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Using simulation-based forecasting, workforce managers are

able to more accurately determine the staffing requirements.

Mixed integer programming can then be used to provide optimal

staffing plans based on a service performance goal. Finally, the

simulation results can be used to develop sensitivity analysis

charts to help workforce managers analyze staffing trade-offs

that influence service quality, profit and cost.

Traditional planning for contact centers involves both long term

strategic planning and short term tactical staff scheduling.

Long term strategic planning is particularly challenging as the

lead time to hire and train agents must be taken into account.

In addition, contact centers typically experience high attrition

rates among their agents.

INTRODUCTION

OBJECTIVES

Traditional long-term workforce planning methods use:

A. Erlang-C equations using a set of demand constraints to

estimate staffing requirements

B. Historical average approaches to determine inter-day and

intra-day forecast

C. Ad-hoc hiring plans based on subjective reasoning and prior

planning experience

CHALLENGES

We describe a solution that allows for simulation-based

forecasting, optimal staffing plans and staffing trade-off analyses

1. Discrete Event Simulations

2. Forecast

A. Inter-day and intra-day forecast (see figure below)

B. Performance forecast

C. Monthly/Weekly forecast using time-series methods

3. Mixed Integer Programming

Mixed integer programming models are formulated based on

business rules of the contact center network. This allows us to

develop mathematically optimal staffing plans which include:

A. Hiring plans that account for lead time to hire and train

each new class of agents

B. Extra-time and under-time plans

C. Outsourcing plans to determine the optimal mix of call

volumes allocated to outsourced services

METHODOLOGIES

4. Sensitivity Analysis

Sensitivity analysis are derived from the discrete event

simulation results and represent the range of feasibility options

varied against an output parameter. This can then be used to

determine staffing trade-offs and analyze the effect on

service quality, profit and cost.

200

300

400

500

600

10 11 12 13 14 15 16

Conta

ct

Volu

me

Hour Of Day

Hourly Interval Contact Arrival Volume (Monday)

Week A

Week B

Week C

Week D

Figure B: Conceptual model of contact center simulation

RESULTS

4. Sensitivity analysis charts determine staffing tradeoffs

60.0 62.0 64.0 66.0 68.0 70.0 72.0 74.0

12/7/2011 12/14/2011 12/21/2011

Requir

ed S

taff

Weeks

Comparison of Erlang-C and Simulation Staffing Requirements

Erlang

Simulation

Actual

1. Discrete event simulations provide increased accuracy

over Erlang- C

Erlang-C overstates staffing requirements by between 2% and 7%.

2. Historical inter-day and intra-day distributions applied to

weekly forecast yield high accuracy

3. Mixed integer programming provides optimal staffing plan

30

50

70

90

110

March April May June July August September Serv

ice L

evel

Months

Comparison of Historical and Forecasted Performance

Historical

Forecasted

$223

$225

$227

$229

$231

60 65 70 75 80 85 90 95 100

Pro

fit

(in 0

00s)

Service Level (%)

Profit Analysis: Total Profit Vs. Service Level

Current

CONCLUSION

Figure A: Contact center network of a telecommunications organization

R² = 0.912

METHODOLOGIES RESULTS

Using our mixed-integer programming approach, we are able

to determine a balanced approach using a mixture of extra-

time and under-time agents to meet the staffing requirements.

Optimal

35

40

45

50

55

60

65

70

March May July September November January

Agents

(FT

E)

Months

Extra/Under Time Plans for Service level of 80%

Under Time

Extra Time

Effective Staff

Required Staff

David Woo, Amit Garg, Bayu Wicaksono

Long Term Strategic Workforce Planning For Contact Centers Using

Mixed-Integer Programming and Simulation-Based Forecasting