1 flow rate and capacity analysis throughput and capacity resources and resource pools ...

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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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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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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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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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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


ResourceUnit Load(minutes)

Mailroom Clerk 0.6

Data-entry Clerk 4.2


Claims Supervisor 2.2

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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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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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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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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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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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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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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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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


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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Theoretical Capacity for 60% / 40% Mix

Resource pool (p)

Scheduled availability(min./day)

Unit Load(Tp)

(min./claim)


Resource Unit(claims/day)

Number of Units in

Resource Pool


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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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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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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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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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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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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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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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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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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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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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.

1 flow rate and capacity analysis throughput and capacity resources and resource pools ...

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