Summary 1CV50
MANUFACTURING INTEGRATION COURSE
Written for college year 2021-2022
, Chapter 7
A manufacturing system is a goal-oriented network of processes through which parts flow. A plant is made up
of lines which in turn are made up of processes.
Throughput (TH): average quantity of good parts produced per time unit in a line.
Cycle time (CT): time the part spends as WIP
Lead time: time assigned for production of a part on a certain line
Service level: 𝑃(𝐶𝑇 ≤ lead time)
Fill rate: fraction of orders filled from stock
Turnover ratio: ratio of throughput to average inventory
Internal benchmarking: comparisons made inside systems
External benchmarking: comparisons made against outside systems
Parameters:
• 𝝀: arrival rate per time unit
• 𝒎𝒊: number of parallel identical machines at workstation 𝑊𝑖
• 𝒕𝒊𝟎 : raw process time of a machine in workstation 𝑊𝑖
• 𝜹𝒊 : throughput of workstation 𝑊𝑖
• 𝝋: average flow time in the system
Capacity:
• Upper limit on the throughput
𝑚𝑖
• Capacity =
𝑡0𝑖
Little’s law:
• Work in progress 𝑊𝐼𝑃 = 𝑇𝐻 × 𝐶𝑇
o 𝒘: average WIP level in the system
o So, 𝑤 = 𝛿𝜑
• Finished goods inventory 𝐹𝐺𝐼 = 𝑛 × 𝑇𝐻 with 𝑛 the planned inventory time.
Utilization: fraction of time a machine is not idle
𝛿𝑖 𝑡0𝑖
• 𝑢𝑖 = 𝑚𝑖
<1
Descriptors of a line:
• 𝒓𝒃 (bottleneck rate): capacity of the whole line
• 𝑻𝟎 (raw process time): sum of the long-term average process times of each station in the line
• Critical WIP (𝑾𝟎): WIP level in which a line without congestion achieves max TH and min CT
o 𝑊0 = 𝑟𝑏 𝑇0
o Critical WIP cannot exceed the nr of machines 𝑚.
▪ Balanced line: 𝑊0 = 𝑚
▪ Unbalanced line: 𝑊0 ≤ 𝑚
• 𝜶: congestion coefficient
o 𝛼 = 0: no variability, best case
o 𝛼 = 1: practical worst case
o 𝛼 = 0: worst possible case
Balanced line: all stations in a line have the same capacity
Ample equipment: processing is never blocked by lack of equipment
CONWIP: constant WIP meaning that the nr of parts in a line is kept at a constant level.
1
MANUFACTURING INTEGRATION COURSE
Written for college year 2021-2022
, Chapter 7
A manufacturing system is a goal-oriented network of processes through which parts flow. A plant is made up
of lines which in turn are made up of processes.
Throughput (TH): average quantity of good parts produced per time unit in a line.
Cycle time (CT): time the part spends as WIP
Lead time: time assigned for production of a part on a certain line
Service level: 𝑃(𝐶𝑇 ≤ lead time)
Fill rate: fraction of orders filled from stock
Turnover ratio: ratio of throughput to average inventory
Internal benchmarking: comparisons made inside systems
External benchmarking: comparisons made against outside systems
Parameters:
• 𝝀: arrival rate per time unit
• 𝒎𝒊: number of parallel identical machines at workstation 𝑊𝑖
• 𝒕𝒊𝟎 : raw process time of a machine in workstation 𝑊𝑖
• 𝜹𝒊 : throughput of workstation 𝑊𝑖
• 𝝋: average flow time in the system
Capacity:
• Upper limit on the throughput
𝑚𝑖
• Capacity =
𝑡0𝑖
Little’s law:
• Work in progress 𝑊𝐼𝑃 = 𝑇𝐻 × 𝐶𝑇
o 𝒘: average WIP level in the system
o So, 𝑤 = 𝛿𝜑
• Finished goods inventory 𝐹𝐺𝐼 = 𝑛 × 𝑇𝐻 with 𝑛 the planned inventory time.
Utilization: fraction of time a machine is not idle
𝛿𝑖 𝑡0𝑖
• 𝑢𝑖 = 𝑚𝑖
<1
Descriptors of a line:
• 𝒓𝒃 (bottleneck rate): capacity of the whole line
• 𝑻𝟎 (raw process time): sum of the long-term average process times of each station in the line
• Critical WIP (𝑾𝟎): WIP level in which a line without congestion achieves max TH and min CT
o 𝑊0 = 𝑟𝑏 𝑇0
o Critical WIP cannot exceed the nr of machines 𝑚.
▪ Balanced line: 𝑊0 = 𝑚
▪ Unbalanced line: 𝑊0 ≤ 𝑚
• 𝜶: congestion coefficient
o 𝛼 = 0: no variability, best case
o 𝛼 = 1: practical worst case
o 𝛼 = 0: worst possible case
Balanced line: all stations in a line have the same capacity
Ample equipment: processing is never blocked by lack of equipment
CONWIP: constant WIP meaning that the nr of parts in a line is kept at a constant level.
1
