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A Hybrid Approach to Minimizing theTotal Costs of Staffing a Call Center

Robert M. SaltzmanDecision Sciences DepartmentSan Francisco State University

San Francisco, CA 94132saltzman@sfsu.edu

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Overview of Talk

Introduction Call Center Staffing Problem

Hybrid Approach Simulation Model

Finding a Good Solution Experimental Results Conclusion

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Introduction Inbound call center in travel industry

Open M thru F, 6 AM 9 PM ~2300 calls/day (May 2002)

Non-stationary call pattern:A v e r a g e C a l l V o l u m e ( M a y 2 0 0 2 )

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

1 4 0

1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9

P e r io d ( 1 = 6 : 0 0 - 6 : 3 0 a m )

N u m

b e r o f

C a l l s

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Introduction 60-70 agents per day

Almost all shifts run 8.5 hours Shifts include one -hour lunch and two 15-minute

breaks Possible staffing goals:

1. Hit a target service level in each period, or in a high % of periods

2. Minimize total costs per day, including costs of labor,waiting & abandonment

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Call CenterStaffing Problem

Calls are answered 15 hours/day Switch data are summarized by -hour period,so agent demand varies by -hour

Capacity changes every -hour How many agents should start work at the

beginning of each -hour period? Balance overages & underages:

Minimize total costs per day

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The Real Staffing Problem

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Hybrid Approach = Excel + ArenaInput: 1) Agent demand by period; and

2) Matrix of shifts (see spreadsheet)Find initial staffing plan (X 1, Z1):

For total # of agents T = Tmin to Tmax:* Excel Solver : Finds plan that best

matches agent supply with demand* Arena : Evaluates plans daily cost

Next TFind improved staffing plan (X 2, Z2):

Tabu Search finds alternative plans* Arena : Evaluates plans daily cost

Stop after k iterations or time limit reached

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Simulation Model Straight-forward structurally

(except perhaps for abandonment logic) Input consists of:

Agent capacity, by -hr (from Excel) Call arrival rate means, by -hr Talk time & extension out time means, by -hr

Abandonment time mean Output to Excel via VB consists of:

Ave. # callers waiting on hold Ave. # of abandoned calls/day

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Model ValidationAdjusted mean abandonment time until output

agreed with real data:

51.552.2ASA (sec.)

94.995.4AnsweredCalls (%)

118.3118.1Abandoned

Calls/day

2297.92302.3OfferedCalls/day

ModelMean

ObservedMean

PerformanceMeasure

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Find a Good SolutionFor each total # of agents T, solve an IP:

Minimize i|Ci D i|s.t. A iX = C i, for i = 1, 2, , 60

jX j = TX j 0, integer, for j = 1, 2, , 22

D i = # agents required in period i to have a 10% prob. of delay in an M/M/N system (standard)

Convert to an ILP before solving Arena simulation model evaluates cost/day

Lowest cost solution = (X 1, Z1)

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Find a Better SolutionTabu Search to improve on (X 1, Z1): Heuristic: Near-optimality Short-term memory only

Each iteration, derive a list of candidate solutions by 1changes to the incumbent solution

Evaluate cost of a candidate via the simulation model Choose best admissible candidate Lowest cost solution = (X 2, Z2)

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Results - I Scenario I [Travel Industry]:

CAb = $25/abandoned callCLq = $20/hour/waiting callCs = $15/hour/agent

# of Labor Aband Wait Total Agents Costs Costs Costs Costs

Base: 58 $6,960 $2,958 $666 $10,584Best: 63 $7,560 $930 $210 $ 8,700

Hybrid routine reduces costs by 17.8%

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Results - II Scenario II [Tech. Support?]:

CAb = $10/abandoned callCLq = $15/hour/waiting callCs = $25/hour/agent

Higher service, lower wait costs

# of Labor Aband Wait Total Agents Costs Costs Costs Costs

Base: 58 $11,600 $1,183 $500 $13,283Best: 55 $11,000 $ 944 $384 $12,328

Hybrid routine lowers costs by 7.2%

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Conclusion Time-varying arrivals & use of full-time staff

Overstaffing & understaffing in different periods Appropriate performance measure:

Total daily cost of a staffing plan

Hybrid routine is Excel-based Excel Solver & VB Tabu Search find staffing plans Call Arena simulation model to evaluate plan costs

Best plans found may save 7-18% of total costs up to several 100K per year

Future: Look at part-time staff