fuzzy multi-objective optimization

Incentive by the recent global trend in greenhouse gases (GHG) emission reduction strategies and considering the evolution of business models from traditional to multi-channel, in this research, we analyze a dual-channel green supply chain in which a manufacturer delivers a product through one direct channel and one retail channel whose demand are uncertain and prices in channels can effect on customer demand. Modeling this chain is carried out by accounting for the optimal price of distribution channels, total profit optimization, and reduction of transportation cost, we well as minimizing CO2 emission that the CO2 emission is investigated through transportation mode choice. The proposed model has developed first a mixed-integer nonlinear programming and a theoretical technique is applied to linearizing the problem. To solve the proposed multi-objective Possibilistic programming model, the Jimenez and TH approach has been used. The model is verified by numerical experiments and then several sensitivity analyses have performed. Computational results proved the efficiency of the model in finding a trade-off between economic and environmental objectives so that if transportation costs are equal to both markets, in order to balance the goals, the model uses vehicles that have a less environmental impact. In addition, the proposed solution method enables the decision maker to determine the importance of each objective function. The decision-maker is also able to influence the optimal price of distribution channels by changing the parameters in the demand-price equation and maximize the total profit of the supply chain.