A Two-Stage Optimization Algorithm for Booking Allocation in Short-Term Group Apartment Rentals: A Case Study

In the world of business, managing a hotel or a rental property often feels like a game of high-stakes juggling. Owners must decide who gets to stay, when they arrive, and how much to charge, all while trying to fill every available bed without leaving empty spaces that lose money. For decades, experts have focused heavily on the price tag, using complex math to figure out the perfect rate to charge for a room on a specific night. However, there is another side to this puzzle that is just as critical but often overlooked: the physical act of fitting people into rooms. Imagine a large apartment building with dozens of beds spread across many units. When a group of travelers arrives, they might need ten beds, but those beds might be scattered across three different apartments. The challenge is not just setting a price, but figuring out which specific apartments to use, ensuring the group stays together in one building, and making sure no two groups are assigned to the same space at the same time. This is a problem of allocation, a combinatorial puzzle where the goal is to pack people into available space as tightly and efficiently as possible. While large corporations have expensive software to solve these puzzles, smaller businesses often struggle with spreadsheets and manual guesswork, leaving money on the table and wasting valuable time.

This is the story of a small rental company in Tel Aviv called "Our Place" and the researchers who helped them solve this specific puzzle. The company usually manages a few buildings year-round, but during the summer, they expand to about ten buildings to host organized groups of young travelers. Unlike standard hotel bookings, these groups do not have a fixed price list. Instead, each group proposes its own price per bed for their stay, along with their specific dates and the number of people in their party. For years, the company's chief operating officer spent weeks every season manually sorting through these overlapping proposals, deciding which groups to accept and which apartments to assign them to. It was a slow, exhausting process that often delayed responses to customers and relied entirely on human judgment under pressure. To improve this, a researcher named Hana Tzur worked directly with the company to build a new system. Instead of trying to change the prices, the system focused entirely on the allocation problem: selecting the best mix of proposals and fitting them into the available apartments to maximize the total money earned.

The solution they built is a two-step process that mimics how a human might think, but with the speed and precision of a computer. The first step is the heavy lifter. It looks at all the incoming requests and the hard rules of the business—such as the total number of beds available in each apartment and the rule that a group cannot be split across different buildings. It uses a mathematical method called integer programming, which is essentially a way of testing millions of possible combinations to find the single best arrangement that fits all the rules. This step decides which groups to accept and which to turn away to ensure the company makes the most money possible. Once the best groups are selected, the second step takes over. This stage does not change who is staying; instead, it fine-tunes where they sleep. It looks for small improvements, such as placing a group in apartments that are right next to each other or ensuring there is very little empty time between one group's departure and the next group's arrival. This second step is designed to make the operation run smoother and leave fewer awkward gaps in the calendar.

The researchers tested this new system using the company's actual booking data from 2023. They ran the algorithm on the same set of requests that the human manager had handled the previous year and compared the results. The computer's plan generated about 3.5% more revenue than the manual decisions. In real money, this meant an extra 139,000 Israeli shekels for that single season. Beyond the money, the system changed the workflow entirely. What used to take the manager weeks of intense work was reduced to a process that took only a fraction of the time, cutting the allocation time by roughly 90%. This allowed the company to respond to customers much faster and freed up the manager's time for other tasks. The system was built using a low-code platform, which is a type of software that allows people to build applications without writing complex code from scratch, and it ran on a cloud server that only turned on when needed. This kept the cost incredibly low, at about 200 shekels per month, making advanced optimization accessible to a small business that could never afford expensive commercial software.

However, the researchers were careful to note that this success came with specific trade-offs and limitations. The system was not perfect, and in one instance, a small error in how the software was written meant that one part of the fine-tuning step did not actually work as intended. Fortunately, because the main goal was to maximize revenue and the error only affected a minor preference for how close apartments were to each other, the overall result remained strong. The researchers also ran simulations with made-up data to see how the system would perform under different conditions. They found that as the demand for rooms got higher and the competition for space became more intense, the advantage of using the computer over a human grew significantly. In the most crowded scenarios, the computer's ability to pack groups efficiently led to revenue improvements of over 65% compared to a simple, unoptimized method. This suggests that the more crowded the market, the more valuable this kind of smart allocation becomes.

The study also highlighted a broader lesson for small businesses. It proved that you do not need a team of data scientists or a massive budget to solve complex logistical problems. By using open-source tools and simple cloud computing, a small operator can achieve results that were previously only available to large corporations. The researchers documented the entire process, including the mistakes and the workarounds, to show that this approach is viable for others. They found that the most important part of the system was simply fitting the groups into the available beds as tightly as possible. The other fancy features, like making sure groups are in adjacent rooms, were nice to have but not strictly necessary for the main financial gain. This means that even a very simple version of the system could provide most of the benefits.

Ultimately, this paper reframes how we think about managing short-term rentals. It shows that for businesses dealing with group bookings, the biggest opportunity for growth often lies not in changing prices, but in getting better at the physical assignment of space. The human manager at "Our Place" was skilled and experienced, but the sheer number of variables involved in overlapping dates and varying group sizes made it impossible for a human to see every possible combination. The computer did not replace the manager's judgment; it simply gave them a tool to see the full picture. The result was a business that made more money, responded faster to customers, and operated with less stress. For other small operators facing similar challenges, this case study offers a clear path forward: start with the hard constraints, use simple tools to find the best fit, and let the data handle the complexity that the human mind cannot easily hold.