Chapter 7
Balanced line: when all machines in the line have the same rate
Capacity of a station (per hour) = number of machines * (1/process time)
Congestion Coefficient (α): A unitless measure of congestion
- Zero variability: α=0
- Practical worst-case: α=1
- Worst possible case: α=W(o)
Effective production rate: the maximum average rate at which the workstation can
process parts
Fill rate: the fraction of orders that are filled from stock immediately
Inventory turns / Turnover ratio: the ratio of throughput to average inventory
Lead time: time allocated for production of a part on a routing or line
Service level = probability of (cycle time ≤ lead time)
Touch time: the actual working time
Utilization: fraction of time a workstation is not idle = arrival rate/effective production
rate
Little’s Law
WIP = Throughput * Cycle time
Cycle time / Flow time / Throughput time (CT): the average time from release of a job
at the beginning of the routing until it reaches an inventory point at the end of the routing
Throughput (TH): the average quantity of good parts produced per unit time
Cycle time: Throughput:
,Work in Progress
Work in progress (WIP): inventory between start and end points of a product routing
Critical WIP (Wo): the WIP level for which a line with given values of r(b) and T(o) but
having no variability achieves maximum throughput with minimum cycle time
W(o) = rb * To
Raw process time (To): the sum of the long-term average process times of each
workstation in the line
Bottleneck rate (rb): the rate of the workstation having the highest long-term utilization
When we have two machines we can calculate the bottleneck rate by calculating the
utilization. Because some parts are scrapped we should take this into account. The
percentage of rate r scrapped is 1-y so the percentage kept is r*y. Therefore the utilization of
machine 2 is different than machine 1.
Performances
1. Best-case performance: maximum throughput and minimum cycle time (no randomness)
o In a balances line: W(o) = number of machines
o In an unbalanced line: W(o) is always less than number of machines
, 2. Worst-case performance: maximum cycle time and minimum throughput (no
randomness)
3. Practical worst-case performance: considers randomness, represents the maximum
randomness case
Every possible state occurs with equal frequency. In order for all states to be equally likely,
three conditions are required:
1. The line must be balanced
2. All stations must consist of single machines
3. Process times must be random and occur according to the exponential distribution
(memoryless)
Balanced line: when all machines in the line have the same rate
Capacity of a station (per hour) = number of machines * (1/process time)
Congestion Coefficient (α): A unitless measure of congestion
- Zero variability: α=0
- Practical worst-case: α=1
- Worst possible case: α=W(o)
Effective production rate: the maximum average rate at which the workstation can
process parts
Fill rate: the fraction of orders that are filled from stock immediately
Inventory turns / Turnover ratio: the ratio of throughput to average inventory
Lead time: time allocated for production of a part on a routing or line
Service level = probability of (cycle time ≤ lead time)
Touch time: the actual working time
Utilization: fraction of time a workstation is not idle = arrival rate/effective production
rate
Little’s Law
WIP = Throughput * Cycle time
Cycle time / Flow time / Throughput time (CT): the average time from release of a job
at the beginning of the routing until it reaches an inventory point at the end of the routing
Throughput (TH): the average quantity of good parts produced per unit time
Cycle time: Throughput:
,Work in Progress
Work in progress (WIP): inventory between start and end points of a product routing
Critical WIP (Wo): the WIP level for which a line with given values of r(b) and T(o) but
having no variability achieves maximum throughput with minimum cycle time
W(o) = rb * To
Raw process time (To): the sum of the long-term average process times of each
workstation in the line
Bottleneck rate (rb): the rate of the workstation having the highest long-term utilization
When we have two machines we can calculate the bottleneck rate by calculating the
utilization. Because some parts are scrapped we should take this into account. The
percentage of rate r scrapped is 1-y so the percentage kept is r*y. Therefore the utilization of
machine 2 is different than machine 1.
Performances
1. Best-case performance: maximum throughput and minimum cycle time (no randomness)
o In a balances line: W(o) = number of machines
o In an unbalanced line: W(o) is always less than number of machines
, 2. Worst-case performance: maximum cycle time and minimum throughput (no
randomness)
3. Practical worst-case performance: considers randomness, represents the maximum
randomness case
Every possible state occurs with equal frequency. In order for all states to be equally likely,
three conditions are required:
1. The line must be balanced
2. All stations must consist of single machines
3. Process times must be random and occur according to the exponential distribution
(memoryless)
