What dispatching rule minimizes average cycle time for a deterministic single machine? What rule minimizes maximum tardiness? How can one easily check to see if a schedule exists for which there are no tardy jobs?

Understanding the concept of average cycle time is crucial when optimizing production systems. It represents the average time taken from the start of one job to the start of the next. This metric is particularly important as it gives manufacturers and managers insights into production efficiency and helps to identify bottlenecks.

For instance, suppose you have a single machine and a set of jobs. Each job takes a different amount of time to process. To optimize your schedule, you aim to minimize the average time each job spends in the system, from its beginning to its end. A key dispatching rule is the Shortest Processing Time (SPT) rule, which sequences jobs by their processing lengths, starting with the shortest. This method often leads to a minimized average cycle time, enhancing overall productivity.

Maximum tardiness is the longest delay experienced by any job past its due date within a set of jobs being processed. This measure is a critical component of effective scheduling as it reflects the delay in delivering products to customers. High tardiness can lead to customer dissatisfaction and contractual penalties.

To minimize the impact of maximum tardiness, the Earliest Due Date (EDD) rule is commonly applied. By scheduling jobs in ascending order of their due dates, the EDD approach prioritizes those jobs that need to be completed sooner, thus reducing the likelihood of incurring significant delays. It's a cornerstone of due-date-related performance optimization in job scheduling scenarios.

The Shortest Processing Time (SPT) dispatching rule is a simple yet powerful technique in operations management. It dictates that a set of jobs should be ordered and executed based on the amount of time they require to be completed, starting with the one with the smallest time requirement.

Applying the SPT rule has several benefits, such as reducing the average cycle time, which means jobs, on average, are completed faster. It also minimizes the amount of time a job spends in the queue waiting to be processed and generally improves the throughput of a system. An added advantage is its ease of implementation since it only requires knowledge of the processing times of jobs.

The Earliest Due Date (EDD) rule is a scheduling strategy focused on priorities based on due dates. The main idea is that jobs with the nearest due dates are addressed first, regardless of how long they will take to complete.

Implementing EDD can significantly reduce the maximum tardiness across all jobs, as it ensures that imminent deadlines are met first. However, while the EDD rule is excellent for managing due dates, it's important to note that this strategy does not typically minimize the average cycle time. For checking the existence of a schedule with no tardy jobs, sequencing through EDD and then reviewing for any delayed jobs provides a straightforward verification method.