Advanced decision making in the process industries requires efficient use of information available at different decision levels. Traditionally, planning, scheduling, and optimal control problems are solved in a decoupled way, neglecting their strong interdependence. Integrated planning, scheduling and optimal control (iPSC) aims to address this issue. Formulating the iPSC, results in a large scale nonconvex mixed integer nonlinear programming problem. In the present work, we propose a new approach for the iPSC of continuous processes aiming to reduce model and computational complexity. For the planning and scheduling, a Traveling Salesman Problem-based formulation is employed, where the planning periods are modeled in discrete time while the scheduling within each week is in continuous time. Another feature of the proposed iPSC framework is that backlog, idle production time, and multiple customers are introduced. The resulting problem is a mixed integer programming problem and different solution strategies are employed and analyzed.