1. 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

2. 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?

3. Activities and Buffers
Resources in a Process
Process
Management
Information
structure
Network of
Activities and Buffers
Inputs
Outputs
Goods
Services
Flow units
(customers, data,
material, cash, etc.)
Resources
Labor + Capital

4. 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 to
perform several activities.
Unit Load of a Resource Unit (Tp): The amount of time the resource works to
process each flow unit.

5. Activity, Work Content, Resource, and Unit Load
(minutes)
Mailroom
Mailroom Clerk
0.6
Data Entry
Data-entry Clerk
4.2
Initial Processing
Claims processor
4.8
Inspection
Claims Supervisor
2.2
Final Processing
1.8
Resource
Unit Load
(minutes)
Mailroom Clerk
0.6
Data-entry Clerk
4.2
Claims processor
6.6
Claims Supervisor
2.2

6. 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

7. Theoretical Capacity
Cross train Claim supervisor to help Mail room clerk
 Increase Theoretical Capacity

8. 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

9. Theoretical Capacity for Physicians Claims
Claims supervisors are the bottleneck. Cross train claim processor to do a part of claim supervisor job  increase theoretical capacity
Throughput ( due to internal constraints and external constraints) is always less than the theoretical capacity.
Suppose while Theoretical capacity = 545.5, Throughput = 480

10. Capacity Utilization
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
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%
88%

11. 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)
UL (60%-40%) mix
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

12. 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
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

13. 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
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

14. 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
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

15. Optimal Product Mix

16. From Theoretical Capacity to Effective Capacity; Setup Batch, Total Unit Load, and Net Availability
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
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
Setup batch (also lot size): number of units processed consecutively after a setup
EXAMPLE: painting cars->how many cars before you change paint color

17. 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
Setup batch (also lot size): number of units processed consecutively after a setup
EXAMPLE: painting cars->how many cars before you change paint color

18. Total Unit Load for Product mix
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
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
= 1.9
(2.1×0.75)+(1.3×0.25)=1.9

19. Net Availability Theoretical Capacity of a resource unit =
(1/Unit load) ×Load batch ×Scheduled availability
Scheduled availability – the scheduled time period during which a
resource 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 its
slowest resource pool (effective bottleneck).

20. Effective Capacity of a Resource Pool and Process

21. 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)

22. 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

23. 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.

24. 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.

25. 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.