Popularity has increased for semi-flexible transit systems because they combine the flexibility of a Demand Responsive Transit with the affordable fare of Conventional Public Transport. In this study, we investigate a Flex-Route Transit: a shuttle performs several trips in a pre-defined service area; it follows a main route between origin and destination terminals and must pass through some mandatory checkpoints along this route. Between any consecutive checkpoints, an available slack time is available for shuttles to deviate from the main route to pick-up and drop-off customers. We implement a Mixed-Integer Linear Programming formulation from the literature with an added shuttle capacity constraint. We use it to perform a sensitivity analysis of the system using a full factorial experimental design over three parameters, namely: shuttle capacity, level of demand and available slack time. The combined influence of the parameters is analyzed using the method called Analysis of Variance.