A stock-dependent inventory model in an imperfect production process

The paper deals with an economic manufacturing quantity model for stock-dependent demand in an imperfect production process. In long run of a manufacturing process, the system undergoes out-of-control state and the process begins to produce imperfect quality products. The production of imperfect quality items depends on time and reliability parameter. These imperfect items are reworked at a cost to restore to its original quality. Moreover, the development cost that varies with reliability parameter of the manufacturing system is introduced to reduce the percentage of imperfect quality items. In our model, the unit production cost is a function of reliability parameter and production rate. The profit function is maximised by Euler-Lagrange method by considering different type's costs. The unit production cost and development cost which are functions of reliability parameter vary with changes with technology and resources. Concavity of the profit function in the numerical example establishes the existence of the global maximum solution which is graphically illustrated. The inventory/production versus time and optimal development cost versus optimal reliability are also demonstrated graphically.