Webinar on call center WFM:Why is Erlang C unsuitable for call center

safety staffing?

March 27, 2020Ger Koole, PhD

Steps in agent scheduling

• What is load*? • Load = FC x AHT in same time unit• Equal to # fully active agents needed to work away incoming work• E.g., FC = 60 in quarter = 4/min , AHT = 3 minutes: load = 4 x 3 = 12• Load has no dimension: commonly called Erlang

Workload forecasting Safety staffing Agent scheduling(net) head count(forecasted) load

*See Glossary @ WFM fellowship for definitions

Safety staffing

• How many agents to schedule? • Forecasted load is not enough because of

fluctuations in actual load• How much safety staff* to schedule to

mitigate the impact of fluctuations?• Safety staff = The additional # of agents

needed to reach SL• How to compute? Erlang C• Note: Safety staff ≠ shrinkage• Shrinkage is added when scheduling

Fluctuations in arrivals

Fluctuations in load

*equivalent to safety stock in logistics

forecasted load

Erlang C calculations

FC = 4AHT=3 14

SL = 61%/20s, ASA = 43s

FC + AHT + agents → SL, ASA• Invented by A.K. Erlang (1878-1929)

• Gives SL and ASA*

• Takes fluctuations in input into account

• Example: safety staffing = 2, total = load + safety = 14

• Still some calls have to wait and SL < 100%

*Online calculator on CCmath.com

Erlang C calculations

FC = 4AHT=3 16

SL ≥ 80%/20s

FC + AHT + SL → agents

• Also for backward calculation: determines safety staffing for given SL or ASA

Leads to some overstaffing

FC = 4AHT=3 16

SL = 87%/20s, ASA = 9s

FC + AHT + agents → SL, ASA

Erlang C: disadvantages

• Erlang C gives SL “forecast” – without fluctuations!• Erlang C was invented before call centers existed, does not “model”

all aspects – especially abandonments

SL fluctuations

• Erlang C predicts SL – without fluctuations!• Actual SL fluctuates – 80% is luck !• Result: if you staff for 80% you get

a SL < 80% in 50% of the cases• How to quantify? • Simulation• Demo*

• Erlang C = very long simulation (by a quick calculation)

*Simulation tool: www.gerkoole.com/CCO/1-skill-simulator.php

SL fluctuations

• Fluctuations are less:• over longer periods• in bigger call centers

• But decrease slowly… (with √)• Real-time performance management remains necessary• Also because of unforeseen changes in load & capacity

Calculations from PhD thesis Alex Roubos

Abandonments

• Erlang C does not tell the whole story…• What happens when a call center is

understaffed?• In reality calls abandon

• In all situations• Especially when understaffed

• Solution: Erlang X

Erlang X

• Gives abandonment %

• Requires average patience (“willingness-to-wait”)

• Also:• Redials• Finite # of lines• Non-integer staffing

• Less staffing required than Erlang C

• Gives always good answer – also when understaffed

FC = 4AHT=3 14

SL = 77%/20s

Erlang X

av. patience = 5 min

ab = 4%

FC = 4AHT=3 15

SL ≥ 80%/20s

av. patience = 5 min

ab = 3%

Redials

• Even with 100% redials higher SL than Erlang C

FC = 4AHT=3 14

SL = 77%/20s

av. patience = 5 min ab = 4%

FC = 4AHT=3 14

SL = 73%/20s

av. patience = 5 min ab = 5%

50%

Excel Office 365 demo

Learning more

• www.wfmfellowship.com• Online trainings for

workforce management• At you own time & place• Videos, exercises,

assignments • Supported by CCmath

professionals• Subscribe online or at

info@ccmath.com

Excel CCmath Erlang add-in

• Windows add-in• Runs locally• Requires software to be installed (xla, dll)

• Office365• Ready in a few weeks!• Requires add-in (xml)• Connects to CCmath server

• Implemented in CCmath WFM cloud suite

• Information: info@ccmath.com

Next week

• Friday April 3, 16:00 AMS time• Subject: to be determined• Suggestions: koole@ccmath.com

• Questions? Chat or voice