Problem : More Process Analysis

The White Tooth Device Company is a manufacturer of high-end electric toothbrushes. For each toothbrush, there is a sequence of assembly steps performed by five workers. Each worker does two tasks. Inventory buffers are allowed between workers.

a) What is the capacity of this process in toothbrushes per hour?

a) Suppose two workers are hired, F and G, and they take the same time to complete tasks as the current five workers. F and G can be assigned to work on the same pair of tasks as one of the current workers. For example, F could be assigned tasks T1 and T2 (just like worker A) while G is assigned T5 and T6 (just like worker C). They cannot be assigned tasks that are currently assigned to two workers. For example, F cannot be assigned to tasks T2 and T3 (because they are currently being done by workers A and B).  What is the capacity in toothbrushes per hour of this process with workers F and G included?

a) Return to the case with 5 workers. Suppose the assignment of tasks to workers can change but the sequence of tasks must remain the same, workers must be assigned to consecutive tasks, and each task can be assigned to only one worker. For example, worker A could do tasks T1-T3 (because they are consecutive) but cannot be assigned T1, T2 and T4. If worker A is assigned to tasks T1-T3, then worker B's first task must be T4 (worker B cannot also be assigned to task T3). Because a U-shaped line is used, tasks T1 and T10 can actually be considered consecutive tasks - worker A could be assigned tasks T10, T1 and T2. What tasks should be assigned to each worker in order to maximize the capacity of the process?  What is the resulting process capacity in toothbrushes per hour?