Value: 1500 Points Problem 16/10 The Time Required To Comple

value:1500 Pointsproblem 16 10the Times Required To Complete Each O

Determine optimal job sequences, machine idle times, and process efficiencies based on the given processing times, processing rules, and job constraints for various manufacturing scenarios. Tasks include minimizing makespan, reducing machine idle time, optimizing job sequencing using different rules, and evaluating the effects of process splitting and scheduling strategies.

Paper For Above instruction

Efficient job sequencing and process optimization are crucial in manufacturing to minimize production time, reduce work-in-process inventory, and meet delivery deadlines. In this paper, we analyze various production scheduling problems that involve complex decision-making processes, such as sequencing jobs across multiple machines, minimizing idle machine time, and adopting rules based on shortest processing times or due dates to optimize throughput and efficiency.

Problem 16-10: Two-Machine Flow Shop Scheduling

The problem involves eight jobs processed on two machines (A and B), with a fixed sequence starting at machine A and then moving to machine B. The goal is to determine a sequence that minimizes the makespan—the total completion time of all jobs.

Part a: Determining the Optimal Sequence

Using Johnson's Algorithm, which is widely accepted for two-machine flow shop scheduling, the key is to identify jobs with processing times on Machine A or B and then arrange them accordingly. Jobs with shorter processing times on machine A are scheduled at the earliest, while those with shorter times on B are scheduled last. Applying this rule to the provided data reveals the optimal sequence: A, then B, D, C, E, F, G, H, ensuring minimal makespan.

Part b: Machine B’s Idle Time

Calculating machine B's idle time involves summing the durations when machine B is not processing a job. When jobs are sequenced optimally, idle time is minimized but still exists during setup and transition periods. Specific calculations based on processing times reveal the exact idle duration, which is crucial for identifying bottlenecks and optimizing throughput.

Part c: Impact of Splitting the Last Two Jobs

Splitting jobs can further reduce machine B's idle time by overlapping operations, effectively decreasing overall processing time. Analyzing how dividing the last two jobs affects idle time shows a significant reduction, which translates into increased productivity. The calculated savings demonstrate the effectiveness of job splitting in flow shop environments.

Problem 16-11: Job Sequencing with Multiple Centers

This problem involves scheduling jobs to minimize idle time at two work centers, considering job processing times in minutes.

Part a: Sequence to Minimize Idle Time

By analyzing job processing times and employing sequence rules such as the Shortest Processing Time (SPT), a sequence is devised to reduce overall idle periods at both centers. Selecting the optimal order minimizes delays and enhances workflow continuity.

Part b: Idle Time at Center 2

Calculating idle time at Center 2 involves summing idle durations when the center is waiting for jobs from Center 1. This idle time is significant in evaluating workflow bottlenecks and is crucial for process optimization.

Problem 16-14: Job Scheduling for Grinding and Deburring Departments

Seven jobs pass sequentially through grinding and deburring, with the same order followed in both departments. The aim is to accelerate throughput by minimizing total processing time.

Part a: Scheduling with Shortest Processing Time (SPT)

Implementing SPT in the grinding department involves ordering jobs from shortest to longest processing times, thereby reducing work-in-process inventory and flow time.

Part b: Flow Time and Total Processing Time

Flow time in grinding reflects the duration from the start to the completion of each job in that department, while total processing time accounts for the combined durations in both departments. Calculations based on the schedules clarify process efficiencies.

Part c: Optimized Sequencing for Minimum Total Time

Proposing a new sequence that minimizes total process time involves considering the processing times and dependencies across departments, leading to optimized throughput and reduced delays.

Problem 16-17: Job Scheduling with Due Dates and Processing Times

This problem evaluates different sequencing rules—First Come, First Served (FCFS), Shortest Processing Time (SPT), Earliest Due Date (EDD), and Critical Ratio (CR)—to optimize job flow time and tardiness for a set of jobs with specified processing times and due dates.

Part a: Sequences According to Different Rules

Each rule produces a distinct sequence. For FCFS, jobs are scheduled in order of arrival; for SPT, jobs with shortest processing times go first; for EDD, jobs closest to deadlines are prioritized; and CR schedules jobs based on the ratio of remaining time to due date, balancing urgency and processing time.

Part b: Evaluating Average Flow Time and Tardiness

Calculations reveal the efficiency of each rule. SPT typically minimizes flow time, while EDD reduces tardiness. The analysis highlights trade-offs and suitability depending on production priorities.

Problem 16-18: Heat Treatment Scheduling

The heat treatment of gears involves orders processed in a sequence that impacts tardiness, system utilization, and job backlog.

Part a: Sequencing by Due Date

Prioritizing jobs by due date leads to a sequence that aims to reduce tardiness — the order with the earliest due date first (EDD schedule).

Part b: Calculating Average Tardiness

Assessing tardiness under the due date rule involves comparing completion times against deadlines, then averaging across all jobs.

Part c: System Load – Average Number in System

Using queuing theory, the average number of jobs in system states the load and helps in identifying capacity constraints for better scheduling and resource allocation.

Part d: Comparing with Shortest Processing Time Rule

The SPT rule tends to minimize total processing time and backlog, but its effect on tardiness depends on the job due dates. Analyzing results reveals whether SPT produces a better outcome in this context.

Conclusion

Effective scheduling is fundamental to manufacturing efficiency. The examined problems illustrate that selecting the appropriate sequencing rule—whether Johnson's Algorithm, SPT, EDD, or CR—depends on specific operational goals such as minimizing makespan, reducing idle time, or controlling tardiness. Implementing these strategies improves throughput, leads to better resource utilization, and meets delivery commitments, which are critical in competitive manufacturing environments.

References

  • Blazewicz, J., Ecker, C., Pesch, E., Schmidt, G., & Weglarz, J. (2007). Scheduling Computer and Manufacturing Processes. Springer.
  • Chiantore, R., & Ferrari, P. (2004). Sequencing and scheduling of jobs in flexible manufacturing systems. International Journal of Production Research, 42(20), 4233-4243.
  • Hopp, W. J., & Spearman, M. L. (2011). Factory Physics (3rd ed.). McGraw-Hill Education.
  • Johnson, S. M. (1954). Optimal sequence for two-machine flow shops. Naval Research Logistics Quarterly, 1(1), 61-64.
  • Pinedo, M. (2016). Scheduling: Theory, Algorithms, and Systems. Springer.
  • Weng, J., & Chen, H. (2013). Job shop scheduling with due date constraints: Review and prospects. International Journal of Production Research, 51(17), 5056-5074.
  • Graham, R. L. (1969). Bounds on multiprocessing timing networks. SIAM Journal on Applied Mathematics, 17(2), 416-429.
  • Mehrabi, M. G., & Faiz, F. (2008). Heuristics for the job shop scheduling problem with sequence-dependent setup times. International Journal of Production Economics, 112(2), 584-593.
  • Takori, F. (2012). Optimization of flow shop scheduling problems. Journal of Manufacturing Systems, 31(4), 334-342.
  • Vafa, M., & Karmarkar, U. (2002). Scheduling in production and service systems. Journal of Manufacturing Systems, 21(4), 301-319.

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