Employee scheduling is an important activity in the service industry as it has a significant impact on costs, sales, and profitability. While a large amount of mathematical models and methods have been established in the literature for finding optimized schedules, only few propose optimization methods for practically relevant problem settings including uncertainty, which is an important aspect of employee scheduling in the service industry.

This article contributes to narrowing this research gap by addressing a practice-inspired employee scheduling problem arising in retail stores. In particular, the scheduling problem under study includes short demand perturbations, potentially leading to an increase of the demand in some time intervals, and the possibility of assigning overtime work by extending shifts to cope with a lack of employees in real-time. The goal is to find an initial schedule minimizing the sum of demand fulfillment and employee preference-related costs, where each cost term is expressed as a convex function of an appropriate variable. The cost of a schedule is evaluated using a simulation-based approach reproducing the materialization of demand perturbations and shift extensions.

In order to find reasonably good robust employee schedules within a relatively short computation time for practical-sized instances, we propose two integer programming models taking into account the demand uncertainty and shift extension possibilities in different ways. In the first model, a bonus term is assigned in the objective function for shifts that can cover some perturbation demand within their extension period, while in the second model, a potential demand is derived from the perturbations and its under-coverage is penalized. Extensive computational results on retail store instances reveal that the two proposed robust models improve the schedule quality significantly when compared with a basic non-robust model. This result further underpins the value of including uncertainty information and recourse actions in the employee scheduling activity.