Graphical methods for Order-of-Addition experiments
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2025 · Volume 87 · Issue 5
Abstract
In an Order-of-Addition (OofA) experiment, the order in whichmcomponents are added to a system influences a response. Although much research has been done on optimal OofA experiments, existing methodologies typically assume that allm!orders are possible. However, in many practical examples, there are directed constraints on the pairwise order of components, making some of them!orders infeasible. These constraints can be represented by a directed acyclic graph (DAG). The goal of the OofA experiment is to find an optimal order, which is equivalent to finding an optimal topological sort of the DAG. A multiplicative algorithm is used to identify approximateϕ-optimal designs for an arbitrary DAG. Simulated annealing (SA) is proposed as a method to identify efficient exact designs. It is shown that the SA designs have very high efficiency relative to the approximateϕ-optimal designs. A general procedure is proposed to search for the optimal order on a DAG given the results of an OofA experiment using two popular models. An application to a sequential job scheduling problem is investigated.
Keywords
design of experiments, graph theory, pairwise ordering model
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