Class-6b

1
Operations Management Performance Modeling

• 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

2
Accurate Response to Demand Uncertainty when you
can order only once L.L. Bean

• L.L. Bean is planning the order size for winter
  parkas. Each parka costs the company 70 and
  sells for 140. Any unsold parkas at the end of
  the season are disposed off by a sale at 40.
  Using historical data and a feel for the market,
  L.L. Bean forecasts the winter season demand
• Demand 21 22 23 24 25 26 27 28
• Probability 3 4 5 8 10 15 12 10
• Cumulative 3 7 12 20 30 45 57 67
• Demand 29 30 31 32 33 34 35
• Probability 9 6 5 4 4 3 2
• Cumulative 76 82 87 91 95 98 100
• How many parkas should L.L. Bean plan
  (make/order)?

3
Accurate Response Find optimal order level Q
with Excel
4
Accurate response Find optimal Q from formula

• Cost of overstocking by one unit Co
• the out-of-pocket cost per unit stocked but not
  demanded
• Say demand is one unit below my stock level.
  How much did the one unit overstocking cost me?
  E.g. purchase price - salvage price.
• Cost of understocking by one unit Cu
• The opportunity cost per unit demanded in excess
  of the stock level provided
• Say demand is one unit above my stock level.
  How much could I have saved (or gained) if I had
  stocked one unit more? E.g. retail price -
  purchase price.
• Given an order quantity Q, increase it by one
  unit if and only if the expected benefit of being
  able to sell it exceeds the expected cost of
  having that unit left over.
• At optimal Q, do not order more if
• smallest Q such that stock-out probability lt
  critical fractile Co / (Co Cu)

Prob( Demand gt Q ) lt Co /(Co Cu ).
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.

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
Probability
Flow Time (minutes)
7
Telemarketing with variability in arrival times
activity times

• In reality service times
• exhibit variability
• In reality arrival times
• exhibit variability

8
Telemarketing with variability The effect of
utilization

• Average service time
• 9 minutes
• Average service time
• 9.5 minutes

9
Why do queues form?

• utilization
• throughput/capacity
• variability
• arrival times
• service times
• processor availability

10
Cycle Times in White Collar Processes
11
Queuing Systems to model Service Processes A
Simple Process
Order Queue buffer size K
Sales Reps processing calls
Incoming calls
Answered Calls
Calls on Hold
MBPF Inc. Call Center
Blocked Calls (Busy signal)
Abandoned Calls (Tired of waiting)
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

13
Performance Measures

• Sales
• Throughput R
• Abandonment
• Cost
• Server utilization r
• Inventory/WIP in queue/system
• Customer service
• Waiting/Flow Time time spent in queue/system
• Probability of blocking

14
Queuing Theory Variability Utilization
Waiting

• Throughput-Delay curve
• Pollaczek-Khinchine Form
• Probwaiting time in queue lt t 1 - exp(-t /
  Ti ) where

mean service time
utilization effect
variability effect
x
x
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

16
Example 1 MBPF Calling Center one 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.
• MBPFs waiting cost

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?

18
Example 3 MBPF Calling Center Resource 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)

19
Example 4 MBPF Calling Center Staffing

• 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

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.

21
National Cranberry Cooperative
22
Real Processes exhibit variability in order
placement time and type
National Cranberry on Sept 23, 1970