Joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles

This study deals with an imperfect EPQ (economic production quantity) price dependent inventory model over two types of cycles: in the first cycle, the retailer sells only good product with actual price and, in the second, he sells the products with a discount price. In the production run-time, the non-conforming items are produced at a random rate and they are reworked after the regular production run time and the reworked items are almost perfect as good as original quality items. The retailer starts the second cycle when a certain percent of good items are left to him, after the completion of regular production. The retailer continues simultaneously two cycles up to which both types of the products are available to him. Now, our objective is to find out optimal ordering lot size and optimal price for which the profit of the integrated model is maximum. Also, we check the best strategy of retailer for the time of starting second cycle. A numerical example is provided to illustrate the behavior and application of the model.