Quantitative issues in contact centers

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Quantitative issues in contact centers

• Ger Koole
• Vrije Universiteit
• seminar E-commerce OR
• 18 January 2001
• Lunteren

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What is a contact center?

• Central place for all customer contacts
• Typically
• Different types of contacts (information, sales,
  after sales, etc.)
• Different channels (telephone, email, fax,
  regular mail, internet)

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Why contact centers?

• Improves customer contacts
• ICT enabled it
• Contacts over different channels in one hand
• Grown from call centers

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Math issues in contact centers

• Planning
• Need for agents and their training
• Types of contracts
• Scheduling
• Construction of agent rosters
• Operational control
• Matching customers to agents

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Quantitative management objective

• Satisfy service level constraints
• Minimize (personnel) costs

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Service level

• Service level depends on channel
• Typically
• Telephone 80 within 20 seconds (max. 3
  abandonments)
• Email within 4 hours
• Fax within 1 day
• Call me button between 1 and 2 minutes

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Presentation overview

• Show current scheduling practice
• Identify problems
• Suggest possible solutions
• Flexibility in staffing and task assignment
• Relate to multi-channel contact center

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Current scheduling practice

• Step 1 Forecasting traffic load
• Step 2 Determining staffing levels
• Step 3 Making schedules

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Forecasting traffic model

• Customer contacts arrive by piece-wise constant
  inhomogeneous Poisson process
• Handling times (incl. wrap-up time) depend on
  channel-skill combination
• Arrival rates depend on day of week, time of day,
  and many other factors

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Forecasting current practice

• Standard statistical methods with explanatory
  variables
• Sometimes stand-alone software, sometimes part of
  workforce management package

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Staffing levels model

• Per interval with constant arrival rate
• Arrival rate ? and average handling time ? (both
  in same time unit)
• Load a ? ? (unitless, Erlang)
• Suppose we schedule s dedicated agents
• Productivity a / s
• Overcapacity s - a

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Staffing levels current practice

• Low service level requirements take
  s?a?
• High service level requirements (calls) have
  to take random variations in arrival process and
  service times into account ? schedule just enough
  overcapacity to satisfy service level using
  Erlang formula

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Staffing levels Erlang formula
Steep, therefore sensitive to input changes
1
P( waiting time gt t )
0
?
s/?
Demonstration
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Making schedules model
shifts
t
time
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Making schedules current practice

• Workforce management software
• Formulate as mathematical programming problem
• Solve it using CSP / simulated annealing /
  genetic programming
• Still often by hand!

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Forecasting problems

• Too many explanatory variables
• Non-predictable events (e.g., weather)
• ? Point estimate does not work
• Solution
• Give confidence interval for arrival rate ?
• Interval for staffing level!

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Staffing problems

• Staffing reflects operational control
• By staffing separately we need more capacity
• economies of scale (demonstration)
• low service level classes can be used to fill
  random fluctuations in load (e.g., the 4th agent
  becoming available handles an email) important
  in case of long holding times!

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Scheduling problems

• Incompatibility shifts and staffing levels
• Shortening shifts means more overhead
• Unpredictable events meetings, absence

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The flexible contact center

• Flexibility in staffing
• Flexible contracts
• Non-contact center personnel on stand-by
• Flexibility in task assigment
• Cross-skill training
• Multiple channels

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The benefits of flexibility

• Flexibility in staffing can help solve
• Variations in load
• Unpredictable absence
• Cross-skill training gives
• Advantages of scales
• Switching between channels helps solving
• High load problems (switch to calls)
• Unproductivity due to random variations
• Staffing peaks over the day

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Conclusions

• Contact centers desirable from a math perspective
• Stimulate shift from high to low service level
  channels
• Advanced models partly implemented
• Based on joint work with Erik van der Sluis,
  Sandjai Bhulai, and Geurt Jongbloed

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