lOMoAR cPSD| 233498
Lecture 1 Capacity & variability
Chapter 0: Foundations
Performance aspects: performance is what characterizes a supply chain.
• Cost
• Quality
• Speed
• Service – use dependability
• Variety – referred to as flexibility
Hopp: You want to produce at low cost, high quality and high speed and high variety.
Often dependability and flexibility (mixed/volume changes) are used instead of service and variety.
Example: OTIF: on-time-in-full (percentage of products delivered on time and completely).
Relationship between multiple performance aspects: Strategic trade-offs and efficient frontiers
Determining the frontier
A frontier could be determined based on company data (DEA), using linear programming.
• What? It shows each company’s positions relative to the frontier, on the frontier or distance
to the frontier (also for more than 2 Performance aspects).
• This enables benchmarking studies
Supply chain (HOPP): a goal-oriented network of processes
and stock points used to deliver goods and services.
• Can be seen at different levels (e.g. SC-network or
production network).
Stock points:
1. Decoupling (anticipation, cycle (Batching), safety stocks) to buffer against uncertainty.
2. Queuing (stock not built on purpose) can result because of
a. Congestion (waiting for capacity)
b. Assembly (waiting for other parts)
c. Transport (waiting for scheduled event)
d. Batching (waiting for similar events)
Decoupling: not yet decided in which production order the stocked item will be processed next.
Queuing this decision has already been made (I need it for a order, but cannot yet be processed).
Customer order decoupling point: stock point after which the customer order is known. Can be at
different stages in a process (e.g. make-to-order (stock at the start), make to stock (stock at the end)).
Book structure – 3 Level issues:
1. Station level (1 process + feeding stock): capacity, variability, batching
2. Line level (1 path): flow, buffering, control (push/pull)
3. Network level (multiple paths): inventory, risk/pooling, coordination
, lOMoAR cPSD| 233498
Notice:
1. One station may have multiple servers – not just 1 machine
2. Entities: it can be many things and they flow through a system (orders, products, patients)
Chapter 1: Capacity
Definitions:
• Throughput (TH): rate at which entities are processed by the system (e.g. 15 per
hour)
• Work in process (WIP): number of entities in system (e.g. jobs, orders, people,
hours).
• Cycle time (CT): time it takes an entity to go through the whole system (also
throughput time or lead time).
o Throughput is the rate and throughput time the time it takes to go through
the system
• Capacity: maximum average rate that can be realized within the system.
Capacity determinants: depends on whether it is for a station, line or network!
Station: capacity = base capacity – detractors
o Base capacity: rate of the process under ideal conditions (in practice we don’t have it)
o Detractors: anything that slows the output of the process
In practice diagnosis are done through OEE (overall equipment effectiveness), which looks more
detailed into the detractors.
Capacity of Line or network: capacity is determined by the bottleneck which is the
process that constrains the capacity of the system.
o Bottleneck: process with the highest utilization.
o Utilization: rate into the station / capacity of the station.
OEE: Overall equipment effectiveness
Green are the detractors slowing up the
whole process.
OEE:
What is the remaining valuable operating
time / loading time
What we can deduct from this comparison is:
• What is the valuable percentage of operating time compared to the loading time
, lOMoAR cPSD| 233498
Capacity Principles:
1. Capacity: the output of a system cannot equal or exceed its capacity due to variability!
2. Utilization: cycle time increases with utilization and infinite cycle times will occur when
utilization approaches 100%.
3. Littler’s law: Over the long term avg WIP, Throughput rate and cycle time for any stable process
relate as: WIP = TH *CT
Utilization problems in practice
Managers often try to load a system close
to 100%capacity.
Consequences:
• Cycle times get too long and WIP
too high.
• Overtime to reduce WIP.
• After WIP reduction, back to
normal capacity overtime
vicious cycle. 3.
Managers use overtime to lower the cycle
times but start pushing more work which increases CT again.
Little’s law: WIP = TH x CT
Red cure original situation: release 1 order per hour but that is too close to capacity which increases the
cycle time. Managers introduce overtime then (capacity) to reduce the cycle time.
Chapter 2: Variability
How to determine the curves?
Queuing: at a single station with no limit on the number of entities that can queue up, the waiting time
(WT) due to queuing is given by: WT = V x U x T (HOPP).
o V = variability factor
Squared coefficient of variation:
standard deviation / mean
o U = utilization factor
o T = average effective process time for entity at the station
, lOMoAR cPSD| 233498
Impact of utilization and variability on waiting time (WT):
• Variability increases waiting time
• Utilization increases waiting time
• High variability and high utilization = long waiting times.
• Low variability allows throughput to increase without
increasing waiting times.
• Decreasing variability can lead to lower waiting times under
the same utilization SO:
o Without lowering throughput
Queuing formula only holds for:
1. Stationary systems with all distributions known (there might be variability but stays the same
over time)
2. Priorities either handled on a first-come-first-serve basis or random
Still useful, since it can be seen what the impact is on waiting times, etc. Thus, often you cannot calculate
an exact, WT But it gives an impression of a particular factor’s impact.
Note: variability is not only a problem that causes long waiting times, but can be used as an advantage.
Article: Throughput diagrams
Throughput diagrams are an important instrument to diagnose flow problems.
Diagrams:
• Starting point with amount of entities.
• Anytime an entity goes in/out then it is noted.
• WIP: vertical difference between cumulative input and output
• Cycle time: horizontal difference between input and output (throughput time)
• Throughput rate: rate at which entities are processed by the system (e.g. customers per hour)
o Example: total customers / time in minutes = customer rate per minute Little’s law: WIP = TH x
CT
Lecture 1 Capacity & variability
Chapter 0: Foundations
Performance aspects: performance is what characterizes a supply chain.
• Cost
• Quality
• Speed
• Service – use dependability
• Variety – referred to as flexibility
Hopp: You want to produce at low cost, high quality and high speed and high variety.
Often dependability and flexibility (mixed/volume changes) are used instead of service and variety.
Example: OTIF: on-time-in-full (percentage of products delivered on time and completely).
Relationship between multiple performance aspects: Strategic trade-offs and efficient frontiers
Determining the frontier
A frontier could be determined based on company data (DEA), using linear programming.
• What? It shows each company’s positions relative to the frontier, on the frontier or distance
to the frontier (also for more than 2 Performance aspects).
• This enables benchmarking studies
Supply chain (HOPP): a goal-oriented network of processes
and stock points used to deliver goods and services.
• Can be seen at different levels (e.g. SC-network or
production network).
Stock points:
1. Decoupling (anticipation, cycle (Batching), safety stocks) to buffer against uncertainty.
2. Queuing (stock not built on purpose) can result because of
a. Congestion (waiting for capacity)
b. Assembly (waiting for other parts)
c. Transport (waiting for scheduled event)
d. Batching (waiting for similar events)
Decoupling: not yet decided in which production order the stocked item will be processed next.
Queuing this decision has already been made (I need it for a order, but cannot yet be processed).
Customer order decoupling point: stock point after which the customer order is known. Can be at
different stages in a process (e.g. make-to-order (stock at the start), make to stock (stock at the end)).
Book structure – 3 Level issues:
1. Station level (1 process + feeding stock): capacity, variability, batching
2. Line level (1 path): flow, buffering, control (push/pull)
3. Network level (multiple paths): inventory, risk/pooling, coordination
, lOMoAR cPSD| 233498
Notice:
1. One station may have multiple servers – not just 1 machine
2. Entities: it can be many things and they flow through a system (orders, products, patients)
Chapter 1: Capacity
Definitions:
• Throughput (TH): rate at which entities are processed by the system (e.g. 15 per
hour)
• Work in process (WIP): number of entities in system (e.g. jobs, orders, people,
hours).
• Cycle time (CT): time it takes an entity to go through the whole system (also
throughput time or lead time).
o Throughput is the rate and throughput time the time it takes to go through
the system
• Capacity: maximum average rate that can be realized within the system.
Capacity determinants: depends on whether it is for a station, line or network!
Station: capacity = base capacity – detractors
o Base capacity: rate of the process under ideal conditions (in practice we don’t have it)
o Detractors: anything that slows the output of the process
In practice diagnosis are done through OEE (overall equipment effectiveness), which looks more
detailed into the detractors.
Capacity of Line or network: capacity is determined by the bottleneck which is the
process that constrains the capacity of the system.
o Bottleneck: process with the highest utilization.
o Utilization: rate into the station / capacity of the station.
OEE: Overall equipment effectiveness
Green are the detractors slowing up the
whole process.
OEE:
What is the remaining valuable operating
time / loading time
What we can deduct from this comparison is:
• What is the valuable percentage of operating time compared to the loading time
, lOMoAR cPSD| 233498
Capacity Principles:
1. Capacity: the output of a system cannot equal or exceed its capacity due to variability!
2. Utilization: cycle time increases with utilization and infinite cycle times will occur when
utilization approaches 100%.
3. Littler’s law: Over the long term avg WIP, Throughput rate and cycle time for any stable process
relate as: WIP = TH *CT
Utilization problems in practice
Managers often try to load a system close
to 100%capacity.
Consequences:
• Cycle times get too long and WIP
too high.
• Overtime to reduce WIP.
• After WIP reduction, back to
normal capacity overtime
vicious cycle. 3.
Managers use overtime to lower the cycle
times but start pushing more work which increases CT again.
Little’s law: WIP = TH x CT
Red cure original situation: release 1 order per hour but that is too close to capacity which increases the
cycle time. Managers introduce overtime then (capacity) to reduce the cycle time.
Chapter 2: Variability
How to determine the curves?
Queuing: at a single station with no limit on the number of entities that can queue up, the waiting time
(WT) due to queuing is given by: WT = V x U x T (HOPP).
o V = variability factor
Squared coefficient of variation:
standard deviation / mean
o U = utilization factor
o T = average effective process time for entity at the station
, lOMoAR cPSD| 233498
Impact of utilization and variability on waiting time (WT):
• Variability increases waiting time
• Utilization increases waiting time
• High variability and high utilization = long waiting times.
• Low variability allows throughput to increase without
increasing waiting times.
• Decreasing variability can lead to lower waiting times under
the same utilization SO:
o Without lowering throughput
Queuing formula only holds for:
1. Stationary systems with all distributions known (there might be variability but stays the same
over time)
2. Priorities either handled on a first-come-first-serve basis or random
Still useful, since it can be seen what the impact is on waiting times, etc. Thus, often you cannot calculate
an exact, WT But it gives an impression of a particular factor’s impact.
Note: variability is not only a problem that causes long waiting times, but can be used as an advantage.
Article: Throughput diagrams
Throughput diagrams are an important instrument to diagnose flow problems.
Diagrams:
• Starting point with amount of entities.
• Anytime an entity goes in/out then it is noted.
• WIP: vertical difference between cumulative input and output
• Cycle time: horizontal difference between input and output (throughput time)
• Throughput rate: rate at which entities are processed by the system (e.g. customers per hour)
o Example: total customers / time in minutes = customer rate per minute Little’s law: WIP = TH x
CT
