Designing discrete sequential tests via mixed integer programming

We show that the optimal design of non-randomized discrete sequential tests, i.e., tests whose test statistics take on only a countable number of states, can be modeled as a mixed integer linear problem. This is done by reformulating the difference equations describing the random walk on the integer lattice in terms of linear mixed integer constraints. We outline the general procedure and give a simple example to show how the proposed method can be used in practice.