This paper addresses the problem of optimizing production schedules of multiproduct continuous manufacturing facilities where a wide range of products are produced in small quantities, resulting in frequent changeovers. A real-world scheduling problem from the polyamide fiber plant is investigated. The problem involves a sequencing of products. The problem is formulated as a mixed-integer linear programming (MILP) model. The mathematical model has a linear objective function to be maximized. A simulated annealing (SA) algorithm is proposed for this scheduling problem. The computational results show that a satisfactory solution can be obtained in reasonable computation time. Case study demonstrates the effectiveness and the applicability of the model and the proposed methods.