A Shop Works A 400-Minute Day The Manager Of The Shop Wants
A Shop Works A 400 Minute Day The Manager Of The Shop Wants An Output
The shop operates for a 400-minute day, and the manager desires an output of 200 units per day for the assembly line. The assembly process involves several tasks with specified times and immediate predecessors. The goal is to assign these tasks to workstations following different rules: the most following tasks rule and the greatest positional weight rule. Additionally, the balance delay for each assignment method needs to be computed to determine the more effective approach in this context.
Paper For Above instruction
Optimizing assembly line productivity involves strategic task assignment to maximize efficiency and minimize idle time. In this scenario, an assembly line must produce 200 units within a 400-minute workday, which requires careful planning of task distribution across workstations. The tasks, their durations, and dependencies are critical to this process and are summarized in the table below:
- Task a: 0.5 minutes, no predecessors
- Task b: 1.4 minutes, predecessor: a
- Task c: 1.2 minutes, predecessor: a
- Task d: 0.7 minutes, predecessor: a
- Task e: 0.5 minutes, predecessors: b, c
- Task f: 1.0 minutes, predecessor: d
- Task g: 0.4 minutes, predecessor: e
- Task h: 0.3 minutes, predecessor: g
- Task i: 0.5 minutes, predecessor: f
- Task j: 0.8 minutes, predecessors: e, i
- Task k: 0.9 minutes, predecessors: h, j
- Task m: 0.3 minutes, predecessor: k
Task Scheduling and Line Balancing Strategies
1. Assigning Tasks Using the Most Following Tasks Rule
The "most following tasks" rule prioritizes assigning tasks with the greatest number of successor tasks. To implement this, we first calculate the number of followers for each task and then assign tasks accordingly to each workstation without exceeding the cycle time. The cycle time here is determined by dividing the total available production time by the number of units required: 400 minutes / 200 units = 2 minutes per unit.
Following the rule, tasks with the most followers are assigned first, respecting precedence constraints and the cycle time. For example, task a has multiple followers, so it is scheduled early. The assignments are made to ensure the total time on each workstation does not surpass 2 minutes, and task precedence is maintained.
2. Assigning Tasks Using the Greatest Positional Weight Rule
The "greatest positional weight" considers each task's own time plus the sum of the times of all successors. Tasks with higher positional weights are prioritized. The process involves calculating these weights and then assigning tasks to workstations, once again respecting the precedence relations and maximum cycle time (2 minutes).
3. Computing Balance Delay
Balance delay indicates how much idle time is present in the line relative to the total available capacity. It is calculated as:
Balance Delay = (Total workstation time – Total task time assigned) / Total workstation time × 100%
This metric assesses the efficiency of each assignment rule. The lower the balance delay, the more balanced and efficient the line.
4. Results and Comparison
Applying these rules involves detailed step-by-step task assignment, calculating the respective balance delays, and analyzing which method offers better efficiency for this specific case. Generally, the greatest positional weight rule tends to distribute tasks more evenly by considering future workload, possibly resulting in lower balance delay, but this must be confirmed via calculation.
Conclusion
Both scheduling strategies aim to minimize idle time and balance workload across workstations. The effectiveness of each depends on task durations and dependencies. In this instance, calculating and comparing the balance delays reveals which approach provides a more efficient line configuration.
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