Engine shop visit (ESV) scheduling is a critical component of airline maintenance planning, directly impacting operational continuity, cost management, and long-term fleet value. Despite its importance, existing approaches often overlook fleet-level considerations, such as additional lease engines and spare engine management. Whilst maintenance planning has been widely studied, the specific dynamics associated with engine shop visit planning remain relatively unexplored. This paper presents a Mixed-Integer Linear Programming (MILP) framework to solve the engine maintenance problem as an adaptation of the Resource Constrained Project Scheduling Problem (RCPSP). The classical formulation has been adapted significantly, as time precedence constraints have been omitted, and extensions have been introduced to incorporate engine health metrics and component-level scheduling. Furthermore, the model has been extended to allow for additional lease engine activation and to manage the number of available spare engines. The framework is applied to the operational contexts of a major European airline operating wide-body aircraft in a mixed global network, integrating airline-specific constraints and assumptions. Through sensitivity analyses on key parameters and several use-case scenarios, including an Unexpected Engine Removal (UER), the model successfully generated feasible shop visit plans under varying conditions whilst providing valuable insights to decision-makers. The results highlight the benefits of integrated planning and support operational and strategic engine fleet management.