Optimal Multi-Skilled Workforce Scheduling for Contact Centers Using Mixed Integer Linear Programming : A Method to Automatize Workforce Management

Abstract: This master thesis in optimization and systems theory is a development of two different optimization models formulated to schedule multi-skilled agents for contact centers depending on the forecasted demand, assigned by Teleopti. Four mixed integer linear programming models are created with the optimization programming language GAMS and solved by the internet based solver NEOS. Two of the models are formulated to perform an optimal scheduling that matches a forecasted demand per skill and day and the remaining two models are formulated to perform an optimal scheduling that matches a forecasted demand per skill, day and half hour. The first two models are referred to as the Basic Models and the second two are referred to as the Complex Models. The Basic Models includes seven constraints and the Complex Model includes nine constraints, describing regulations at the contact center. The main goal of the project is to find an optimal solution that results in an as even distribution of under or over scheduling. The scheduling optimization covers a period of 28 days, starting on a Monday which results in four weeks. The optimization models are based on two sets of data, there are 104 assigned agents that possesses one, two or three of the skills Channel, Direct and Product. All agents are bound to work according to a contract specified through the constraints. In the Basic Model the forecasted demand is given in amount of hours per day and skill, the demand is non-cyclical. In the Complex model the forecasted demand is given in amount of half hours per day, skill and half hour. Each day is scheduled from 7 a.m. to 11 p.m. resulting in 32 available half hours. All optimization models are developed to correctly mathematically formulate the constraints specified by Teleopti. Any non-linear equation that arises are linearized to maintain linearity, this is favourable in the sense of computational time solving the models. The objective functions in this thesis are formulated to describe the main goal of even distribution as correctly as possible. The result for the Basic Model shows that an optimal solution is achieved after 34 seconds. This model contains 169,080 variables and 39,913 equations. In the Complex Models integer solutions are achieved, but no optimal solution is found in 8 hours of computational time. The larger Complex Model contains 9,385,984 variables and 1,052,253 equations and the smaller Complex Model contains 5,596,952 variables and 210,685 equations. Teleopti’s scheduler produces an integer solution matching the Complex Model in 4 minutes.