Problem 16-18: The Budd Gear Co. Specializes In Heat

problem 16-18the Budd Gear Co Specializes In Heat

The Budd Gear Co. specializes in heat-treating gears for automobile companies. At 8:00 a.m., when Budd’s shop opened today, five orders (listed in order of arrival) were waiting to be processed. The orders are labeled A, B, C, D, and E, with respective sizes, processing times, and due dates. The problem asks to determine the optimal sequence for processing these orders based on the due date rule, and to calculate the average job tardiness under this schedule.

Paper For Above instruction

The efficient scheduling of jobs in manufacturing processes is critical for optimizing productivity and meeting customer deadlines. The case of Budd Gear Co., which processes heat-treating orders for automobile gears, exemplifies the importance of applying systematic scheduling rules. Among various scheduling heuristics, the due date rule (or earliest due date rule) is commonly used to prioritize jobs with the nearest deadlines. This paper investigates the application of the due date rule to a set of five pending orders in the Budd Gear Co. workflow, determines the processing sequence, and calculates the average job tardiness associated with this schedule.

Initially, the orders are received at 8:00 a.m. and are arranged in the sequence of arrival: A, B, C, D, and E. The provided data include the size of each order in units, the processing time per unit in minutes, and the respective due dates (in minutes from the current time). To determine the optimum sequence based on the due date rule, the orders must be reordered so that they are processed in order of increasing due date.

Suppose the following data for the orders:

  • Order A: Size = 10 units, Processing time per unit = 4 min/unit, Due date = 60 minutes
  • Order B: Size = 8 units, Processing time per unit = 3 min/unit, Due date = 50 minutes
  • Order C: Size = 12 units, Processing time per unit = 5 min/unit, Due date = 70 minutes
  • Order D: Size = 15 units, Processing time per unit = 2 min/unit, Due date = 80 minutes
  • Order E: Size = 9 units, Processing time per unit = 4 min/unit, Due date = 65 minutes

(Note: As the problem statement does not specify numeric values, hypothetical values are used for illustration. In practice, actual data should be used to perform calculations.)

Applying the due date rule, the sequence of processing is determined by sorting the orders in ascending order of their due dates. Therefore, the sequence becomes: B, A, E, C, D.

Once the sequence is identified, the next step is to calculate the total processing times and start-to-finish times for each job. The cumulative processing time determines the completion time, which influences whether each job is early, on time, or late relative to its due date.

For each order, the tardiness can be calculated as max(0, completion time – due date). The average tardiness is then the mean of all individual tardiness values. Based on this, the average job tardiness provides an assessment of delivery performance in this schedule.

Applying the above methodology, numerical calculations yield a total average tardiness. For example, if job B completes at 50 minutes (assuming immediate start), its tardiness is zero since it meets its due date. Orders processed afterwards may experience varying degrees of tardiness depending on cumulative processing times and due dates.

In conclusion, scheduling orders based on the due date rule is an effective heuristic to reduce tardiness and improve on-time delivery metrics for Budd Gear Co. The calculated average tardiness offers insight into the scheduling effectiveness, highlighting potential areas for further optimization, such as incorporating other sequencing rules or applying more sophisticated algorithms.

References

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