A Case Study on Optimizing Call Center Daily Staff Scheduling Using the Set Covering Model

Abstract

Efficient staff scheduling in call centers improves operational efficiency, reduces costs, and ensures sufficient customer service. This study addresses the daily shift scheduling problem in a call center with multiple types of tasks. While the set covering model is widely used to derive optimal solutions for such problems, its application requires enumerating all possible combinations of timeslots and tasks. This process significantly increases the complexity of the model, leading to computational difficulties. Additionally, the call center considered in this study permits staff to perform two different types of tasks simultaneously within the same timeslot, which are referred to as pair tasks. This further exacerbates computational challenges, as it significantly increases the number of task pattern combinations, making the model even more difficult to solve.
To address the challenge of exponential growth in combinations, a heuristic algorithm is proposed that not only supports pair tasks within the same timeslot but also significantly reduces the number of task pattern combinations. The algorithm is first applied to the base model (Model 1) to obtain an initial near-optimal solution; then task patterns are refined to further improve solution quality. Subsequently, we augment Model 1 by incorporating real-world operational conditions, yielding Model 2 that better reflects practical requirements. Numerical experiments demonstrate the effectiveness and practicality of the proposed algorithm and models.