The priority rule that is most consistent with the objective of meeting due dates is slack time per operation. Slack time per operation is a priority rule that assigns a priority index to each job based on the ratio of the remaining slack time to the remaining number of operations. Slack time is the difference between the due date and the expected completion time of a job. A lower ratio means a higher priority, as it indicates that the job has less slack time per operation and is more likely to be late. Slack time per operation is a dynamic priority rule, as it updates the priority index after each operation is completed. Slack time per operation can help minimize the number of tardy jobs and the average tardiness of jobs, as it gives preference to the jobs that are closer to their due dates and have more operations left.

First-come-first-served (FCFS) is not a priority rule that is consistent with the objective of meeting due dates. FCFS is a priority rule that processes jobs in the order of their arrival or release times. FCFS is a simple and fair rule, but it ignores the processing times and due dates of jobs. FCFS can result in poor due date performance, as it can delay urgent or short jobs behind long or non-urgent jobs.

Shortest processing time (SPT) is not a priority rule that is consistent with the objective of meeting due dates. SPT is a priority rule that processes jobs in ascending order of their processing times. SPT is an effective rule for minimizing the average flow time and work-in-process inventory of jobs, as it clears out small jobs quickly and reduces congestion in the system. However, SPT does not consider the due dates of jobs, and it can make long or urgent jobs late.

Fewest operations remaining is not a priority rule that is consistent with the objective of meeting due dates. Fewest operations remaining is a priority rule that processes jobs in ascending order of their remaining number of operations. Fewest operations remaining is a rule that can reduce the variability and complexity of jobs, as it tends to complete jobs faster and reduce their flow times. However, fewest operations remaining does not take into account the slack times or due dates of jobs, and it can make urgent or short jobs late.

References := Priority Rules - Tripod, Dispatching rules - Oxford Reference, Sequencing Rules and Due-Date Assignments in a Job Shop - JSTOR