intelligent procedures for intra-day updating of call center agent schedules university of montreal...

Intelligent Procedures for Intra-Day Updating of Call Center Agent Schedules

University of Montreal Call Center Workshop, May 2006

Vijay Mehrotra and Ozgur OzlukDepartment of Decision Sciences, College of Business

San Francisco State University

Spring 2006Spring 2006

Presentation Roadmap

“Who is this Guy?”

Customer Conversations / Embedded Problems

Intra-Day Re-Scheduling Framework Literature Components

Numerical Experiment and Results

Questions and Extensions


About Vijay

PhD in OR, Stanford University, 1992

1993 – 1994: Consultant, DFI

1994 - 2002: Co-Founder and CEO, Onward Inc.

2002 - 2004: Vice President of Solutions, Blue Pumpkin Software


More Than 1200 Companies Depend on Blue Pumpkin/Witness For Workforce Management Software

Retail & Catalog

Insurance & Lending

Manufacturing

Technology

Communications

Healthcare

Consumer Goods

Travel & Transportation

Outsourcers

Banking & Brokerage

DowR

M O N S A N T OFood Health Hope


About Vijay

Fall 2003: “Radical Portfolio Adjustment” Return to Academic World

• SFSU Dept of Decision Sciences, College of Business• Full-Time Tenure Track Position• Teach Courses in Statistics, Operations, Quality, and

Project Management to Undergraduates and MBAs

Still in “Real World”• Regular Stream of Consulting Projects • Focus on Call Center Operations, Enterprise Software,

and Revenue Management

Thrust into Brave New World – Spring 2004• Became First-Time Father• Moved to East Bay from SF


Call Center WFM: The Right Number of Agents Working at the Right Times to Deliver the Right Queues – Not So Hard, Right?

Several Hundred Papers in the Academic Literature on Different Aspects of the Call Center WFM problem

Gans, Koole, and Mandelbaum (MSOM 2003) is an excellent literature survey

But We Still Have Many Managers and Executives with Real, Unsolved Call Center WFM Problems


So Many “Improvements” to Consider:The Exploding Head of the CC Manager

MORE Routing Complexity Skill-Based Routing Multiple Customer Channels Inbound/Outbound Blended MultiSite / Outsourcing

MORE Demand Uncertainty New Policies/Processes for

Existing Businesses New Businesses/Services M&A Activity New Operating Hours Increased Service Level Goals Cross-Channel Dynamics

MORE Pressure / Urgency Tighter Budgets “Solve the Problem Now”


Vijay’s Grand Theory of EvORything

Optimization/Performance Model

Optimization/Performance Model

System Definition,Available

Resources,And Restrictions

System Definition,Available

Resources,And Restrictions

Uncertain Demand(Forecasted)

Uncertain Demand(Forecasted)

Costs and ObjectivesCosts and Objectives

RecommendedDeployment of

Resources

RecommendedDeployment of

Resources

EstimatedSystem Performance

EstimatedSystem Performance


The Focus of This Paper: Short-Term Decision Making Based on Newly Available Information

Strategic Cycle

Tactical Cycle

Real Time Cycle

Historical Data

Hiring and Training Plan Available Staff

Schedules & New Call FCs Plan for Future Week(s)

Adjustments to SchedulesAdjustments to Forecasts


Conversation 1: Customer=VP of Operations for Huge Division of Massive FinSvcs Conglomerate Vijay: “So where else do you guys need help?”

Customer (upbeat): “We do our forecasts and schedules about a month ahead of time.”

C: “But things are changing all the time, so we are monitoring and updating our forecasts all the time, every single day.”

C: “Then, we react by trying to commit and de-commit resources as best we can – ratchet outsourcers up and down, offer our employees OT or VTO, offer more hours to our PT staff…”

C: “Last year, we estimate that we saved about $8mm doing this.”

V (nervously): “So what’s the problem with that?”

C: “First of all, we have no idea if we’re doing well or not, and we think we might be leaving a lot of money on the table.”

C: “Secondly, it’s all one big email nightmare, and it drives our ops staff nuts trying to keep all of it straight.”

V: “Hmmm….Thanks…”


Conversation 2: Customer=VP of Finance for Big Division of Large Financial Svcs Conglomerate Customer (abruptly): “How does your system quantify the risk?”

Vijay: “What do you mean by ‘risk’?”

C: “From what you’ve said, you take my forecasts and my service goals and come up with a number of agents for each 15-minute interval. Then, your scheduling algorithm tries to match that target.”

V (excited – customers never get this!): “That’s right! You’ve got it!!”

C: “So what percentage of the time will we actually meet our goals with that staffing plan?”

V: “Well, what you’d need to do is to do a Monte Carlo simulation on your forecasts and do a bunch of replications…And the

answer depends on how you respond to different levels of demand, and on how accurate your forecasts are…”

C: “Your product doesn’t do that for us?”

V: “Uh, no. But I’ll put it on the list…”


Framework for Intra-Day Schedule Updating

Initial CallAnd AHTForecasts

Initial AgentRequirements

Per Period

M/M/sQueueingEquations


Initial ScheduleAssignments (Typically

1-4 Weeks Prior)

IndividualAgents’ Availability

InformationActual Call

Volumes(1,2,..u-1) Updated FCs Info on Actual Agent

Attendance as of u-1

M/M/s QueueingEquations

M/M/s QueueingEquations

IncrementalAgent Reqs(u, u+1, …T)

UpdatedAgent

Schedules for u, u+1,…T

UpdatedAgent



Key Relevant Literature: Workload FC and Update

Identifying and Modeling Arrival Rates Per Period as Random Variables…

• Thompson (1999), Chen & Henderson (2001)• Ross (2001), Jongblooed & Koole (2001)• Whitt (2004)

…Which Are Correlated with One Another• Brown et al (2002)• Avramidis et al (2004)• Steckley et al (2004)


Key Relevant Literature: RT Schedule Adjustments

Models for “Real Time Schedule Adjustments” for Service Systems

• Thompson (1999)• Hur, Mabert, and Bretthauer (2004)• Easton and Goodale (2005)

Surprisingly Small List

Absent from the Literature: RT Schedule Updating Papers in the Context of Call Centers


Framework for Intra-Day Schedule Updating



Per Period




1-4 Weeks Prior)


InformationActual Call

Volumes(1,2,..u-1) Updated FCs Info on Actual Agent





UpdatedAgent


UpdatedAgent



Step 0: Operating Parameters & Initial Schedules


1-4 Weeks Prior)


Step 1: Update Workload Forecast and Demand for Agents

Actual Call Volumes(1,2,..u-1)


Step 1: Update Workload Forecast

As in (Whitt 99) and (Avramidis et al 2005), we model arrival process as NHPP with Random Arrival Rate (s) = H * ((s): s >=0),

where is piecewise constant on intervals 1,2,…T and H is a (scalar) Random Variable with E[H] = 1 E[] =

Actual Call Volumes(1,2,..u-1)

Updated Call Forecasts for(u, u+1, u+2,…T)


Step 2: Update Demand for Agents

Actual Call Volumes

(1,2,..u-1) Updated FCs Info on Actual Agent





Use Standard Queueing Equation for Translation (minimum s to satisfy SL goals for M/M/s queue) based on updated forecasts to determine incremental agent needs t for t=u,u+1, …T


Step 3: Update Agent Schedules for periods u…T

Initial ScheduleAssignments


Information


UpdatedAgent


UpdatedAgent




Dimensionality of IP is Quite Small [ TxN Integer Variables, Tx(T+N) Constraints ]



When Arrival Rate Variability Dominates Attendance:

Special Cases Strictly overstaffed

• H<1 t <=0 for all t=u,u+1, …T

• Address with Voluntary Time Off and/or Release of Contracted Agents

Strictly understaffed

• H>1 t >=0 for all t=u,u+1, …T

• Address with “Holdover OT” and “Call-In OT”


Experimental Framework

Goal: Test Methodology on Real Call Center Data to Understand Dynamics

Model From Saltzman 2005 Sales-and-Service Call Center in Travel Industry

Relatively Small Call Center

• Roughly 360 agent hours/day

• Mixture of FT and PT Agents


Experimental Framework

Build initial schedulesBased on values

(expected arrival rates)

Choose a value for H,And simulate arrivals for

Periods 1,2,..u-1


Results for Overstaffed Cases (0.5 <= H < 1)

Lesson: After recognizing that original FCs are too high, our Update Methodology delivers desired SLs with less staff/lower cost


Results for Understaffed Cases (1 < H <= 1.5)

Key Lessons Not responding to new information is very damaging to service quality When H is large, Schedule Updating cannot fully make up for initial

poor performance during first four hours


Results for Understaffed Cases (1 < H <= 1.5):The Rest of the Story

When staffing based on expected , cannot meet goals easily without “Call-in” OT

? Given plans to update, where should initial staffing be set?

? What structure for contingent resource contracts makes sense given different arrival rate uncertainties?


Questions and Ideas? Please Call or Email!

Vijay Mehrotra & Ozgur OzlukDepartment of Decision Sciences

San Francisco State [email protected] / 650-465-8443

[email protected] / 415-338-1007

Vijay Mehrotra & Ozgur OzlukDepartment of Decision Sciences

San Francisco State [email protected] / 650-465-8443

[email protected] / 415-338-1007


Extension to this Research [Currently in Progress]

Almost all Call Center Research to date assumes that # arrivals in a period is Poisson distributed

Data often strongly refutes this e.g., mean = 2000, std dev = 500 or more

Model arrival process as B ((t): t ¸ 0), (Whitt 99), where is piecewise constant


Random Arrival Rates: A Graphical View

t

t)


Extension to this Research [Currently in Progress]

Where to set initial staffing? Hypothesis: Performance (and Cost-Effectiveness) can be

improved by accounting for Arrival Rate Variability in setting initial staffing levels

Method: Use Analytic Approximations from (Steckley, Henderson, and Mehrotra 2005) to determine # of agents needed to achieve particular SL when creating initial weekly schedule



Per Period




1-4 Weeks Prior)


Information

SHM Performance

MeasureApproximations

SHM Performance

MeasureApproximations

(Higher) Initial Agent

RequirementsPer Period

intelligent procedures for intra-day updating of call center agent schedules university of montreal...

Documents

extensions slide

sf slide

brave new world spring

available resources

center wfm problems

center operations

blue pumpkin software

center workshop