square-root safety rule, based on the Poisson arrival assumption, has been commonly used. However, empirical findings suggest that arrival processes often exhibit an ``over-dispersion'' phenomenon, in which the variance of the arrival exceeds the mean. In this paper, we develop a new doubly stochastic Poisson process model to capture a significant dispersion scaling law, known as Taylor's law, showing that the variance is a power function of the mean. We further examine how over-dispersion affects staffing, providing a closed-form staffing formula to ensure a desired service level. Interestingly, the additional staffing level beyond the nominal load is a power function of the nominal load, with the power exponent lying between $1/2$ (the square-root safety rule) and $1$ (the linear safety rule), depending on the degree of over-dispersion. Simulation studies and a large-scale call center case study indicate that our staffing rule outperforms classical alternatives.Comment: 55 page

Learning to Simulate: Generative Metamodeling via Quantile Regression

Stochastic simulation models, while effective in capturing the dynamics of complex systems, are often too slow to run for real-time decision-making. Metamodeling techniques are widely used to learn the relationship between a summary statistic of the outputs (e.g., the mean or quantile) and the inputs of the simulator, so that it can be used in real time. However, this methodology requires the knowledge of an appropriate summary statistic in advance, making it inflexible for many practical situations. In this paper, we propose a new metamodeling concept, called generative metamodeling, which aims to construct a "fast simulator of the simulator". This technique can generate random outputs substantially faster than the original simulation model, while retaining an approximately equal conditional distribution given the same inputs. Once constructed, a generative metamodel can instantaneously generate a large amount of random outputs as soon as the inputs are specified, thereby facilitating the immediate computation of any summary statistic for real-time decision-making. Furthermore, we propose a new algorithm -- quantile-regression-based generative metamodeling (QRGMM) -- and study its convergence and rate of convergence. Extensive numerical experiments are conducted to investigate the empirical performance of QRGMM, compare it with other state-of-the-art generative algorithms, and demonstrate its usefulness in practical real-time decision-making.Comment: Main body: 36 pages, 7 figures; supplemental material: 12 page

Virtual Group Learning Effectiveness via eLearning Mediums

Online learning provides the potential for more differentiated, integrated, and open learning environments to solve team project assignments. We argue that although it is feasible to increase information richness via adopting multimedia technologies, the effectiveness to promote interpersonal skills, critical thinking, and cognitive learning processes via virtual group discussion is uncertain. To substantiate the argument, we invited 156 subjects, divided into 46 groups, to resolve decision- and intellective-tasks in text-messaging and audio-conferencing e-learning environments. A pedagogical interpretation of how we can use these two e-learning systems to improve effectiveness for group-based tasks was posited

FEE-BASED ONLINE SERVICES: EXPLORING CONSUMERS\u27 WILLINGNESS TO PAY

Many online service businesses are beginning to charge fees for services that they used to provide for free. It is unclear whether consumers are ready to embrace this practice. This study explores consumer attitudes toward fee-based online services. The results of the study indicate that consumers\u27 willingness to pay for online services is likely to be influenced by their perceived value of convenience these services provide, and by the extent to which they utilize these services. While consumers appear more willing to pay for services that are qualitatively better than free services, there is also indication that the belief remains strong among many that online services that were free in the past should remain free