Final answer:
To design an assembly line with a cycle time of 10 minutes, work elements should be assigned to stations following their predecessor relationships and duration constraints, to ensure maximum throughput without exceeding the cycle time at any station.
Step-by-step explanation:
The question you've asked involves organizing work elements into stations for an assembly line with a cycle time of 10 minutes. To do this, we consider the immediate predecessor relationships and the durations of each work element to assign tasks in such a way that the total time for each set of tasks at a station does not exceed the cycle time.
Here's a step-by-step process to break down the work elements:
- Begin with the first work element that has no predecessors. Place it in the first station if it fits within the cycle time.
- Continue adding work elements to a station as long as the sum of the durations does not exceed the cycle time and the predecessor requirements are met.
- When a station reaches the limit of the cycle time, start a new station and continue the process.
- Repeat this process until all work elements are assigned to a station.
With the durations provided (5, 10, 5, 2, 10, 7, 5, 2, 5, 7 minutes), we would start by assigning element 1 to Station 1 (since its duration is 5 minutes). Next, since element 2 exceeds our cycle time, it would be assigned to Station 2 by itself. Following the immediate predecessor sequence and duration limits, each subsequent work element would be assigned to a station to ensure the total time does not exceed 10 minutes per station.
Remember, an efficient assembly line design is one where the total processing time across all stations is balanced so that the throughput is maximized, while ensuring that no station's workload exceeds the specified cycle time.