Home service operations planning with employees preferences and uncertainty – HOPES

The project adopts an integrated methodological approach to address the complexity of home service planning problems. It relies on advanced mathematical optimisation models, including mixed-integer programming, to jointly model scheduling and routing decisions over multiple periods.

To better represent real-world conditions, the project incorporates uncertainty, such as variability in service times, and employee availability, through stochastic programming approaches, including scenario-based modelling.

Efficient solution methods are developed to address the computational complexity of these large-scale problems. These include decomposition techniques such as Benders decomposition, Branch-and-Price, and hybrid approaches combining mathematical programming with metaheuristics.

Overall, the methodology integrates optimisation, data science, and stochastic modelling into a unified decision-support framework.

The project led to several significant scientific and practical contributions. Two PhD students were successfully trained and defended their theses.

A major outcome is the development of an open-access Python library for modeling employee scheduling problems in a generic and flexible way. This library allows the representation of complex working rules using formal languages and enables the automatic generation of mathematical optimization models.

In addition, an open-access framework was developed to solve integrated employee scheduling and routing problems using advanced techniques such as branch-and-price.

From a methodological perspective, the project demonstrated the importance of integrating scheduling and routing decisions. Solving these problems jointly leads to more robust and realistic solutions, particularly in the presence of demand variability.

The project also showed that incorporating uncertainty, such as variability in service times and employee availability, significantly improves the adaptability of solutions to real-world conditions.

Finally, the project contributed to bridging a gap in the literature by proposing a general and automated approach to modeling employee scheduling problems, unifying and extending existing methods based on formal languages.

The HOPES project opens several promising research perspectives.

A first direction concerns the integration of additional sources of uncertainty, particularly demand uncertainty, and the evaluation of its impact on solution quality and robustness.

Another perspective is the exploration of alternative approaches for modeling and solving stochastic problems. While the project relied on two-stage stochastic programming, other methods such as chance-constrained optimization or robust optimization could provide more scalable or efficient solutions.

The project also highlights the need for a deeper investigation of the integration between scheduling and routing decisions. In particular, it would be valuable to assess whether explicitly modeling routing is always necessary, or whether its impact can be approximated to improve scalability.

Additional challenges include the integration of employee preferences into the models and improving the scalability of solution methods for large-scale instances.

Overall, these perspectives aim to enhance the applicability of the proposed approaches and to further advance the state of the art in home service operations planning.

HOPES project aims at addressing multi-period employee scheduling and routing problems for home services operations planning. HOPES will propose innovative decision-support-tools to solve these complex problems including working regulations, individual preferences, and different sources of uncertainty. To that end, we will formulate and design new optimisation approaches that will integrate techniques drawn from data science, and deterministic and stochastic optimisation. Instead of proposing a method that only works for a specific application, HOPES aims at proposing a general framework that can be extended to solve different variants of the problem. The decision-support-tools developed are expected to improve the quality of service for the users, the well-being of the employees, and to improve the planning and execution of home services operations.