Proficiency based agent scheduling to maximize infrastructure utilization in call-centers

We consider the issue of call-center scheduling coupled with capacity planning of both service agents (servers) and physical seats (space) in an environment where call arrival rates are highly variable and the call center is subjected to a global service level constraint. The paper is motivated by the work with the business process outsourcing unit providing technical support services from growth markets like India where realestate is one of the major cost drivers along with human capital. Our paper has two distinctive features. Firstly, we model capacity planning problem for seats and scheduling of agents as one single optimization problem leveraging variable service rates of human agents; information which is ignored by workforce planning teams while modeling. Secondly, we formulate the problem as a mixed integer linear programming (MILP) problem which is not trivial given the non-linear nature of service level constraint. We show that the set of linear inequalities required to represent service level constraint for each period can be generated cheaply. We conduct extensive experimentation to compare solutions of the MILP formulation recognizing variability in service rate with the traditional formulation based on mean valued service rates. We find that, in general, our formulation provides a significant reduction in space requirement and the solution minimizes the over-achievement of service level requirement.