We explore the implications of consistency and monotonicity in sequencing problems. We first identify all rules satisfying Pareto indifference, individual rationality from random arrival, and consistency. Next, we ask whether there is a rule satisfying the three axioms together with either one of two monotonicity requirements, time monotonicity and cost monotonicity. As it turns out, the minimal transfer rule is the only rule satisfying Pareto indifference, individual rationality from random arrival, consistency together with either time monotonicity or cost monotonicity. We also investigate how the maximal transfer rule responds to changes in the service time and waiting cost.
