A Characterization of the Rau Class of Sequential Problems

Rau (Rau, J. G. 1971. Minimizing a function of permutations of n integers. Oper. Res.19 237–240.) presents a class of sequential problems including two important special cases from the search literature. Rau's class is presented there in terms of conditions that certain functions must satisfy. Here those conditions are reformulated to show what Rau's restrictions imply. A subclass of Rau's class is discussed that contains both of the important special cases, and which was used for further analysis in the paper of Kadane and Simon (Kadane, J. B., H. A. Simon. 1977. Optimal strategies for a class of constrained sequential problems. Ann. Statist.5 237–255.).