Quantitative issues in contact centers Ger Koole Vrije Universiteit seminar E-commerce & OR 18 January 2001 Lunteren

What is a contact center? Central place for all customer contacts Typically: Different types of contacts (information, sales, after sales, etc.) Different channels (telephone, , fax, regular mail, internet)

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

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

Quantitative management: objective Satisfy service level constraints Minimize (personnel) costs

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

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

Current scheduling practice Step 1: Forecasting traffic load Step 2: Determining staffing levels Step 3: Making schedules

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

Forecasting: current practice Standard statistical methods with explanatory variables Sometimes stand-alone software, sometimes part of workforce management package

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

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

Staffing levels: Erlang formula P( waiting time > t ) s/  Steep, therefore sensitive to input changes 1 0 Demonstration

Making schedules: model time shifts t

Making schedules: current practice Workforce management software: Formulate as mathematical programming problem Solve it using CSP / simulated annealing / genetic programming Still often by hand!

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!

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

Scheduling: problems Incompatibility shifts and staffing levels Shortening shifts means more overhead Unpredictable events: meetings, absence

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

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

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