Consider the line-of-balance problem. Why should the conveyor time \(c\) be greater than the maximum time assigned at any station? What might happen if it were not?

The line-of-balance problem deals with managing and optimizing the workflow in an assembly line production environment. A crucial aspect of this problem is the allocation of time for different tasks or operations at various workstations. The conveyor time \(c\) represents the amount of time allocated for the assembled product to move through the entire assembly line.

In order to maintain a smooth and efficient production process, it is important that the conveyor time \(c\) is greater than the maximum time assigned at any station for a task or operation. This ensures that the assembly line does not experience bottlenecks, where one station's output is held up due to insufficient time allocated for the operation at that station. For example, if the maximum time assigned at any station is \(t_{max}\), we must have \(c > t_{max}\) to ensure smooth operation.

If the conveyor time \(c\) is not greater than the maximum time assigned at any station, several issues can arise, which negatively affect the efficiency and productivity of the assembly line: 1. Bottlenecks: Workstations with longer operation times would cause delays, halting the progress of the entire production line. This leads to idle time for other stations, reducing the overall productivity. 2. Lower throughput: With insufficient conveyor time, the assembly line will not be able to process as many units as it potentially could, resulting in lower overall production output. 3. Increased costs: Delays and idle times can lead to increased labor and overhead costs, as well as potentially affecting the quality of the finished product. 4. Reduced flexibility: An assembly line with insufficient conveyor time has less flexibility to accommodate any changes in the production process, such as the introduction of new products or revisions to existing products. By ensuring that the conveyor time \(c\) is greater than the maximum time assigned at any station, these issues can be minimized or avoided, leading to a more efficient and effective assembly line production process.