Technical Note—There are No Undiscovered Priority Index Sequencing Rules for Minimizing Total Delay Costs

There are two known priority index rules for minimizing total delay costs in sequencing a finite group of independent tasks on a single processor. One of these rules applies when delay costs are linear and the other when they are restricted to a class of exponential functions. We prove that there are no other classes of delay cost function for which a simple priority index rule is optimal.