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Effect of carbon emission on multi-stage economic order quantity model with backlogging under fuzzy environment

Due to increasing global warming and environmental consciousness, to avoid/reduce carbon emission is a challenge in today's business scenario. In this study, a three stage (buyer-distributer-vendor) economic order quantity strategy is presented. The objective of this study is to analyse the carbon emissions caused during transportation and holding of the inventory. In order to increase the utility of the proposed model, besides all cost parameters, carbon emission costs and transportation costs at every step of supply network are also considered as fuzzy and denoted by fuzzy numbers. Shortages are allowed and backlogged unconditionally for this study. The optimal solution are obtained by using (a non derivative) arithmetic geometric inequality method. Further the optimization model is studied under the following policies (i) without considering carbon emission and (ii) with carbon emission. Here closed form solutions are obtained. Proposed models are analysed environmentally and economically for the decision variables. A numerical example is used to demonstrate the work in a better way and obtained results are compared under both policies. Finally, the results of two models proved that, the model with carbon emission is better for cost reducing and environmental consciousness both. Sensitivity analysis is also performed with respect to all important parameters.