Consider a two-station process below with zero space for inventory. Each unit needs processing on both stations.

Zero Inventory

RM FG

[3, 9] [3, 9]

The processing time for a unit at station is uncertain and the range is 3 to 9 minutes per unit. The average time is 6 minutes per unit.

The rules for running the process are as follows: (1) Infinite supply of raw materials, (2) WS2 moves a unit to finished goods as soon as its processing on WS2 is complete, (3) WS1 moves a unit to WS2 when its processing on WS1 is complete and also WS2 is empty, and (4) WS1 starts working on a new unit as soon as WS1 is empty.

The simulation run of the line for 600 minutes (10 hours) has the following results:

The average output in 600 minutes is 86 units (or, 8.6 units per hour).

The average amount of time a unit spends on WS1 is 6.97 minutes.

The average amount of time a unit spends on WS2 is 6 minutes.

Station WS1 always has a unit (either completed or blocked). So, the average inventory on WS1 is 1 unit.

Station WS2 has a unit only when it is working on it.

Part 1: Explain why a unit spends 6.97 minutes on WS1 while the mean process time is 6 minutes?

Part 2: For what fraction of time is WS2 busy working on a unit? For what fraction of time does it starve?

Part 3: What is the total inventory in the process (sum for WS1 and WS2)?

Part 4: Using the total inventory from Part 3 and the flow rate of 8.6/60 units per minute, calculate the flow time using Littles Law.