Transcript OPNS Process Analysis Module

Managing Business Process Flows: Ch 8
Capacity Planning in Services
 Matching Supply and Demand
 The Service Process
 Performance Measures
 Causes of Waiting
 Economics of Waiting
 Management of Waiting Time
 The Sof-Optics Case
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Matching Supply and Demand
 Goods vs. Services
– Make to Stock vs. Make to Order
– Produce in advance vs. on demand
– Safety Inventory vs. Safety Capacity
 Examples
– Banks (tellers, ATMs, drive-ins)
– Fast food restaurants (counters, drive-ins)
– Retail (checkout counters)
– Airline (reservation, check-in, takeoff, landing, baggage claim)
– Hospitals (ER, OR, HMO)
– Call centers (telemarketing, help desks, 911 emergency)
– Service facilities (repair, job shop, ships/trucks load/unload)
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The DesiTalk Call Center
The Call Center Process
Incoming Calls
(Customer Arrivals)
Calls
on Hold
(Service Inventory)
Blocked Calls
Abandoned Calls
(Due to busy signal) (Due to long waits)
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Sales Reps
Processing
Calls
Answered Calls
(Customer Departures)
(Service Process)
Calls In Process
(Due to long waits)
3
The Service Process
 Customer Inflow (Arrival) Rate (Ri)
– Inter-arrival Time = 1 / Ri
 Processing Time Tp
– Processing Rate per Server = 1/ Tp
 Number of Servers (c)
– Number of customers that can be processed simultaneously
 Total Processing Rate (Capacity) = Rp= c / Tp
 Buffer Capacity (K)
– Maximum Queue Length
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Operational Performance Measures
 Flow time T








=
Ti
+
Tp
Inventory I
=
Ii
+
Ip
Flow Rate R
=
Min (Ri, Rp)
Stable Process =
Ri < Rp,, so that R = Ri
Little’s Law: I = Ri  T, Ii = Ri  Ti, Ip = Ri  Tp
Capacity Utilization u = Ip / c = Ri  Tp / c = Ri / Rp < 1
Safety Capacity Rs = Rp - Ri
Number of Busy Servers = Ip= c  = Ri  Tp
Fraction Lost Pb = P(Blocking) = P(Queue = K)
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Financial Performance Measures

Sales
– Throughput Rate
– Abandonment Rate
– Blocking Rate

Cost
– Capacity utilization
– Number in queue / in system

Customer service
– Waiting Time in queue /in system
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Flow Times with Arrival Every 4 Secs
Customer
Number
Arrival
Time
Departure
Time
Time in
Process
1
0
5
5
2
4
10
6
3
8
15
7
4
12
20
8
5
16
25
9
6
20
30
10
3
7
24
35
11
2
8
28
40
12
9
32
45
13
10
36
50
14
10
9
Customer Number
8
7
6
5
4
1
0
10
20
30
40
50
Time
What is the queue size?
What is the capacity utilization?
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Flow Times with Arrival Every 6 Secs
Arrival
Time
Departure
Time
Time in
Process
10
1
0
5
5
9
2
6
11
5
8
3
12
17
5
4
18
23
5
5
24
29
5
6
30
35
5
7
36
41
5
2
8
42
47
5
1
9
48
53
5
10
54
59
5
Customer Number
Customer
Number
7
6
5
4
3
0
10
20
30
40
50
60
Time
What is the queue size?
What is the capacity utilization?
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8
Effect of Variability
Customer
Number
Arrival
Time
Processing
Time
Time in
Process
1
0
7
7
2
10
1
1
3
20
7
7
4
22
2
7
5
32
8
8
6
33
7
14
7
36
4
15
8
43
8
16
9
52
5
12
10
54
1
11
10
9
8
Customer
7
6
5
4
3
2
1
0
10
20
30
40
50
60
70
Time
Queue Fluctuation
4
What is the queue size?
What is the capacity utilization?
Number
3
2
1
0
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64
Time
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Effect of Synchronization
Customer
Number
Arrival
Time
Processing
Time
Time in
Process
1
0
8
8
2
10
8
8
8
3
20
2
2
7
4
22
7
7
6
5
32
1
1
5
6
33
1
1
4
7
36
7
7
3
8
43
7
7
2
9
52
4
4
1
10
54
5
7
10
9
0
10
20
30
40
50
60
70
What is the queue size?
What is the capacity utilization?
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Conclusion

If inter-arrival and processing times are constant, queues will build up if and only
if the arrival rate is greater than the processing rate
 If there is (unsynchronized) variability in inter-arrival and/or processing times,
queues will build up even if the average arrival rate is less than the average
processing rate
 If variability in interarrival and processing times can be synchronized (correlated),
queues and waiting times will be reduced
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Summary: Causes of Delays and Queues

High Unsynchronized Variability in
– Interarrival Times
– Processing Times

High Capacity Utilization u = Ri / Rp, or Low Safety Capacity Rs = Rp –
Ri, due to
– High Inflow Rate Ri
– Low Processing Rate Rp = c/ Tp
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The Queue Length Formula
Ii 
Utilization
effect
u
2(c 1)
Ci2  C p2
1 u
2
x
Variability
effect
where u  Ri / Rp, where Rp = c / Tp, and
Ci and Cp are the Coefficients of Variation
(Standard Deviation/Mean) of the inter-arrival
and processing times (assumed independent)
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Throughput- Delay Curve
Average
Flow
Time T
Variability
Increases
Tp
Utilization (ρ)
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100%
u
14
Computing Performance Measures
 Given
– Interarrival times: 10, 10, 2, 10, 1, 3, 7, 9, and 2
– Processing times: 7, 1, 7, 2, 8, 7, 4, 8, 5, 1
– c=1
 Compute
– Capacity Utilization  = Ri / Rp = 0.833
– Ci = 3.937/6 = 0.6562
– Cp = 2.8284/5 = 0.5657
 Queue Length Formula
– Ii = 1.5633
 Hence
– Ti = Ii / R = 9.38 seconds, and Tp = 5 seconds, so
– T = 14.38 seconds, so
– I = RT = 14.38/6 = 2.3966
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Effect of Increasing Capacity
 Given
– Interarrival times: 10, 10, 2, 10, 1, 3, 7, 9, and 2
– Processing times: 7, 1, 7, 2, 8, 7, 4, 8, 5, 1
– c=2
 Compute
– Capacity Utilization  = Ri / Rp = 0.4167
– Ci = 3.937/6 = 0.6562
– Cp = 2.8284/5 = 0.5657
 Queue Length Formula
– Ii = 0.07536
 Hence
– Ti = Ii / R = 0.45216 seconds, and Tp = 5 seconds, so
– T = 5.45216 seconds, so
– I = RT = 5.45216/6 = 0.9087
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The Exponential Model

Poisson Arrivals
– Infinite pool of potential arrivals, who arrive completely randomly, and independently
of one another, at an average rate Ri  constant over time

Exponential Processing Time
– Completely random, unpredictable, i.e., during processing, the time remaining does
not depend on the time elapsed, and has mean Tp

Computations
– Ci = Cp = 1
– If c = 1, T = 1/(Rp  Ri), then I = Ri  T,...
– If c ≥ 2, and K < ∞ , use Performance.xls
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Example
 Interarrival time = 6 secs, so Ri = 10/min
 Tp = 5 secs = 0.833 mins
c
u
1
0.833
2
0.417
Rs
Ti
T
I
0.0333 4.162
0.416
0.499
4.995
0.2333 0.175
0.018
0.101
1.0087
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Ii
18
Synchronization

Matching Capacity with Demand
 Capacity
– Short term Control
– Long term Planning

Demand
– Pricing
– Scheduling
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Performance Improvement Levers
 Capacity Utilization / Safety Capacity
– Demand Management (arrival rate)

Peak load pricing
– Increase Capacity (processing rate)
 Number of Servers (scale)
 Processing Rate (speed)
 Variability Reduction
– Arrival times

Scheduling, Reservations, Appointments
– Processing times
 Standardization, Specialization, Training
 Synchroniztion
– Matching capacity with demand
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Effect of Pooling
Ri/2
Server 1
Queue 1
Ri
Ri/2
Server 2
Queue 2
Server 1
Ri
Queue
Server 2
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Effect of Buffer Capacity
 Process Data
– Ri = 20/hour, Tp = 2.5 mins, c = 1, K = # Lines – c
 Performance Measures
K
4
5
6
Ii
1.23
1.52
1.79
Ti
4.10
4.94
5.72
Pb
0.1004
0.0771
0.0603
R
17.99
18.46
18.79
u
0.749
0.768
0.782
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Economics of Capacity Decisions
 Cost of Lost Business Cb
– $ / customer
– Increases with competition
 Cost of Buffer Capacity Ck
– $/unit/unit time
 Cost of Waiting Cw
– $ /customer/unit time
– Increases with competition
 Cost of Processing Cs
– $ /server/unit time
– Increases with 1/ Tp
 Tradeoff: Choose c, Tp, K
– Minimize Total Cost/unit time
= Cb Ri Pb + Ck K + Cw I (or Ii) + c Cs
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Optimal Buffer Capacity
 Cost Data
– Cost of telephone line = $5/hour, Cost of server = $20/hour,
Margin lost = $100/call, Waiting cost = $2/customer/minute
 Effect of Buffer Capacity on Total Cost
K
$5(K + c)
$20 c
$100 Ri Pb
$120 Ii
4
25
20
200.8
147.6
TC
($/hr)
393.4
5
30
20
154.2
182.6
386.4
6
35
20
120.6
214.8
390.4
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Optimal Processing Capacity
c
K=6–c
Pb
Ii
1
5
0.0771
1.542
TC ($/hr) =
$20c + $5(K+c) +
$100Ri Pb+ $120 Ii
$386.6
2
4
0.0043
0.158
$97.8
3
3
0.0009
0.021
$94.2
4
2
0.0004
0.003
$110.8
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Performance Variability
 Effect of Variability
– Average versus Actual Flow time
 Time Guarantee
– Promise
 Service Level
– P(Actual Time  Time Guarantee)
 Safety Time
– Time Guarantee – Average Time
 Probability Distribution of Actual Flow Time
– P(Actual Time  t) = 1 – EXP(- t / T)
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Flow Time Management: Review

Waiting occurs due to
– low processing capacity in relation to the inflow rate
– variability in inter-arrival and processing times

Waiting can be reduced by
– managing demand
– pooling arrival streams
– increasing capacity (number of servers  service rate)
– reducing the variability in arrivals and processing

Optimal level of service involves a tradeoff
– cost of waiting, lost business and cost of service
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Flow Time Management Levers

Manage Arrivals
– Demand Management: Price incentives
– Pool arrivals

Increase Capacity
– Scale: Servers, Part-timers, customer participation
– Speed: Simplify, Automation, Information, Training

Decrease Variability
– Arrivals: Forecast, Reservations, Pooling
– Processing: Standardize

Reduce Impact of Waiting
– Comfortable, Distract, Entertain, Perception
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Sof-Optics (A)

Competitive Priorities

Operational Problems

Economic Significance

Process Characteristics

Performance Measures

Short term Solutions

Long term Solutions
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Arrival and Processing Rates
Matching Supply and Demand at Sof-Optics
120
Half Hourly Rate
100
80
60
Arrival Rate
Processing Rate
40
20
0
Time of Day
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Processing Time
Distribution of Processing Time
0.7
Frequency
0.6
0.5
0.4
Frequency
0.3
0.2
0.1
0
85
120
220
450
Time (seconds)
Average Processing time = 131 seconds = 2.18 minutes/call
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Analysis of Sof-Optics (A)
Ar rival Se r vice Num be r Buffe r Ave rage Pr obability Pr obability Ave rage Ave rage Ave rage Ave rage
Rate
Tim e
of
Capacity Utilization
of
of Waiting Num be r Wait in
Flow Num be r
Se r ve r s
Block ing
(if not
in
Que ue Tim e
in the
Block e d) Que ue
Sys te m
Alte r native R i
Tp
c
K

P(block)
P(w ait)
Ii
Ti
T
I
Effect of Adding Servers
1
2.55
2.18
5
7
94.48%
15.02%
82.80%
3.46
1.60
3.78
9.6133
2
2.55
2.18
6
6
86.08%
7.09%
60.34%
1.70
0.72
2.90
7.3865
3
2.55
2.18
7
5
76.64%
3.50%
38.11%
0.74
0.30
2.48
6.3284
4
2.55
2.18
8
4
68.13%
1.95%
21.45%
0.30
0.12
2.30
5.865
Effect of Adding Telephone Lines
5
2.55
2.18
5
8
95.27%
14.31%
85.38%
4.11
1.88
4.06
10.338
6
2.55
2.18
5
9
95.92%
13.72%
87.47%
4.78
2.17
4.35
11.083
7
2.55
2.18
5
10
96.46%
13.24%
89.19%
5.47
2.47
4.65
11.848
8
2.55
2.18
5
11
96.91%
12.83%
90.62%
6.18
2.78
4.96
12.632
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Sof-Optics (A): Recommendations

Short term solutions

Effect of adding CSRs

Effect of adding telephone lines

Demand management

Workforce management
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