This paper introduces a new approach to solve the Shift-Design Personnel Task Scheduling Problem with an Equity criterion. This problem has been introduced in the context of drug evaluation, which requires to assign a set of medical tasks,fixed in time, to a set of skilled employees, whose shifts are to design. Employees' schedules must consider both legal and organizational constraints. The optimality criterion concerns the equity of the workload sharing. Two dedicated methods, one based on Constraint Programming and the other on a two-phase method, have been proposed in the literature to solve this problem. In this paper, we propose a new approach by improving the Constraint Programming model with a Large Neighborhood Search and we show that this new method clearly outperforms existing literature.