On ordering problems: a statistical approach

In ordering problems, the goal is to find the optimal order. Each ex-perimental run of an order problem is a permutation of m components. Because m! is typically large, it is necessary to select a subset of the m! sequences. Ex-isting selection methods are based on parametric models. However, it is difficult to determine a good approximate model for an ordering problem before collecting the experimental data. With this in mind, we propose a method for choosing the subset for searching for the optimal order without assuming a prespecified model. The proposed method explores the inherent characteristics of the possible orders by using the distance between the positions of the components. We propose a sys-tematic construction method for selecting a subset with a flexible run size, and also show its optimality. Compared with existing model-based methods, the proposed method is more appropriate when the model choice is not clear a priori.