تخمین یادگیری چند سطحی و فراموشی توسط یک مدل متراکم تک سطحی
Abstract
1- Introduction
2- Multiple-level learning and forgetting models
3- Data generation for numerical experiments
4- Forecasting accuracy of single-level approximation
5- Conclusions
References
Abstract
In a large organization, learning and forgetting may occur at different rates at the various levels of the organization. Recently, it has been shown that a multiple-level learning model works effectively for the accurate measurement and prediction of learning and forgetting in such an organization. Due to a lack of sufficiently detailed data at each organizational level, however, it is often necessary to use the conventional aggregated single-level model to estimate the learning and forgetting of the entire organization. In such an approximation, the potentially different impacts of learning and forgetting at different levels of the organization is not explicitly considered. This paper investigates the accuracy of this single-level approximation. The single-level approximation, of course, cannot be used to explain how the learning and forgetting occur at various levels of an organization. However, numerical experiments based upon the Liberty ships dataset show that the single-level approximation can provide surprisingly good estimates of the organization’s key performance measure, e.g., production time per unit. It can therefore yield good estimates of the learning and forgetting rates aggregated for the entire organization, and these estimates can be used to compare the performance of one organization to another. The single-level approximation is shown to perform particularly well when the data exhibit a large amount of dispersion, the number of units used for fitting is large, the learning occurs slowly, or the forgetting rate is high.
Introduction
Organizational learning is a well-known phenomenon evidenced by numerous empirical studies. Since Wright’s (1936) application of the log-linear learning curve function to aircraft manufacturing, many different forms of learning curve functions have been proposed and examined in various types of processes across different industries. Yelle (1979) provided an extensive survey of the classical learning curve functions published in the management and engineering literature. Jaber (2011) provided a collection of recent developments in learning curve models and their applications in the area of management, economics, engineering, and psychology. Nembhard and Uzumeri (2000) empirically compared various functional forms of the learning curve. Balasubramanian and Lieberman (2011) estimated learning curve rates in over 250 U.S. industries, finding a wide range of rates between and within industries. More recently, Grosse, Glock, Christoph, and Müller (2015) fit eleven different learning curve functions to over a hundred datasets to determine which functions obtained the best fit for different types of data. For many industries, learning models have been incorporated into broader planning models in pursuit of better resource allocation decisions (Grosse, Glock, & Christoph, 2015a,2015b; Nadeau, Kar, Roth, & Kirchain, 2010; Nembhard & Bentefouet, 2015; Van Peteghem & Van Houcke, 2015). Given the large variations in learning rates across and within industries, a key element of successful planning is determining an accurate estimate of future learning. The reverse of learning, i.e., forgetting, has also been recognized at the organizational level and incorporated into learning curve functions. Argote, Beckman, and Epple (1990) developed a discrete time forgetting model and applied it to the construction of Liberty ships during World War II. Other authors applied similar models to other industries (Benkard 2000; Darr, Argote, & Epple, 1995; Epple, Argote, & Murphy, 1996). Using a new, disaggregated dataset for the Liberty ship data, Thompson (2007) developed a forgetting model in which knowledge was assumed to depreciate continuously over time.