Tardiness Risk at a Steel Mill

A customer who places a tentative order at a steel mill customarily receives a due-date quotation, namely the date by which the mill says that it will ship the order. The steel mill wants the due date to be early enough so that the customer won’t balk (withdraw the order), but late enough so that the probability of tardiness is low. This note obtains expressions for the tardiness probability at a continuous caster steel mill under the assumption that orders for different steel grades arrive as independent grade-dependent renewal processes and the time spent in the melt process is the waiting time in an M/M/1 queue. Some expressions require less stringent assumptions. The model reflects the fact that the melt process can be initiated only after the cumulative tonnage of non-balking unprocessed orders reaches a minimum batch size. This key feature occurs in other process industries such as aluminum and copper casting. 1