Transcript Slide 1

Chapter 5
Flow Rate and Capacity Analysis
Based on Anupindi
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5.1 Resources
Tp = unit load = total time resource works to process flow unit.
Example 5.1
See Table 5.1 for data.
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Theoretical capacity of a process = theoretical capacity of bottleneck
Capacity = 1/unit load = 1 / Tp
Resource Pool Capacity = cp / Tp
Example 5.2
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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
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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
Based on Anupindi
Given: R = 480 / day
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Demonstration of concepts thus far.
Example 5.5
See Table 5.6 for Work Content and Resources
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Given: R = 5.5 patients per hour
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5.3 Effect of Product Mix on Theoretical Capacity
Example 5.7
Theoretical capacity for Hospital Claims:
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Theoretical capacity for 60%/40% Mix
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Example 5.8
See Table 5.12 for Activities, Work Content and Resource Pools for a
Standard Shed
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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)
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Improving Theoretical Capacity
1. Decrease the unit load on the bottleneck
resource pool (work faster, work smarter.
2. Increase the load batch of resources in the
bottleneck resource pool (increase scale of
resource).
3. Increase the number of units in the bottleneck
resource pool (increase scale of process).
4. Increase the scheduled availability of the
bottleneck resource pool (work longer).
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How increase capacity?
Summary of Typical Actions

Key action = optimize only bottleneck management
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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.
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Based on Anupindi
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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
Components
Based on Anupindi, et al, MBPF (2e)
Activity 2
Activity 3
Finished Product
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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
= 13 + 11 + 8 = 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.
X  1 unit
Flow rate
4.3 Labor Content and Idle Time
Labor content = sum of activity
times with labor = 13 min/unit + 11
+ 8 = 32 min/unit
To correctly compute the
cost of direct labor, we need
to look at two measures:
Cost of direct labor =
Total wages per unit of tim e
Flowrate per unit of tim e
Wages per week

Scooters produced per unit of tim e
3 x $12 / h x 35 h / wk

125 scooters/ wk
 $10.08 / scooter
• The number of scooters
produced per unit of time (the
flow rate).
Cachon and Terwiesch, Matching Supply with Demand.
• The amount of wages we pay
for the same time period.
Exhibit 4.1
TIME TO PROCESS A QUANITY X STARTING WITH AN EMPTY PROCESS
1.
2.
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
3.
Time to finish X units
X  1 unit
Time to make X units = Time through empty system +
Flow rate
Conveyor Belt
Components
Finished Xootrs
Activity 1
Activity 2
Activity 3
Figure 4.4. : A machine paced process lay-out (Note:
conveyor belt is only shown for illustration)
Cachon and Terwiesch, Matching Supply with Demand.
Q 4.1 a.
Exhibit 4.2
SUMMARY OF LABOR COST CALCULATIONS
1.
Compute the capacity of all resources; the resource with the lowest capacity is the
bottleneck (see previous methods) and determines the process capacity.
2.
Compute Flow rate = Min {Available input, Demand, Process Capacity};
compute Cycle time =
3.
Compute the total wages (across all workers) that are paid per unit of time:
Cost of direct labor =
4.
1
Flow rate
Total wages
Flowrate
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
5.
Compute the labor content of the flow unit: this is the sum of all activity times
involving direct labor
6.
Add up the idle times across all resources (total idle time); then compute
Average labor utilization 
Cachon and Terwiesch, Matching Supply with Demand.
Labor content
Labor content  Total idle tim e
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
16.8 minutes/unit
- 13 minutes/unit
= 3.8 minutes/unit
16.8 minutes/unit
- 11 minutes/unit
= 5.8 minutes/unit
16.8 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% + 65.5% + 47.6%) = 63.5%
Or = 32 / (32 + 18.4) = 63.5%
{Total = 18.4
min/unit}
Cachon and Terwiesch, Matching Supply with Demand.
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.
Utilization
Worker 1
Worker 2
Worker 3
3.57 / 4.61 = 77%
3.57 / 5.45 = 65.5%
3.57 / 7.5 = 47.6%
Cachon and Terwiesch, Matching Supply with Demand.
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.