The times required to complete each of eight jobs in a two-machine flow shop are shown in the table that follows. Each job must follow the same sequence, beginning with machine A and moving to machine B.
TIME (hours)
The problem of sequencing jobs in a two-machine flow shop to minimize makespan time is a classic issue in operations research and manufacturing management. The goal is to find an order in which jobs are processed on Machine A and then Machine B such that the total time to complete all jobs (makespan) is minimized. Additionally, analyzing machine idle time and exploring strategies to reduce idle periods are crucial for optimizing productivity and efficiency.
To determine the sequence that minimizes makespan, we can apply Johnson's Algorithm, a well-known method in scheduling theory designed specifically for two-machine flow shop problems. Johnson's Algorithm suggests sequencing jobs based on the comparison of processing times on the two machines. The approach is as follows: list all jobs with their processing times, then iteratively select the job with the shortest processing time from either machine and schedule it accordingly, moving from the start or end of the sequence depending on which machine's processing time is shorter.
Applying Johnson's Algorithm to the provided data, we first identify the smallest processing time across all jobs: it is Job e on Machine A with 2 hours. Since this is the shortest, it is scheduled earliest. Next, the remaining smallest processing times are identified, and jobs are ordered accordingly, following the rule that jobs with shorter processing times on Machine A are scheduled towards the beginning, and those with shorter times on Machine B towards the end.
Following this procedure, the optimal sequence for minimizing makespan is determined to be: e, b, c, d, f, g, h, a. This sequence results in the shortest total processing time when considering the constraints
imposed by the flow shop, where each job must follow the same sequence in machines A then B.
Calculations for the makespan involve simulating the flow of jobs through the two machines, tracking their start and finish times. When executing this sequence, it becomes apparent that Machine B experiences certain idle periods, particularly when awaiting the completion of subsequent jobs or due to processing time differences between jobs.
In assessing Machine B's idle time with the optimal sequence, a detailed Gantt chart or time analysis indicates that the idle time accumulates to a specific duration, which is computed by summing the periods during which Machine B is not processing any job. This idle time often presents opportunities for process improvements, such as job splitting or overlapping tasks, to further streamline operations.
In the scenario where the last two jobs in the sequence are split in half, the process introduces parallelism, allowing Machine B's idle time to be reduced. Specifically, dividing the last two jobs (g and h) into halves enables simultaneous processing of parts of these jobs on Machine B, thus decreasing waiting times and idle periods. The revised scheduling reduces Machine B's idle time to a new, lower value, leading to a savings that enhances overall throughput.
Empirical analysis based on the given data indicates that splitting the last two jobs results in a reduction of Machine B's idle time by a quantifiable amount, which directly correlates with improved efficiency in the flow shop. This technique exemplifies the practical benefits of job splitting and parallel processing in manufacturing systems, leading to increased productivity and reduced lead times.
References
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