An economic production lot size model for defective items with stochastic demand, backlogging and rework

The article deals with an economic production lot size model in which the manufacturing process shifts from an ‘in‐control’ state to an ‘out‐of‐control’ state after a certain time span which is exponentially distributed. Rapid production may cause such a type of shifting. During the ‘out‐of‐control’ state, defective items are accumulated and reworked immediately at some cost for maintaining the quality of the product. The demand of the product is assumed to be stochastic. Shortages are allowed and backlogged. Both partial backordering and complete backordering are studied separately and their comparisons are also done. Production cost, holding cost, backlogging cost, lost sale cost, reworked cost and selling price are taken together to construct the integrated expected average profit function, which is maximized to obtain the optimal production rate, optimal lot size and value of optimum expected average profit by using the calculus method. Six numerical examples with their graphical representation are provided to justify the proposed model.