The surprising mathematics behind housekeeping scheduling

Problem formulation

Imagine that you are responsible for the cleaning of a hotel. Say that on a given day, 120 rooms should be cleaned with the help of ten available room attendants. How should you allocate these tasks fairly and efficiently? Should you sequentially allot specific sections of the hotel to individual shifts, covering the hotel successively? Maybe, but then how do you know that the shifts are evenly balanced throughout the hotel? And how should you divide the hotel into sections with roughly the same number of tasks? And if a new guest wants to check in early, then we don’t want to be stuck with a predetermined schedule, but rather be able to prioritize their room and offer early check-in. Finally, how do you accommodate the difference between stayover and checkout cleanings, which require different amounts of effort? Clearly, scheduling is more complicated than meets the eye. In fact, today hotel managers spend hours each day scheduling, trying to account for all the above facts [1]. In this post, we present how Zaplar is taking a different approach by applying modern optimization research to streamline operations and free up time to let the staff focus on higher-value tasks.

At its core, housekeeping scheduling is a constrained optimization problem. The system must assign every cleaning task to an available shift, while respecting a collection of operational constraints. A cleaner cannot be assigned more work than can reasonably be completed during the shift, some rooms have higher priority, and different tasks require different amounts of time. These goals often conflict, which means that there is rarely one obvious allocation. As a simple toy model, the objective could be to find

where A is an assignment of tasks to shifts, ℱ is the set of feasible assignments, WI, WD, DV, and SC denote workload imbalance, walking distance, deadline violation, and schedule changes, respectively, and α, β, γ, and δ denote weights determining how hotels trade off competing priorities.

Zaplar’s take

At Zaplar, our vision has always been to build something that does not exist today. Many existing PMS firms ‘integrate AI’ by adding a chatbot on top of their existing system. We take a different architectural approach by building an AI-native operating system from the ground up, where rooms, employees, tasks, and priorities are represented within the same underlying system. While this is a much more demanding task, it has the significant benefit of allowing a deep, holistic understanding of the hotel, which is a necessity to solve tasks like scheduling optimally. By representing rooms as nodes on a graph, with weighted edges capturing time required to move between them, we can resort to modern combinatorial optimization algorithms to solve the scheduling problem in a matter of seconds: With a single click, our program presents a solution that is mathematically optimal for the specified objective and constraints. Moreover, by additionally optimizing over distance covered, in our initial tests on tens of schedules, the optimized assignments reduces the estimated walking distance by an average of 20% compared to the corresponding manually prepared schedule.

Of course, an optimal schedule can only be optimal with respect to a particular definition of what “good” means. Minimizing walking distance alone could leave one employee with a significantly heavier workload than others. Perfectly balancing the expected cleaning time could instead send employees back and forth across the hotel. Prioritizing every early check-in might disrupt the schedule and hence increase the risk of overtime work. The important task is therefore not only to solve the optimization problem, but to formulate it in a way that reflects how the hotel actually wants to operate. This is where domain knowledge enters: having spoken to hundreds of hotel owners and managers helps us understand which constraints and trade-offs matter in practice, and we can tailor the optimization based on any specific hotel’s needs.

Beyond its speed and accuracy, yet another benefit of our approach is its flexibility. Let us revisit the issue of the early check in: Say that a guest arrives two hours before their scheduled check in time and asks if they can check in immediately. With a static, hand-made schedule, this person would simply have to wait until the predetermined schedule reached their room. With our solution, the system can respond to such changes and can notify the cleaner least affected by inserting this task into their schedule. Importantly, this does not require a complete resolve of the problem: it affects one room attendant’s schedule.

Something important to mention is that this does not mean that the housekeeping manager disappears from the process. Hotels differ in their layouts, working practices, employee preferences, and definitions of a fair schedule. The manager must therefore be able to understand why assignments were made, change priorities, and override the system when necessary. The purpose of the algorithm is not to eliminate operational judgment, but to convert that judgment into a feasible schedule and continuously handle the administrative work required to maintain it.

Takeaway

Housekeeping scheduling illustrates a broader challenge in hotel operations. Rooms, guests, employees, maintenance tasks, deadlines, and physical distances are not isolated pieces of information; they are interdependent. Hence, automating these operations requires more than letting a chatbot try to make sense of an existing system and making broad guesses on optimality. It requires a system capable of understanding the hotel as a connected whole, together with its operational objectives and constraints.

This is what we are building at Zaplar. By combining a unified representation of hotel operations with modern optimization methods, our objective is to eliminate hours of repetitive planning while giving staff greater visibility and control. The surprising part is not merely that housekeeping scheduling involves mathematics. It is how useful that mathematics becomes when it is built around the way hotels actually operate.

References

1. Audrey Walravens (2026). Hotel Schedule Management. https://shyfter.com/en/sectors/hotels/hotel-schedule-management