Fuzzy multi-objective, multi-item, multi-supplier, lot-sizing considering carbon footprint

Optimum order size plays a key role for minimising carbon footprint of a supply chain. However, managers often face difficulty in handling conflicting objectives like cost reduction and carbon emission reduction for supply chain operation. As of now, very few studies have reported multi-objective, multi-item, multi-supplier lot-sizing problem taking consideration of carbon emission under fuzzy environment. This study fills the gaps of earlier research and proposes a fixed carbon cap model incorporating carbon footprint factor. The model has been subsequently modified to carbon offset and multi-objective fuzzy models. The proposed models have been solved by using different methodologies (mixed integer programming, interactive fuzzy goal programming, additive interactive fuzzy goal programming, weighted goal programming, and interactive fuzzy ε constraint method) and their results are compared. As theoretical contribution, this study extends interactive fuzzy goal programming and ε constraint method to additive interactive fuzzy goal programming and interactive fuzzy ε constraint method, respectively. The effectiveness of the proposed models has been explained through illustrative examples and various scenarios have been generated by varying different model parameters. This study will help managers to take prudent decision in carbon constrained world.