Variability Basics - Effects of Blocking

Question

With respect to the General Blocking Models, we assume that the arrival rate is greater than the production rate. Give the approximation formula for the average WIP level for these assumptions.

Answer 1

WIPnb ≈ (( Ca^2 + Ce^2)/2) * ((1/u^2)/(1-1/u)) + (1/u)

Answer 2

If utilization (u) goes to 1, the U-term in the VUT equation goes to infinity and so does CTq (=VUT).
A utilization going to 100% is very unrealistic.

Answer 3

b = A + 2 (1 for the second machine + 1 for the first machine) + 3 (buffer at backside of first machine)
(Similarly, the rack at the backside of the 2nd machine belongs to the (infinite) buffer between the 2nd and 3rd machine).

Answer 4

Because represents the rate of potential arrivals in systems with blocking, which will be greater than the rate of actual arrivals. Hence, is an overestimation and so will .
Only because of this definition can it exceed 100%, in able to correctly determine long-run WIP, TH, CTq etc.
This answers the second question. Utilization exceeding 100% depends on the definition. In real life, a machine cannot be used more than 100% of course.

Answer 5

No blocking = 1, blocking = 2
A: 1
B: 2 (WIP & CT have to be low to be flexible)
C: 2 (WIP has to be low whilst TH can afford to be low too)
D: 1
E: 2 (TPS is a production system with a lot of pull elements)
(Information on p. 295)