A Hybrid Approach to Minimizing the
Total Costs of Staffing a Call Center
Robert M. Saltzman
Decision Sciences Department
San Francisco State University
San Francisco, CA 94132
saltzman@sfsu.edu
Overview of Talk
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Introduction
Call Center Staffing Problem
Hybrid Approach
Simulation Model
Finding a Good Solution
Experimental Results
Conclusion
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 ll V o lu m e ( M a y 2 0 0 2 )
140
120
100
80
60
40
20
P e r io d ( 1 = 6 :0 0 - 6 :3 0 a m )
29
27
25
23
21
19
17
15
13
11
9
7
5
3
0
1
Number of Calls
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Introduction
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60-70 agents per day
Almost all shifts run 8.5 hours
Shifts include one ½-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
Call Center
Staffing Problem
• Calls are answered 15 hours/day
– Switch data are summarized by ½-hour period,
so agent demand varies by ½-hour
– Capacity changes every ¼-hour
• How many agents should start work at the
beginning of each ½-hour period?
– Balance overages & underages:
Minimize total costs per day
The Real Staffing Problem
Hybrid Approach = Excel + Arena
Input: 1) Agent demand by period; and
2) Matrix of shifts (see spreadsheet)
Find initial staffing plan (X1, Z1):
For total # of agents T = Tmin to Tmax:
* Excel Solver: Finds plan that “best”
matches agent supply with demand
* Arena: Evaluates plan’s daily cost
Next T
Find improved staffing plan (X2, Z2):
Tabu Search finds alternative plans
* Arena: Evaluates plan’s daily cost
Stop after k iterations or time limit reached
Simulation Model
• Straight-forward structurally
(except perhaps for abandonment logic)
• Input consists of:
– Agent capacity, by ¼-hr (from Excel)
– Call arrival rate means, by ½-hr
– Talk time & extension out time means, by ½-hr
– Abandonment time mean
• Output to Excel via VB consists of:
– Ave. # callers waiting on hold
– Ave. # of abandoned calls/day
Model Validation
Adjusted mean abandonment time until output
agreed with real data:
Performance
Measure
Offered
Calls/day
Abandoned
Calls/day
Answered
Calls (%)
ASA (sec.)
Observed
Mean
2302.3
Model
Mean
2297.9
118.1
118.3
95.4
94.9
52.2
51.5
Find a Good Solution
For each total # of agents T, solve an IP:
• Minimize Σi|Ci – Di|
s.t. AiX = Ci, for i = 1, 2, …, 60
ΣjXj = T
Xj ≥ 0, integer, for j = 1, 2, …, 22
• Di = # 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 = (X1, Z1)
Find a Better Solution
Tabu Search to improve on (X1, Z1):
• Heuristic: Near-optimality
• Short-term memory only
• Each iteration, derive a list of candidate solutions by ±1
changes to the incumbent solution
• Evaluate cost of a candidate via the simulation model
• Choose best admissible candidate
• … Lowest cost solution = (X2, Z2)
Results - I
• Scenario I [Travel Industry]:
CAb = $25/abandoned call
CLq = $20/hour/waiting call
Cs = $15/hour/agent
# of
Agents
Base: 58
Best: 63
Labor
Costs
$6,960
$7,560
Aband
Costs
$2,958
$930
Wait
Total
Costs Costs
$666 $10,584
$210 $ 8,700
• Hybrid routine reduces costs by 17.8%
Results - II
• Scenario II [Tech. Support?]:
CAb = $10/abandoned call
CLq = $15/hour/waiting call
Cs = $25/hour/agent
• Higher service, lower wait costs
# of
Agents
Base: 58
Best: 55
Labor Aband
Costs Costs
$11,600 $1,183
$11,000 $ 944
Wait
Total
Costs Costs
$500 $13,283
$384 $12,328
• Hybrid routine lowers costs by 7.2%
Conclusion
• Time-varying arrivals & use of full-time staff Î
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