Airbnb, the burgeoning business model that has revolutionized the lodging and tourism industry, is not just about renting out a spare room or a whole property. It's about providing a unique, unforgettable experience for guests from across the globe, which inherently calls for high standards of cleanliness.

Selecting the ideal cleaner for your Airbnb property is not just about finding someone who can dust and mop. It requires a comprehensive comprehension of the specific needs of Airbnb hosts and the expectations of the guests. Choosing the perfect cleaner is a multivariate problem, one that requires analysis across diverse dimensions.

A deep dive into the Harvard Business School case study, "Airbnb, Etsy, Uber: Acquiring the first thousand customers", elucidates the significance of customer satisfaction in propelling the success of sharing economy businesses like Airbnb. An Airbnb cleaner plays a crucial role in maintaining this customer satisfaction, which can be ascertained through strategic questioning.

Firstly, understanding the cleaner's familiarity with Airbnb's operations is fundamental. Ask: "What experience do you have with Airbnb properties?" This question aims to assess their grasp of the specific nuances that differentiate Airbnb cleaning from traditional home cleaning. A seasoned Airbnb cleaner will understand that they’re preparing for guests, not just cleaning a house. They'll know that everything must be picture-perfect, strategy-wise and aesthetics-wise, for the best guest experience.

The second question that is imperative to ask is: "What is your familiarity with deep cleaning versus turnover cleaning?" This instance calls for the application of the economic theory of division of labour. Turnover cleaning, which is akin to hotel cleaning, involves general cleaning tasks and ensuring the property is ready for the next guest. Deep cleaning is a more intensive process that usually takes place every few months and involves tasks such as cleaning behind appliances, scrubbing grout, and washing walls. An ideal Airbnb cleaner will be proficient in both, maintaining a balance that optimizes cost and quality.

Thirdly, one must ask: "How flexible is your schedule?" The unpredictable nature of bookings necessitates a cleaner who can adapt to changing schedules. This also entails understanding the cleaner's capacity to handle multiple properties, if applicable, and their ability to respond to unforeseen circumstances such as last-minute bookings or cancellations.

The fourth question should be: "How do you handle property damages or missing items?" Similar to risk management in financial mathematics, an effective cleaner will have a systematic strategy to report any damage or missing items, to mitigate potential losses.

Lastly, inquire about their supplies: "Do you bring your own cleaning supplies, or use those provided on the property?" This question addresses the logistical aspect of cleaning. While there's no right or wrong answer, their response will provide insight into their operational style and allow you to plan accordingly.

In conclusion, selecting the perfect Airbnb cleaner is a multilayered decision process that requires an acute understanding of the unique needs of the sharing economy. By posing these strategic queries, Airbnb hosts can ensure they find a cleaner who upholds the high standards required and contributes to an unforgettable guest experience.

Remember, in this line of business, customer satisfaction is not just a variable, it is the equation.