Variability Basics - Effects of Blocking
5 important questions on Variability Basics - Effects of Blocking
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.
WIPnb ≈ (( Ca^2 + Ce^2)/2) * ((1/u^2)/(1-1/u)) + (1/u)
Why does queue length go to infinity when utilization approaches 100%? Is this realistic?
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.
Consider three machines in series, with a buffer of size A in between the first two machines and with an infinite buffer in between the second and third machine. The first machine has a small rack at the backside of it that can hold 3 processed jobs. The second machine has a similar rack on the back that can hold 1 processed job. The behavior of machine in the middle and buffer in between the first two machines can be modeled as an M/M/1/b system. What size is b?
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).
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Why can the utilization for a machine in a system with blocking exceed 100%, according to the text in 8.7.1? Can it exceed 100% in real life?
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.
Would you expect a production system with large/extremely large buffers (almost no blocking) or with small buffers (blocking) in the following cases?
- A: a company that values TH over anything else
- B: a company that has to be very flexible
- C: a company that has very high inventory cost in comparison to its profit per product sold
- D: vice versa of C
- E: the toyota production system
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)
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