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5. Flow Rate and Capacity Analysis
Flow Rate and Capacity Analysis
Throughput and Capacity
Resources and Resource Pools
Theoretical capacity
Bottleneck resources
Capacity utilization
Product mix and its effect on theoretical capacity and
profitability
Capacity Improvement
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5. Flow Rate and Capacity Analysis
Throuhput and Takt Time
Throughput: Average Flow Rate
The average number of flow units that flow through a process per unit of time in a stable process
Takt time = 1/(throughput)
The time interval between exit of two consecutive products. The average activity time at a workstation on an assembly line.
Process Capacity
The maximum sustainable flow rate of a process
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5. Flow Rate and Capacity Analysis
Resources in a Process
Inputs Outputs
GoodsServices
Informationstructure
Network ofActivities and Buffers
Flow units(customers, data, material, cash, etc.)
Resources
ProcessManagement
Labor + Capital
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5. Flow Rate and Capacity Analysis
Resources and Resource Pools
Resources» Capital – Fixed Assets such as land, buildings, facilities, equipment
and machinery» Labor – people such as engineers, operators, assemblers, chefs
customer-service representatives, etc.
Resource Unit: An individual resource (chef, mixer, oven etc)
Resource Pool: A collection of interchangeable resource units that can perform an identical set of activities
Resource Pooling: The combining of separate resource pools into a single pool to perform several activities
Unit Load of a Resource Unit (Tp): The amount of time the resource works to process each flow unit
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5. Flow Rate and Capacity Analysis
A Resource Pool
Activity ResourceWork Content
(minutes)
MailroomMailroom Clerk 0.6
Data EntryData-entry Clerk 4.2
Initial Processing
Claims processor 4.8
InspectionClaims Supervisor 2.2
Final Processing
Claims processor 1.8
ResourceUnit Load(minutes)
Mailroom Clerk 0.6
Data-entry Clerk 4.2
Claims processor 6.6
Claims Supervisor 2.2
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5. Flow Rate and Capacity Analysis
Flow Rate Measurement
Theoretical capacity of a resource unit – maximum sustainable flow rate if it were fully utilized
Theoretical capacity of a resource pool – sum of all the theoretical capacities of all the resource units in that pool
Bottleneck – the slowest resource pool of a process
Theoretical bottleneck – The resource pool with the minimum theoretical capacity
Theoretical capacity of a process – theoretical capacity of the theoretical bottleneck
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5. Flow Rate and Capacity Analysis
The Theoretical Capacity
Theoretical Capacity of a Resource unit = 1/unit load = 1/ Tp
Theoretical capacity of a Resource pool = Rp = cp/ Tp
Resource pool (p)
Unit Load(min./claim)(Tp)
Theoretical Capacity of a Resource Unit = 1/Tp claims/min
Number of Units in Resource Pool = cp
Theoretical Capacity of Resource Pool Rp=cp/Tp
claims/min
Mailroom clerk
0.6 1.6666 1 1.66
Data-entry clerk
4.2 0.2380 8 1.90
Claims processor
6.6 0.1515 12 1.82
Claims supervisor
2.2 0.4545 5 2.27
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5. Flow Rate and Capacity Analysis
Other Factors Affecting Theoretical Capacity
Load batching – a resource processes several flow units simultaneously (one oven and 10 loaves of bread)
Scheduled availability – The amount of time that a resource is schedule for operation. (certain hours, certain days, total hours per week)
Theoretical capacity of a resource unit =
(1 / Tp) × Load batch × Scheduled availability
Theoretical capacity of a resource pool =
Rp =(cp / Tp) × Load batch × Scheduled availability
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5. Flow Rate and Capacity Analysis
Theoretical Capacity for Physicians Claims (Revised)
Resource pool (p)
Scheduled availability(min/day)
Unit Load(min/claim)(Tp)
Theoretical Capacity of Resource Unit(claims/day)
Number of Units in Resource Pool
Theoretical Capacity of Resource Pool (claims/day) (Rp)
Mailroom clerk
450 0.6 450/0.6 = 750 1 760×1 = 750
Data-entry clerk
450 4.2 450/4.2=107.1 8 107.1×8 = 856.8
Claims processor
360 6.6 360/6.6=54.5 12 54.5×12 = 654
Claims supervisor
240 2.2 240/2.2=109.1 5 109.1×5 = 545.5
Claims supervisors are the bottleneck and theoretical capacity is 545 claims per day
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5. Flow Rate and Capacity Analysis
Throughput and Capacity Utilization
Throughput is rarely equal to theoretical capacity because of
» Internal inefficiencies (resource unavailability or idleness)
» External inefficiencies (low inflow/supply or low outflow/demand)
Capacity utilization of a resource pool (ρp) – Measures degree to
which resources are effectively used by a process.
ρp = Throughput/Theoretical capacity of a resource pool = R/Rp
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5. Flow Rate and Capacity Analysis
Capacity Utilization
Resource pool (p)Theoretical Capacity of Resource Pool (claims/day) (Rp)
Capacity Utilization(ρp=R/Rp)
Mailroom clerk 750 480/750=64%
Data-entry clerk 856.8 480/857=56%
Claims processor 654 480/654=73%
Claims supervisor 545.5 480/545=88%
The capacity utilization of the entire process is 88%
Throughput = 480
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5. Flow Rate and Capacity Analysis
VOH Hospital: Work Content and Resources
Activity Description Work Content min/pat
Resources Allocated
Start Patient leaves Dr office --- ---
1 Patient walks to the X-ray 7 ---
2 X-ray request travels to X-ray lab by messenger 20 Messenger
3 X-ray technician fills form 6 X-ray tech
4 Receptionist receive patient info 5 Receptionist
5 Patient undresses for X-ray 3 Changing room
6 A lab technician takes X-rays 7.5 X-ray tech, X-ray lab
7 A darkroom technician develop X-rays 15 Dark room tech, darkroom
8 The lab technician develop X-ray 2.5 X-ray tech
9 Patient puts on clothes and get ready to leave 3 Changing room
10 Patient walls back to Dr’s office 7 ---
11 The X-rays are transferred to the Dr. by a messenger 20 Messenger
12 Patient and X-rays arrive at the Dr’s office --- ---
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5. Flow Rate and Capacity Analysis
Theoretical Capacity and Capacity Utilization
Resource pool (p)
Unit load (min/ pat)
Theoretical Capacity of Resource Unit (patients per hour)
Number Units in Resource Pool (Cp)
Theoretical Capacity of Resource Pool (patients per hour) (Rp)
Capacity Utilization (%)
ρp = R/Rp
Messenger 20+20=40 60/40=1.5 6 1.5×6=9 5.5/9=61.11%
Receptionist 5 60/5=12 1 12×1=12 5.5/12=45.83%
X-ray tech 6+7.5+2.5+16
60/16=3.75 4 3.75×4=15 5.5/15=36.67%
X-ray lab 7.5 60/7.5=8 2 8×2=16 5.5/16=34.38%
Darkroom tech
15 60/15=4 3 4×3=12 5.5/12=45.83%
Darkroom 15 60/15=4 2 4×2=8 5.5/8=68.75%
Changing room
3+3=6 60/6=10 2 10×2=20 5.5/20=27.50%
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5. Flow Rate and Capacity Analysis
Unit Load for a Product Mix
Unit load for a given product mix is computed as the weighted average of unit loads of individual products.
Billing: Physician claims, Hospital claims, and 60/40 mix
Resource Pool UL (Physician)min. /claim
UL (Hospital)min. /claim
UL (60%-40%) mixmin. /claim
Mailroom clerk 0.6 1.0 0.6(.6)+1(.4) =0.76
Data-entry clerk 4.2 5.2 4.60
Claims processor 6.6 7.5 6.96
Claims supervisor 2.2 3.2 2.60
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5. Flow Rate and Capacity Analysis
Theoretical Capacity for Physicians Claims
Resource pool (p)
Scheduled availability(min/day)
Unit Load(min/claim)(Tp)
Theoretical Capacity of Resource Unit(claims/day)
Number of Units in Resource Pool
Theoretical Capacity of Resource Pool (claims/day) (Rp)
Mailroom clerk
450 0.6 450/0.6 = 750 1 760×1 = 750
Data-entry clerk
450 4.2 450/4.2=107.1 8 107.1×8 = 856.8
Claims processor
360 6.6 360/6.6=54.5 12 54.5×12 = 654
Claims supervisor
240 2.2 240/2.2=109.1 5 109.1×5 = 545.5
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5. Flow Rate and Capacity Analysis
Theoretical Capacity for Hospital Claims
Resource pool (p)
Scheduled availability(min./day)
Unit Load(Tp)
(min./claim)
Theoretical Capacity of
Resource Unit(claims/day)
Number of Units in
Resource Pool
Theoretical Capacity of
Resource Pool (Rp) (claims/day)
Mailroom clerk
450 1.0 450 / 1.0 = 450 1 450× 1 = 450
Data-entry clerk
450 5.2 450 / 5.2= 86.5 8 86.5 × 8 = 692
Claims processor
360 7.5 360 / 7.5 = 48 12 48 × 12 = 576
Claims supervisor
240 3.2 240 / 3.2 = 75 5 75 × 5 = 375
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5. Flow Rate and Capacity Analysis
Theoretical Capacity for 60% / 40% Mix
Resource pool (p)
Scheduled availability(min./day)
Unit Load(Tp)
(min./claim)
Theoretical Capacity of
Resource Unit(claims/day)
Number of Units in
Resource Pool
Theoretical Capacity of
Resource Pool Rp (claims/day)
Mailroom clerk
450 0.76 450/0.76=592 1 592×1 = 592
Data-entry clerk
450 4.60 450/4.60=98 8 98×8 = 784
Claims processor
360 6.96 360/6.96=51.7 12 51.7×12 = 621
Claims supervisor
240 2.60 240/2.60=92 5 92×5 = 460
Linear Programming: Find the optimal product mix to maximize profit.
Greedy Algorithm. Produce products with highest unit contribution margin
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5. Flow Rate and Capacity Analysis
Resource Pool
No. Units in
Resource Pool
Load Batch
Unit Load Standardminutes
Theoretical Capacity of
resource pool
(standard per hour)
Unit load fancy
minutes
Theoretical Capacity of
resource pool
(fancy per hour)
Unit Load75% - 25%
mix
Theoretical capacity of
resource Pool(75%-25% mix
per hour)
Worker S 1 1 10 6.00 10 6.00 10 6.00Punch press R 1 1 22 2.73 30 2.00 24 2.50Punch press B 1 1 30 2.00 50 1.20 35 1.71Worker PR 1 1 22 2.73 30 2.00 24 2.50Worker PB 1 1 30 2.00 50 1.20 35 1.71Forming machine R 1 1 12 5.00 15 4.00 12.75 4.71Forming machine B 1 1 6 10.00 10 6.00 7 8.57Worker FR 1 1 12 5.00 15 4.00 12.75 4.71Worker FB 1 1 6 10.00 10 6.00 7 8.57Welding gun 1 1 13 4.62 20 3.00 14.75 4.07Worker SA 1 1 13 4.62 20 3.00 14.75 4.07Worker FA 1 1 10 6.00 15 4.00 11.25 5.33Inspector 2 1 36 3.33 40 3.00 37 3.24
Optimizing Profitability: Wonder Shed example
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5. Flow Rate and Capacity Analysis
Optimizing Profitability: Wonder Shed exampl
Decisions of product mix affect process capacity which therefore affect profitability
Optimize profitability by producing products with highest unit contribution margin» keep in mind: unit load, resource capacity, and process capacity
Contribution Margin – revenue less all of its variable costs
Contribution Margin per UnitStandard = $200Fancy = $260
Contribution Margin Per Unit of TimeStandard 2 × $200 = $400 per hourFancy 1.2 × $260 = $312 per hour
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5. Flow Rate and Capacity Analysis
Optimizing Profitability
Shift length 8working days per mo. 25Avail hours 200Demand - Fancy 150Demand - Standard 350CM - Fancy 260CM - Standard 200
Type No. of units No. of hours units per hour C.M. per unit ext. profitFancy 150 125 1.2 $260 $39,000Standard 150 75 2 $200 $30,000
200 $69,000
Standard 350 175 2 $200 $70,000Fancy 30 25 1.2 $260 $7,800
200 $77,800
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5. Flow Rate and Capacity Analysis
Why Wasted Time?
Process capacity is usually less than the theoretical capacity due to process inefficiencies (time wasted).
Resource availability loss: resource is not available » Breakdown or absenteeism» Preventive maintenance
Scheduled availability: the scheduled time period during which a resource unit is available for processing flow units
Net availability = Schedule availability – Lost time due to breakdown and maintenance
Availability loss factor = 1 – (Net Availability/Scheduled Availability)
Resource idleness: resource is available but is not processing» Starvation: Idleness of resources due to the unavailability of inputs» Blockage: When resources are prevented from producing because there is
no place to store (internal), or there is no demand (external)
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5. Flow Rate and Capacity Analysis
Setup Batch, Unit Load, Total Unit Load
Setup or Changeover: activities related to cleaning, resetting and retooling of equipment in order to process a different product.
Qp : Setup batch or lot size; the number of units processed consecutively after a setup;
Sp : Average time to set up a resource at resource pool p for a particular product
Average setup time per unit is then Sp / Qp
Tp = Unit load (it does not count for the setup time)Total unit load = Tp + Sp / Qp
What is the “right” lot size or the size of the set up batch? Lot Size or ?» The higher the lot size, the lower will be the total unit load and thus the
higher the capacity.» The higher the lot size, the higher will be the inventory and therefore, the
higher the flow time.
Reducing the size of the setup batch is one of the most effective ways to reduce the waiting part of the flow time.
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5. Flow Rate and Capacity Analysis
Total Unit Load for Products, and a Product mix
Regular Jumbo Mix
Unit Load (Tp) 2 1 (2×.75)+(1×.25)=1.75
Sp/Qp 30/300=0.1 30/100=0.3 (0.1×0.75)+(0.3×0.25)=0.15
Total unit load 2+0.1=2.1 1+0.3=1.3 (2.1×.75)+(1.33×.25)= 1.9
Two Sizes Tiles Cutting time Setup time Regular 300 units (75%) 2 minutes 30 minutesJumbo 100 units (25%) 1 minute 30 minutes
Load batch: the number of units processed simultaneously. Often constrained by technological capabilities of the resource.
Setup batch: the number of units processed consecutively after a setup. Setup is determined managerially
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5. Flow Rate and Capacity Analysis
Effective Capacity of a Process
Theoretical Capacity of a resource unit: (1/Tp) ×Load Batch ×Scheduled Availability
Effective Capacity of a resource unit : (1/Total Unit Load) × Load Batch ×Net Availability
Effective Capacity takes into account the setup per unit time (Total unit load) and the resource availability loss (Net availability)
The effective capacity of a pool is the effective capacity of all resources in the pool: (cp/Total Unit Load) × Load Batch ×Net Availability
» Cp is the number of units in the resource pool
» Total unit load= Tp+(Sp/Qp)
The effective capacity of a process is the effective capacity of its slowest resource pool (effective bottleneck).
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5. Flow Rate and Capacity Analysis
Resource Pools, Effective Capacity
Resource Pool
No. Units in Resource
PoolLoad
Batch
(Total) Unit Load
Standardminutes
Scheduled avilability hours /day
Loss Factor
Net Availability (Minutes)
Effective Cap. Resource Pool (flow units/day)
Worker S 1 1 10 8 6.25% 450 45.00Punch press R 1 1 22 8 5% 456 20.73Punch press B 1 1 30 8 5% 456 15.20Worker PR 1 1 22 8 5% 456 20.73Worker PB 1 1 30 8 5% 456 15.20Forming machine R 1 1 12 8 10% 432 36.00Forming machine B 1 1 6 8 10% 432 72.00Worker FR 1 1 12 8 6.25% 450 37.50Worker FB 1 1 6 8 6.25% 450 75.00Welding gun 1 1 13 8 10.0% 432 33.23Worker SA 1 1 13 8 6.25% 450 34.62Worker FA 1 1 10 8 6.25% 450 45.00Inspector 2 1 36 8 6.25% 450 25.00
Effective capacity = (cp/Total Unit Load) × Load Batch ×Net Availability
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5. Flow Rate and Capacity Analysis
Levers for Managing Throughput
Theoretical capacity» The theoretical capacity of the theoretical bottleneck. » Rp = cp/Tp × Load batch × Scheduled availability
Effective capacity» Replace Schedule availability with net availability» Replace Unit load (Tp) by Total unit load Tp+Sp/Qp. That is unit load plus
setup per unit in the setup batch
Process capacity» Is less than Effective Capacity Resource idleness due to starvation and
blockages
Throughput » Average flow rate per unit Note: (1/throughput = Takt time)
Throughput ≤ Process capacity ≤ Effective capacity ≤ Theoretical capacity
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5. Flow Rate and Capacity Analysis
Improving Theoretical Capacity
Decrease unit load on the bottleneck: Decrease the work content of the activity performed by the bottleneck resource pool
Increase the Load Batch of the bottleneck resource: Expanding the resource will increase resource capacity
Increase the number of bottleneck resources: Adding units to the bottleneck resource pool will increase resource capacity
Increase Scheduled Availability of bottleneck resource: Add more hours to the resource such as adding overtime or second shift operations
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5. Flow Rate and Capacity Analysis
Internal and External Bottlenecks
Internal Bottleneck: When Throughput is equal to Process Capacity The output of the process is limited by the process’s own
constraints (the bottleneck resource)
External Bottleneck: When Throughput is less than to Process Capacity The output of the process is limited by conditions external to the
the boundaries of the internal process constraints. Examples include: demand for product, raw material shortages
If process capacity is close to throughput, the dominating effect is internal (recourse unavailable; breakdowns, preventative maintenance, set up). You should increase net availability of the bottleneck resource pools and reduce setup waste.
If effective capacity is close to the theoretical capacity the dominating effect is external (starvation, blockage). The way to raise capacity in this case is to reduce idleness.
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5. Flow Rate and Capacity Analysis
Increase net availability, Reduce setup
Increasing net availability
» Regular Maintenance of equipment Reduces breakdowns during manufacturing process Perform maintenance after production line shutdown Have problem solving measures in place to keep the manufacturing
process functioning
Reducing setup waste
» Planning Reduce the frequency of changeovers Managing the product mix
» Reduce the amount of time required to setup a line Caution: Increasing batch size or length of run leads to increased
inventory and longer flow times.
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5. Flow Rate and Capacity Analysis
Decrease resource idleness
Decreasing resource idleness» Starvation and Blockage are the problems.
If we have two raw material for a process and one is unavailable we have a starvation condition
If the buffer is not big enough upstream and there is no place for the product to go we have a blockage condition
» Techniques to avoid Starvation and Blockage Proper buffer size Process flow synchronization
Internal bottle neck will require increasing the capacity of the bottle neck to a capacity where a new bottleneck will appear. Once the old bottleneck does not have the lowest capacity do not continue to increase capacity. It will not increase overall capacity any further.