An EPQ model for a single-machine multiproduct imperfect production system using a hybrid logarithmic barrier method

This paper develops an economic production quantity model for a single-machine multiproduct imperfect production system with a set of alternative assumptions. The system under study can produce different types of products using a single machine. Fresh production and rework of imperfect items are performed on the same production line. The model is developed with different operational possibilities on imperfect items. The model aims to investigate the effects of continuous supply of all products throughout a planning period, unequal production cycles, and removal of idle inventory downtimes. A constrained nonlinear mathematical model is derived for the system. The model is optimized using the logarithmic barrier method that uses Newton's iterative process to calculate the optimal value in each stage. A numerical example and sensitivity analysis are presented to validate the proposed model and optimization method. Some managerial applications of the model are explained.