A production/recycling model with quality consideration

An integrated production–recycling system is investigated. A constant demand can be satisfied by production and recycling. The used items might be bought back and then recycled. The not recycled products are disposed off. Two types of models are analyzed. The first model examines and minimizes the EOQ related cost. The second model generalizes the first one by introducing additionally linear waste disposal, recycling, production and buyback costs. This basic model was examined by the authors in a previous paper. The main results are that a pure strategy (either production or recycling) is optimal. This paper extends the model for the case of quality consideration: it is asked for the quality of the bought back products. In the former model we have assumed that all returned items are serviceable. One can put the following question: Who should control the quality of the returned items? If the suppliers examine the quality of the reusable products, then the buyback rate is strongly smaller than one, a<1. If the user does it, then not all returned items are recyclable, i.e. the use rate is smaller than one, d<1. Which one of the control systems is more cost advantageous in this case?