Conference Agenda

In many organizations, human resources are a primary cost driver. Consequently, careful scheduling of this resource is paramount. The shift design and scheduling process involves several steps, from recognizing staffing requirements to deploying a workable schedule. Based on the staffing requirements and shift design constraints, a set of workable shifts is devised. The shift scheduling process then determines the number of employees and assembles these shifts to a shift schedule. Traditionally, shift design and scheduling are treated as separate problems. This separation fails to address conflicts between design and scheduling objectives, potentially leading to inefficiencies when relying on predetermined shift designs. To address these challenges, we introduce a unified approach that integrates shift design with rotating workforce scheduling. In addition to the shift design objective function, we model an ergonomics objective function for the quality of the schedule. We solve the integrated problem using a branch-and-cut approach based on a compact formulation and graph representation, ensuring feasibility of shift designs by modeling the shift schedule as a Eulerian cycle of work sequences and rest periods. Experiments indicate that our approach can quickly solve problem instances based on the benchmark sets for shift design and rotating workforce scheduling. Results show that an integrated shift design and scheduling enables shift schedules with greatly improved ergonomics without deteriorating the shift design objective compared to the sequential planning approach.

This talk describes an industrial application that helps schedule employees in a call center. The schedules are optimized for a week and aim to plan the activities of 30 to 200 employees, considering 2 to 5 different activities. Each employee has a weekly hourly contract and a skill level for each activity. The demand for the number of employees needed to perform each activity for a given week is determined by 30-minute periods. The goal is to meet this demand, and two penalty objectives are used to achieve this: minimizing understaffing and minimizing overstaffing.

A rule formalism has been defined to cater to each company's specific needs. These rules allow different situations to be modeled, such as "Every employee must perform this activity for a maximum of 3 hours during the day." They are included in the optimization model by adding an objective minimizing the penalty of non-respect for each rule. Furthermore, the employees’ preferences and wishes are considered when creating schedules to improve the quality of work life and retain employees.

This highly combinatorial optimization problem involving complex business constraints has been efficiently modeled using Hexaly. The solver optimized this problem with optimality guarantees for medium-sized instances within 30 seconds of running time. Based on this optimization problem, an industrial web application for workforce planning has been developed and will be demonstrated during the talk.

Railway crew scheduling deals with generating train driver duties to cover a number of trips while minimizing costs. Duty feasibility is subject to various physical restrictions and regulations such as the maximum working time and operational requirements.

In times of strikes and driver shortages, accounting for employees’ preferences gains importance. Including not only financial but also employee-centric goals could improve the satisfaction of the drivers and the attractiveness of the profession.

We consider the crew scheduling optimization tool used by a European railway freight carrier (ERFC). Duties are generated without consideration of any preferences. As preferences are often intangible or a non-linear combination of interacting characteristics, we employ machine learning to detect patterns. We train a classifier on 16,000 duties that were labelled as preferred or not preferred, and incorporate the duty classifier into the crew scheduling tool used by the ERFC.

We take this approach to the field, and test it with planning teams from all planning regions of the ERFC. Planners generate current schedules for their regions, and rate how these schedules meet their preferences. They also indicate duty characteristics that are most decisive for their preferences. We compare these with the influential features of the machine learning classifier, and see that our tool effectively captures preferences of the planners. Moreover, it is able to depict regional differences between planning teams accurately, and can generate schedules with more preferred duties accordingly. We also observe that incorporating preferences leads to schedules with comparable costs.