The effect of imperfect production in an economic production lotsize model

In the basic economic production lotsize model, it is assumed that all produced items are of prefect quality. But in practice, the experience is that no production process can produce all items of perfect quality. Most of the production system produces both perfect and imperfect quality items. In some cases, imperfect quality items are reworked at a cost to repair their quality. This rework cost can be reduced by reducing the product reliability parameter. However, when the product reliability parameter decreases, the development cost of production increases at the same time. The unit production cost is a function of the product reliability parameter and the production rate. Therefore, higher development cost increases unit production cost. In the proposed model, we have assumed that the production process shifts from an in-control state to an out-of-control state at any random time. The total cost in this production system includes the production cost, the setup cost, the holding cost and the cost of reworking the imperfect items produced. Our problem is to find the optimal production rate, optimal production lotsize and optimal product reliability parameter so that the total associated profit is maximum. The analytical solution of the model is derived and the solution is illustrated with the help of numerical examples. The sensitivity of the optimal solution to changes in the values of different system parameters is also studied.