The garment industry in Vietnam is one of the country's strongest industries in the world. However, the production process still encounters problems regarding scheduling that does not equate to an optimal process. The paper introduces a production scheduling solution that resolves the potential delays and lateness that hinders the production process using integer programming and order allocation with a make-to-order manufacturing viewpoint. A number of constraints were considered in the model and is applied to a real case study of a factory in order to view how the tardiness and lateness would be affected which resulted in optimizing the scheduling time better. Specifically, the constraints considered were order assignments, production time, and tardiness with an objective function which is to minimize the total cost of delay. The results of the study precisely the overall cost of delay of the orders given to the plant and successfully propose a suitable production schedule that utilizes the most of the plant given. The study has shown promising results that would assist plant and production managers in determining an algorithm that they can apply for their production process.