Optimal production policy under pollutants´ treatment constraint

This paper firstly develops a basic optimal production model between the manufacturer and retailer (Model 1) under the pollutants´ treatment capacity constraint. Meanwhile, in the perspective of products´ upgrade and contracting design, manufacturer´s upgraded product model (Model 2) and cost-sharing model (Model 3) under the manufacturer´s product upgrade investment strategy are developed. We investigate the optimal production policy and optimal profits of the manufacturer and retailer for each model. Furthermore, it is found that through comparing results, the manufacturer and retailer´ profit can be simultaneously improved under the manufacturer´s upgraded product model if a certain condition is satisfied, which means achieving pareto improvement. And a proper cost-sharing contract can motivate the manufacturer to adopt product upgrade strategy.