<p>With the rapid growth of the sharing economy, decision makers are increasingly confronted with greater complexity and uncertainty, necessitating the formulation of effective online strategies. The challenge of addressing information uncertainty is precisely the context in which online decision-making operates. This paper focuses on the online leasing problem with a piecewise price function, where the exact duration of equipment use remains unknown. Utilizing the competitive analysis method, both optimal deterministic and randomized algorithms are proposed. We introduce a novel perspective to prove the optimal competitive ratio of the randomized strategy. These findings provide a comprehensive theoretical foundation for addressing such problems. Additionally, a numerical example is presented to elucidate the influence factors of the two strategies, offering management insights for practical applications.</p>