Applicability of a static model in a dynamic context in group-screening decision making

When good items have to be separated from bad ones, significant reduction in costs can be achieved by screening the items in groups rather than individually. In this regard, the selection of an efficient group size is crucial. For several decades, a model from Robert Dorfman was the de facto standard to determine the optimal group size. However, more recently, it has been pointed out that the model from Dorfman is a static one, i.e., it postulates that a predetermined large number of items have to be screened that are all present from the beginning, whereas the practical context is usually not static but dynamic: items are not all present initially, they arrive at random moments in time, and in groups of variable sizes.In this paper, we investigate under which circumstances the optimal group size in the static model from Dorfman remains correct in a dynamic context. This is of crucial importance since, although dynamic models and analyses are available now, these are much harder to implement and the processing time is slow due to the numerical work that is involved, such as repeatedly calculating zeroes of functions and solving sets of equations. Static models are much easier to use, and therefore it is important for practitioners to comprehend when they can rely on static results in a dynamic context.The second major contribution of this paper is that we develop efficient heuristics and algorithms for those cases in which results from static models cannot be relied on. These lead to a tremendous reduction in time complexity.