a mathematical model for determining the optimal production lot size of multiple products on a machine

In this research, the production of multi-products using one machine is investigated in continuous time. the machine has limited capacity and can produce only one product at any time. to change the product, the machine should be set up. due to the difference in demand for products, there is no need to equate the number of machine start-ups for these products, by removing this constraint, a nonlinear mathematical model is presented that gives the optimal production lot size for each product. to solve the single-constraint nonlinear model, the lagrange method is used. for a numerical example, the obtained solution is compared with the method of rotating a constant cycle. due to the total cost, the solution was better than the solution of the rotation cycle method. also, contrary to the rotation cycle method, the total holding cost is equal to the total setup costs, which is similar to the wilson inventory basic formula.