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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; its effect on theoretical capacity and profitability
Capacity Improvement
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Flow Rate and Capacity Analysis
Throughput and Takt Time
Throughput: Average Flow Rate
The average number of flow units in a stable process that flow through any given point of a process per unit of time.
Takt time = 1/(throughput)
The time interval between exit of two consecutive products. The average activity time at each workstation on an assembly line.
Chapter 4 was on flow time minimization.
Chapter 5 is on throughput maximization.
Chapter 4 and 5 are both “time” minimization. Why?
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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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Flow Rate and Capacity Analysis
Resources, Resource Pools, and Resource Pooling
Capital Resources – Fixed Assets such as land, buildings, facilities, machinery and equipment .
Human Resources – 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 toperform 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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Flow Rate and Capacity Analysis
Activity, Work Content, Resource, and Unit Load
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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Flow Rate and Capacity Analysis
Theoretical Capacity
Theoretical capacity of a resource unit – maximum sustainable flow rate if it were fully utilized
Theoretical Capacity of a Resource unit = 1/unit load = 1/ Tp
Theoretical capacity of a resource pool – sum of all the theoretical capacities of all the resource units in that pool
Theoretical capacity of a Resource pool = Rp = cp / Tp
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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Flow Rate and Capacity Analysis
Theoretical Capacity
Cross train Claim supervisor to help Mail room clerk
Increase Theoretical Capacity
Resource Unit Load (min./claim): Tp
Theoretical capacity of a Resource Unit: 1/T p claims/min
Number of the Resouce Units in the Resource Pool: c p
Theoretical capacity of Resource Pool: R p =c p /T p
Claims/min
Mailroom clerk
0.6 1.67 1 1.67
Data-entry clerk
4.2 0.24 8 1.90
Claims processor
6.6 0.15 12 1.82
Claims supervisor
2.2 0.45 5 2.27
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Flow Rate and Capacity Analysis
Load Batch and Scheduled Availability
Load batching – a resource processes several flow units simultaneously (one oven and 10 loaves of bread)
Scheduled availability – the scheduled time period during which a resource unit is available for processing flow units (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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Flow Rate and Capacity Analysis
Theoretical Capacity for Physicians Claims
Claims supervisors are the bottleneck. Cross train claim processor to do a part of claim supervisor job increase theoretical capacityThroughput ( due to internal constraints and external constraints) is always less than the theoretical capacity. Suppose while Theoretical capacity = 545.5, Throughput = 480
Resource Pool
Scheduled availability (min/day)
Unit Load (min./claim): Tp
Theoretical capacity of a Resource Unit: (1/T p )(min/day)
claims/day
Number of the Resouce Units in the Resource Pool: c p
Theoretical capacity of Resource Pool: R p =(c p /T p )(min/day)
Claims/min
Mailroom clerk
450 0.6 750.0 1 750.0
Data-entry clerk
450 4.2 107.1 8 857.1
Claims processor
360 6.6 54.5 12 654.5
Claims supervisor
240 2.2 109.1 5 545.5
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Flow Rate and Capacity Analysis
Capacity Utilization
Resource pool (p)Theoretical capacity of Resource pool (claims/day) (Rp)
Capacity Utilization(ρp=R/Rp)
Throughput = 480
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%
Capacity utilization of a resource pool
ρp = Throughput/Theoretical capacity of a resource pool = R/Rp
Capacity utilization of the process
ρ = Throughput/Theoretical capacity of the bottleneck resource pool
88%
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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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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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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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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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Flow Rate and Capacity Analysis
Optimal Product Mix
Resource pool (p) PhyClim HosClaim Needed Available
Mailroom clerk 0.6 1 327.3 <= 450
Data-entry clerk 4.2 5.2 2290.9 <= 3600
Claims processor 6.6 7.5 3600.0 <= 4320
Claims supervisor 2.2 3.2 1200.0 <= 12001 1 545.4545545.45 0
Adjustable CellsFinal Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease$B$8 PhyClim 545.4545455 0 1 1E+30 0.3125$C$8 HosClaim 0 -0.454545455 1 0.454545455 1E+30
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Flow Rate and Capacity AnalysisFrom Theoretical Capacity to Effective Capacity; Setup Batch, Total Unit Load, and Net AvailabilitySetup 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
We can add setup time to work content or subtract it from schedule availability. From a managerial control point which one is better?
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
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Flow Rate and Capacity Analysis
Setup Batch Size
What is the “right” lot size or the size of the set up batch? lot size unit load Capacity. lot size inventory 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.
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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Flow Rate and Capacity Analysis
Total Unit Load for Product mix
Regular Jumbo Mix
Unit Load (Tp) 2 1 (2×0.75)+(1×0.25)=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 1.75+0.15 = 1.9
(2.1×0.75)+(1.3×0.25)=1.9
Product L -Batch S-Batch Cutting time Setup timeRegular 4 units 300 L-batch 2 min/L-batch 30 min/S-BatchJumbo 9 units 100 L-batch 1 min/L-batch 30 min/S-Batch
Compute unit load and total unit load for each Load batch of Regular tile, Jumbo tile, and a product mix of 75% Regular and 25% Jumbo
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Flow Rate and Capacity Analysis
Net Availability
Theoretical Capacity of a resource unit = (1/Unit load) ×Load batch ×Scheduled availability
Scheduled availability – the scheduled time period during which aresource unit is available for processing flow units.
Availability loss factor = 1 – (Net Availability/Scheduled Availability)
Effective Capacity of a resource unit = (1/Total unit load) × Load batch × Net availability
Effective Capacity of a pool = (cp/Total unit load) × Load batch ×Net availability
The effective capacity of a process is the effective capacity of itsslowest resource pool (effective bottleneck).
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Flow Rate and Capacity Analysis
Effective Capacity of a Resource Pool and Process
Resource Pool No. Units in Resource Pool
Load Batch
(Total) Unit Load (minutes )
Scheduled avilability hours /day
Loss Factor
Net Availability (Minutes)
Effective Capacity of the Resource Pool (flow units/day)
Worker S 1 1 10 8 6.25% 450 45.00
Punch press R 1 1 22 8 5% 456 20.73
Punch press B 1 1 30 8 5% 456 15.20
Worker PR 1 1 22 8 5% 456 20.73
Worker PB 1 1 30 8 5% 456 15.20
Forming machine R 1 1 12 8 10% 432 36.00
Forming machine B 1 1 6 8 10% 432 72.00
Worker FR 1 1 12 8 6.25% 450 37.50
Worker FB 1 1 6 8 6.25% 450 75.00
Welding gun 1 1 13 8 10.0% 432 33.23
Worker SA 1 1 13 8 6.25% 450 34.62
Worker FA 1 1 10 8 6.25% 450 45.00
Inspector 2 1 36 8 6.25% 450 25.00
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Flow Rate and Capacity Analysis
From Theoretical Capacity to Throughput
Throughput ≤ Process capacity ≤ Effective capacity ≤ Theoretical capacity Theoretical capacity Effective Capacity
Breakdown or absenteeism (Schedule Availability Net Availability)
Preventive maintenance (Schedule Availability Net Availability) Setup time (Unit load Total unit load) total unit load is unit load
plus setup time per unit, Tp+Sp/Qp,
Effective Capacity Process Capacity Internal starvation (from preceding station) Internal blockage (due to next station)
Process Capacity Throughput External starvation (supply of row material) External blockage (product demand)
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Flow Rate and Capacity Analysis
Improving Theoretical Capacity
Theoretical capacity of a pool =
(cp/Total unit load) × Load batch ×Scheduled availability
Decrease unit load on the bottleneck: Decrease the work content of the activity performed by the bottleneck resource pool.
Increase Scheduled Availability of the bottleneck: Add more hours to the resource such as adding overtime or second shift operations
Increase the Load Batch of the bottleneck: Expanding the resource will increase resource capacity
Increase the number of resources at bottleneck resource : Adding units to the bottleneck resource pool will increase resource capacity
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Flow Rate and Capacity Analysis
Improving Effective Capacity
Increasing net availability Regular Maintenance of equipment Perform maintenance after production time
Reducing setup waste Reduce the setup time Improve product mix
Caution: Increasing batch size or length of run increased inventory longer flow times.
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Flow Rate and Capacity Analysis
Internal Bottlenecks
Internal Bottleneck Throughput is equal to Process Capacity The output of the process is limited by the process’s own
constraints (the bottleneck resource) Starvation: If we have two raw material for a process and
one is unavailable. Blockage: If the buffer is not big enough upstream and
there is no place for the product to go 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.
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Flow Rate and Capacity Analysis
External Bottlenecks
External Bottleneck Throughput is less than to Process Capacity
The output of the process is limited by conditions external to the boundaries of the internal process constraints. Examples include: demand for product, raw material shortages.
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