1. Flow Rate and Capacity Analysis
QUAN 6610
Chapter 5
Flow Rate and Capacity Analysis
Based on Anupindi
Flow Rate and Capacity

2. 5.1 Resources
Tp = unit load = total time resource works to process flow unit.
Example 5.1
See Table 5.1 for data.
Based on Anupindi

3. Theoretical capacity of a process = theoretical capacity of bottleneck
Capacity = 1/unit load = 1 / Tp
Resource Pool Capacity = cp / Tp
Example 5.2
Based on Anupindi

4. Theoretical Capacity of a Resource Unit in a Pool
Scheduled availability = the amount of time that a resource is schedule for operation.
Theoretical Capacity of a Resource Unit in a Pool
= Rp = (cp / Tp) x Load batch x Scheduled availability
Example 5.3
Based on Anupindi

5. Capacity utilization of a resource pool (rp) =
Capacity utilization of a resource pool (rp) measures the degree to which resources are effectively utilized by a process.
Capacity utilization of a resource pool (rp) =
Throughput / theoretical capacity of resource pool p = R / Rp
Example 5.4
Given: R = 480 / day
Based on Anupindi

6. Demonstration of concepts thus far.
Example 5.5
See Table 5.6 for Work Content and Resources
Based on Anupindi

7. Given: R = 5.5 patients per hour
Based on Anupindi

8. 5.3 Effect of Product Mix on Theoretical Capacity
Example 5.7
Theoretical capacity for Hospital Claims:
Based on Anupindi

9. Theoretical capacity for 60%/40% Mix
Based on Anupindi

10. Example 5.8
See Table 5.12 for Activities, Work Content and Resource Pools for a Standard Shed
Based on Anupindi

11. Based on Anupindi

12. Based on Anupindi

13. Based on Anupindi

14. Based on Anupindi

15. 5.4 Other Factors Affecting Process Capacity
Net availability = actual time during which the resource is available for
processing flow units
Available Loss Factor = 1 – (Net Availability / Scheduled Availability)
Based on Anupindi

16. Improving Theoretical Capacity
Decrease the unit load on the bottleneck resource pool (work faster, work smarter.
Increase the load batch of resources in the bottleneck resource pool (increase scale of resource).
Increase the number of units in the bottleneck resource pool (increase scale of process).
Increase the scheduled availability of the bottleneck resource pool (work longer).
Based on Anupindi

17. Based on Anupindi

18. How increase capacity? Summary of Typical Actions
Key action = optimize only bottleneck management
Decrease the work content of bottleneck activities
Never unnecessarily idle (“starve”) bottlenecks = eliminate bottleneck waits:
Reduce variability if it leads to bottleneck waiting
Synchronize flows to and from the bottleneck: sync when resources start an activity
work smarter:
Reduce & externalize setups/changeover times, streamline + eliminate non-value added work
do it right the first time: eliminate rework/corrections
work faster
Move work content from bottlenecks to non-bottlenecks
create flexibility to offload tasks originally assigned to bottleneck to non-critical resource or to third party
Can we offload tasks to cross-trained staff members?
Increase Net Availability of Process
work longer: increase scheduled availability
increase scale of process: invest in more human and capital resources
eliminate unscheduled downtimes/breakdowns
Preventive maintenance, backups, etc.
Based on Anupindi

19. Based on Anupindi

20. Additional Concepts
(Problem Scenario from Cachon and Terwiesch)
Assume three activities with times of 13 min/unit, 11 min/unit and 8 min/unit, each staffed by one worker.
Assume an hourly rate of $12/hour and a demand of 125 scooters per week. Assume the process operates 35 hours per week.
Activity 1
Activity 2
Activity 3
Components
Finished Product
Based on Anupindi, et al, MBPF (2e)

21. 4.2 Time to Process a Quantity X Starting with an Empty Process
Worker-paced system: each worker is free to work at his or her own pace; if the first worker finishes before the first worker is ready to accept the parts, then the first worker puts the completed work in the inventory between them.
Time through an empty worker-paced process = Sum of the activity times
= = 32 minutes
Machine-paced system: all the steps must work at the same rate.
Time through an empty machine-paced process =
Number of resources in sequence x Activity time of the bottleneck step
= 3 x 13 = 36 minutes
Time to make X units = Time through empty system +
Cachon and Terwiesch, Matching Supply with Demand.
Process Labor Costs

22. 4.3 Labor Content and Idle Time
QUAN 6610
4.3 Labor Content and Idle Time
Labor content = sum of activity times with labor = 13 min/unit = 32 min/unit
Cost of direct labor =
To correctly compute the cost of direct labor, we need to look at two measures:
The number of scooters produced per unit of time (the flow rate).
The amount of wages we pay for the same time period.
Cachon and Terwiesch, Matching Supply with Demand.
Process Labor Costs

23. QUAN 6610
Exhibit 4.1
TIME TO PROCESS A QUANITY X STARTING WITH AN EMPTY PROCESS
Find the time it takes the flow unit to go through the empty system:
In worker-paced line, this is the sum of the activity times
In machine-paced line, this is the cycle time x the number of stations
Compute the capacity of the process (see previous methods). Since we are producing X units as fast as we can, we are capacity constrained; thus,
Flow rate = Process capacity
Time to finish X units
Time to make X units = Time through empty system +
Components
Finished Xootrs
Activity 1
Activity 2
Activity 3
Conveyor Belt
Figure 4.4. : A machine paced process lay-out (Note: conveyor belt is only shown for illustration)
Q 4.1 a.
Cachon and Terwiesch, Matching Supply with Demand.
Process Labor Costs

24. Exhibit 4.2 SUMMARY OF LABOR COST CALCULATIONS
QUAN 6610
Exhibit 4.2
SUMMARY OF LABOR COST CALCULATIONS
Compute the capacity of all resources; the resource with the lowest capacity is the bottleneck (see previous methods) and determines the process capacity.
Compute Flow rate = Min {Available input, Demand, Process Capacity};
compute Cycle time =
Compute the total wages (across all workers) that are paid per unit of time:
Cost of direct labor =
Compute the idle time of each worker for each unit:
Idle time for worker at resource i = Cycle time x (Number of workers at resource i) – Activity time at resource i
Compute the labor content of the flow unit: this is the sum of all activity times involving direct labor
Add up the idle times across all resources (total idle time); then compute
Cachon and Terwiesch, Matching Supply with Demand.
Process Labor Costs

25. Table 4.1 Basic Calculations Related to Idle Time
QUAN 6610
Table 4.1 Basic Calculations Related to Idle Time
Worker 1
Worker 2
Worker 3
Activity time
13 min/unit
11 min/unit
8 min/unit
Capacity
1/13 unit/minutes
= 4.61 units/hr
1/11 units/minutes
= 5.45 units/hr
1/8 unit/minutes
= 7.5 units/hr
Process capacity
Minimum {4.61 units/h, 5.45 units/h, 7.5 units/h} = 4.61 units/h
Flow rate
Demand = 125 units/week = 3.57 units/hr
Flow rate = Minimum {demand, process capacity} = 3.57 units/hr
Cycle time
1/3.57 hours/unit = 16.8 minutes/unit
Idle time
{Total = 18.4 min/unit}
16.8 minutes/unit
- 13 minutes/unit
= 3.8 minutes/unit
- 11 minutes/unit
= 5.8 minutes/unit
- 8 minutes/unit
= 8.8 minutes/unit
Utilization
3.57 / 4.61 = 77%
3.57 / 5.45 = 65.5%
3.57 / 7.5 = 47.6%
Average Labor Utilization
= 1/3 x (77.4% % %) = 63.5%
Or = 32 / ( ) = 63.5%
Cachon and Terwiesch, Matching Supply with Demand.
Process Labor Costs

26. 4.4 Increasing Capacity by Line Balancing
QUAN 6610
4.4 Increasing Capacity by Line Balancing
Comparing the utilization levels in table 4.1 reveals a strong imbalance between workers. Imbalances within a process provide micro-level mis-matches between what could be supplied by one step and what is demanded by the following steps. Line balancing is the act of reducing such imbalances. It provides the opportunity to:
Increase the efficiency of the process by better utilizing the various resources
Increase the capacity of the process by reallocating either workers from underutilized resources to the bottleneck or work from the bottleneck to the underutilized resources.
Worker 1
Worker 2
Worker 3
Utilization
3.57 / 4.61 = 77%
3.57 / 5.45 = 65.5%
3.57 / 7.5 = 47.6%
Utilization
3.57 / 4.61 = 77%
3.57 / 5.45 = 65.5%
3.57 / 7.5 = 47.6%
Cachon and Terwiesch, Matching Supply with Demand.
Process Labor Costs

27. QUAN 6610
Observations on Table 3.4
Unlike utilization, implied utilization can exceed 100 percent.
The fact that a resource has an implied utilization over 100 percent does not make it the bottleneck. There is only one bottleneck in the process -- the resource where the implied utilization is the highest.
In the case of capacity expansion of a process, it might be worthwhile to add capacity to these other resources as well, not just to the bottleneck. Depending on the margins we make and the cost of installing capacity, we could make a case to install additional capacity for all resources with an implied utilization above 100 percent.
Capacity requested by demand
Implied Utilization =
Available capacity
Cachon and Terwiesch, Matching Supply with Demand.
Process Capacity