Computer-based system and computer-implemented methods for providing an automated computer network-based, or online, appointment scheduling service through which registered customers are individually capable of scheduling an appointment with a plurality of businesses that are also registered with the online appointment scheduling service. The application describes an optimization algorithm for controlling the start times presented to a customer when selecting an appointment time that seeks to cluster the new appointment to existing appointments for the business in order to reduce time gaps during the day for the business/service provider that are of insufficient duration to schedule other appointments for other customers of the business.