A multi-product system is one of the different types of manufacturing systems, in which a large number of products are produced that complement each other and have interdependence. These types of systems have recently been widely used in various industries. In some types of multi-product manufacturing industries that offer their products as a package, the scheduling of the production of components of each package affects the time it takes to complete the package. Therefore, a new problem has been defined that the primary purpose of its production scheduling, in addition to reducing the completion time of the products, is to make various items forming a package, get ready over a short interval of time and be supplied to the sales unit so that the package can be delivered to the final consumer. The purpose of this paper is to express the problem of production scheduling of multi-product production systems in the form of linear programming. For this purpose, two mathematical models are presented, and their functions are compared. Besides, an efficient genetic algorithm is proposed to solve the problem, which is able to solve the problem in a reasonable time, with acceptable accuracy.