Lot-size models for a hybrid system with different sale prices on newly manufactured items and recovered items

To determine the optimal manufacture and recovery policy, a hybrid system is investigated in which manufacturing and recovering operations co-exist. In this system, the constant demand of customers is fulfilled by newly manufactured products or recovered products. However, only a part of return used products from customers are recovered and the rest are disposed off due to the lower price of the recovered products. The inventory decision-making models on the unit time total profit are formulated under one manufacturing setup and one recovering setup policy, and these models are reduced to the functions with respect only to recovery ratio and recovering lot-size by the elimination theory, and finally the formulae on the optimal manufacturing and recovering lot-sizes, recovery ratio and others are derived. Compared with the related literatures, this study is closer to the reality.