Consider a factory that has a single workstation that processes parts individually. These parts are quite heavy and the company policy is to palletize incoming parts into groups of k items for ease of transportation. These batches are then released into the factory for processing. These k items are processed at the machine and again placed back on the pallet. When the pallet is full, the k items have been processed, the pallet is transported to shipping.

(a) Neglecting the actual transportation time, what is the equation for cycle time of individual parts for this factory. This cycle time includes the waiting time for all batching operations. Compare the batch movement cycle time with that of a system that does not need to batch these items for movement within the factory. How much extra time does an average item incur due to batching for movement purposes?

(b) Assume it takes an average of t1 to move a pallet from the unloading dock to the workstation and an average of t2 to move a pallet from the machine to the next workstation. Assuming no waiting for a forklift to move the pallet, add the transportation time to the model.