Controlling defective items in a complex multi-phase manufacturing system

In manufacturing systems, defective items are produced for machine drift and error. Usually, an imperfect production rate is random, if the not reworked, these considered trash harm environment. The proposed model aims to reduce waste by reworking products maximizing profit. For profit maximization or overall cost minimization of system, setup has significant. A discrete investment each phase introduced with inequality constraint reducing cost. Selling price-dependent demand trained more generalized applications various industries. a multi-phase system optimum batch size, selling price, irregular, rate. Defects detected at first inspection, reworked checked all non-defective in second inspection. conducts two-stage One detecting items, another checking after reworking. solved Karush–Kuhn–Tucker (KKT) method, global maximum obtained. shows that investments should be assigned maximize optimal solution. Reducing better than constant