Question: Consider a two-station productin line in which no inventory is allowed between stations (e.e., the stations are tightly coupled). Station 1 consists of a single machine that has potential daily production of one, two, three, four, five, or six units, each outcome being equally likely (i.e., potential production is determine by the roll of a single die). Station 2 consists of a single machine that has potential daily production of either three or foud units, both of which are equally likely (i.e., it produces three units if a fair coin comes up heads and four units if it comes up tails).
a) Compute the long-term average capacity of each station. Is the line balanced (i.e., do both stations have the same capacity)?
b) Compute the long-term average throughput of the line. Why does this differ from your answer to (a)?
c) Add a second identical machine (in parallel) to station 1 and compute the long-term average throughput of the line. How much does this increase average throughput? What implications might this result have concerning the desirability of a balanced line?
d) Return station 1 to a single machine and add a second identical machine (in parallel) to station 2 and compute the long-term average throughput of the line. How much does this increase average throughput? Is the impact the same from adding a machine at stations 1 and 2? Explain why or why not.