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8/11/2019 Arena Opt 851
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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 [email protected]
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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