This paper proposes a methodology to optimize the dispatch and reserve between multiple units in a Hydroelectric Power Plant (HPP) that makes use of the Hydraulic Short Circuit (HSC) operating mode. HSC allows for the simultaneous generation and pumping from different units of the same plant. The objective of optimal dispatching is to maximize efficiency and reduce the number of start and stop of the machines. We first introduce the original Mixed Integer Programming (MIP) problem and discuss its computational complexity. Then, we propose an optimal dispatching algorithm obtained by efficiently solving a set of convex optimization sub-problems, as opposed to the original MIP. The methodology is applied and validated in two different cases, including one real study case in France. The study cases demonstrate the ability to include HSC in short-term dispatch, consider future set-points for optimizing power trajectory, and find the optimal solution to the HPP dispatching problem while guaranteeing a computationally tractable approach.