Contact Center Workforce Scheduling via MILP Optimization

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Solution Overview

Problem

Current methods for workforce scheduling in contact centers are inefficient and fail to guarantee optimal schedules due to manual processes, lack of evidence for optimality in prior art methods, and limitations of existing Mixed Integer Linear Programming (MILP) models, which struggle with multiple agent skill groups and time-varying workloads.

Innovation Solution

A Mixed Integer Linear Programming (MILP) model is formulated to optimize workforce scheduling, incorporating skills-based and non-skills-based environments, using a Branch and Cut algorithm supplemented by a Rounding Algorithm to ensure necessary and sufficient conditions for optimality, addressing the complexity of multiple agent skill groups and time-varying workloads.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If manual scheduling methods are used, then implementation simplicity is maintained, but scheduling optimality and efficiency deteriorate due to laborious processes and inability to evaluate astronomical number of potential schedules

Engineering Contradiction:

ImproveEase of scheduling implementationVSAvoidScheduling efficiency

Core Design Contradiction:

Ease of manufactureVSProductivity

Solution Approach 1:

The patent replaces manual mechanical scheduling processes with an automated computer-based optimization system that uses mathematical programming algorithms to generate optimal schedules, eliminating the need for manual evaluation of potential schedules while maintaining ease of implementation through software automation

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent transforms the scheduling problem from a manual process into a mathematical optimization problem by defining objective functions and constraints in terms of measurable parameters such as service levels, labor costs, and agent skills, allowing systematic optimization rather than ad-hoc manual adjustments

Inventive Principle:

Principle #35Parameter changes

2Reliability

If traditional MILP models are used, then mathematical rigor is maintained, but model applicability deteriorates when dealing with multiple agent skill groups and time-varying workloads

Engineering Contradiction:

ImproveMathematical optimality guaranteeVSAvoidModel applicability to complex scheduling environments

Core Design Contradiction:

ReliabilityVSAdaptability or versatility

Solution Approach 1:

The patent segments the complex scheduling problem into multiple time periods and skill groups, allowing the MILP model to handle time-varying workloads and multiple agent skills by creating separate decision variables and constraints for each segment while maintaining overall optimality through the unified mathematical framework

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

The patent creates a universal MILP formulation that can handle multiple agent skill groups, time-varying workloads, and various contact types through a single flexible model structure that accommodates different scheduling scenarios without requiring separate specialized models

Inventive Principle:

Principle #6Universality (Multi-functionality)

3Loss of energy

If understaffing is implemented, then labor costs are reduced, but service levels deteriorate with longer waiting times for customers

Engineering Contradiction:

ImproveLabor cost reductionVSAvoidService level quality

Core Design Contradiction:

Loss of energyVSReliability

Solution Approach 1:

The patent uses parameter changes by adjusting the objective function to minimize labor costs while maintaining service level constraints as mathematical boundaries, allowing the optimization to find the precise point where cost reduction does not compromise service quality

Inventive Principle:

Principle #35Parameter changes

Solution Approach 2:

The patent incorporates feedback mechanisms through constraints that monitor service levels and adjust staffing allocations accordingly, ensuring that cost-saving staffing decisions do not result in unacceptable service degradation by continuously evaluating the trade-off between labor costs and service quality

Inventive Principle:

Principle #23Feedback

4Reliability

If overstaffing is implemented, then service levels are improved with lower waiting times, but labor costs increase with underutilized agents

Engineering Contradiction:

ImproveService level qualityVSAvoidLabor cost efficiency

Core Design Contradiction:

ReliabilityVSLoss of energy

Solution Approach 1:

The patent transforms the overstaffing problem into an optimization problem by defining service level targets as minimum constraints and using the objective function to minimize labor costs above these targets, preventing unnecessary overstaffing while maintaining required service levels through mathematically determined optimal staffing levels

Inventive Principle:

Principle #35Parameter changes

Data Source

PatentUS7725339B1Contact center scheduling using integer programming

Publication Date: 2010.05.25 INCONTACT INC

AI summary

The present invention relates to a method for workforce scheduling in which workload and workload types vary during scheduling period. The method acquires agent and skill requirements for all periods and contact types; acquires the contact center information including agent skill groups, agent work groups, tour and shift scheduling rules, agent availability, objective criterion to be optimized and its parameters; develops a Mixed Integer Linear Programming (MILP) model for the scheduling environment; applied an optimization algorithm that uses the Branch and Bound algorithm with a Rounding Algorithm to improve performance; and locates a globally optimal or near optimal workforce schedule in total cost or paid time or agent satisfaction. Detailed schedules may be developed by assigning daily shifts to work patterns, and breaks scheduled to daily shifts.