om&pm/class 6b1 1operations strategy 2process analysis 3lean operations 4supply chain management...
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OM&PM/Class 6b 1
1 Operations Strategy
2 Process Analysis
3 Lean Operations
4 Supply Chain Management
5 Capacity Management in Services– Class 6b: Capacity Analysis and Queuing
» Why do queues build up?
» Performance measures for queuing systems
» The need for safety capacity
» Throughput of queuing system with finite buffer
» Pooling of capacity
6 Total Quality Management
7 Business Process Reengineering
Operations Management & Performance Modeling
OM&PM/Class 6b 5
Telemarketing at L.L.Bean
During some half hours, 80% of calls dialed received a busy signal.
Customers getting through had to wait on average 10 minutes for an available agent. Extra telephone expense per day for waiting was $25,000.
For calls abandoned because of long delays, L.L.Bean still paid for the queue time connect charges.
In 1988, L.L.Bean conservatively estimated that it lost $10 million of profit because of sub-optimal allocation of telemarketing resources.
OM&PM/Class 6b 6
Telemarketing: deterministic analysis
it takes 8 minutes to serve a customer
6 customers call per hour – one customer every 10
minutes
Flow Time = 8 min
Flow Time Distribution
Flow Time (minutes)
Pro
bab
ilit
y
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0 15 30 45 60 75 90
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0%
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30%
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OM&PM/Class 6b 7
Telemarketing with variability inarrival times + activity times
In reality service times– exhibit variability
In reality arrival times– exhibit variability
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e
Flow Time
Pro
bab
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y
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Mor
e
Flow Time
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bab
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y
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OM&PM/Class 6b 8
Telemarketing with variability: The effect of utilization
Average service time = – 9 minutes
Average service time =– 9.5 minutes
0%
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Mor
e
Flow TimeP
rob
abil
ity
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Pro
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OM&PM/Class 6b 9
Why do queues form?
utilization: – throughput/capacity
variability: – arrival times
– service times
– processor availability
0123456789
10
0 20 40 60 80 100 TIME
0
1
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4 5
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TIME
Call #
Inventory (# of calls in system)
OM&PM/Class 6b 10
Industry Process AverageCycle Time
TheoreticalCycle Time
Process Efficiency
Life Insurance New PolicyApplication
72 hrs. 7 min. 0.16%
ConsumerPackaging
NewGraphicDesign
18 days 2 hrs. 0.14%
CommercialBank
ConsumerLoan
24 hrs. 34 min. 2.36%
Hospital PatientBilling
10 days 3 hrs. 3.75%
AutomobileManufacture
FinancialClosing
11 days 5 hrs 5.60%
Cycle Times in White Collar Processes
OM&PM/Class 6b 11
Queuing Systems to model Service Processes: A Simple Process
Sales Repsprocessing
calls
Incoming callsCalls
on Hold
Answered Calls
MBPF Inc. Call Center
Blocked Calls(Busy signal)
Abandoned Calls(Tired of waiting)
Order Queue“buffer” size K
OM&PM/Class 6b 12
What to manage in such a process?
Inputs– InterArrival times/distribution
– Service times/distribution
System structure– Number of servers
– Number of queues
– Maximum queue length/buffer size
Operating control policies – Queue discipline, priorities
OM&PM/Class 6b 13
Performance Measures
Sales– Throughput R
– Abandonment
Cost– Server utilization – Inventory/WIP : # in queue/system
Customer service– Waiting/Flow Time: time spent in queue/system
– Probability of blocking
OM&PM/Class 6b 14
Queuing Theory:Variability + Utilization = Waiting
Throughput-Delay curve:
Pollaczek-Khinchine Form:– Prob{waiting time in queue < t } = 1 - exp(-t / Ti ) where:
Variability
TheoreticalCycle Time
ActualAverageCycleTime, W
Utilization 100%
m
21
122pi
pi
CC
RT
mean service time
utilization effect
variability effectx x
OM&PM/Class 6b 15
Levers to reduce waiting and increase QoS: variability reduction + safety capacity
How reduce system variability?
Safety Capacity = capacity carried in excess of expected demand to cover for system variability– it provides a safety net against higher than expected arrivals
or services and reduces waiting time
OM&PM/Class 6b 16
Example 1: MBPF Calling Centerone server, unlimited buffer
Consider MBPF Inc. that has a customer service representative (CSR) taking calls. When the CSR is busy, the caller is put on hold. The calls are taken in the order received.
Assume that calls arrive exponentially at the rate of one every 3 minutes. The CSR takes on average 2.5 minutes to complete the reservation. The time for service is also assumed to be exponentially distributed.
The CSR is paid $20 per hour. It has been estimated that each minute that a customer spends in queue costs MBPF $2 due to customer dissatisfaction and loss of future business.– MBPF’s waiting cost =
OM&PM/Class 6b 17
Example 2: MBPF Calling Center limited buffer size
In reality only a limited number of people can be put on hold (this depends on the phone system in place) after which a caller receives busy signal. Assume that at most 5 people can be put on hold. Any caller receiving a busy signal simply calls a competitor resulting in a loss of $100 in revenue.
– # of servers c = 1
– buffer size K = 6 What is the hourly loss because of callers not being able to get
through?
OM&PM/Class 6b 18
Example 3: MBPF Calling CenterResource Pooling
2 phone numbers– MBPF hires a second CSR who is
assigned a new telephone number. Customers are now free to call either of the two numbers. Once they are put on hold customers tend to stay on line since the other may be worse ($111.52)
1 phone number: pooling– both CSRs share the same
telephone number and the customers on hold are in a single queue ($61.2)
Servers
Queue
ServerQueue
ServerQueue
50%
50%
OM&PM/Class 6b 19
Example 4: MBPF Calling CenterStaffing
Assume that the MBPF call center has a total of 6 lines. With all other data as in Example 2, what is the optimal number of CSRs that MBPF should staff the call center with?– c = 3
OM&PM/Class 6b 20
Class 6b Learning objectives
Queues build up due to variability.
Reducing variability improves performance.
If service cannot be provided from stock, safety capacity must be provided to cover for variability.
Tradeoff is between cost of waiting, lost sales, and cost of capacity.
Pooling servers improves performance.
OM&PM/Class 6b 21
National Cranberry Cooperative
Hourly Berry Arrivals
539
1395
1792
1269
1713
1477
0
1032
2298
1317
1335 1341
1680
1016
0
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Time
Bbls
OM&PM/Class 6b 22
Real Processes exhibit variability in order placement time and type
Histogram of Truck inter-delivery times
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Truck interarrival time (min)
Fre
quen
cy (
# of
truc
ks)
Histogram of Truck Weights
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cy (
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ks)
National Cranberry on Sept 23, 1970