A Game Theoretic Competitive Supply Chain Network Model with Green Investments and Labour

In light of the recent severe Supply Chain (SC) disruptions that have occurred across multiple industries around the globe, three essential and linked themes have emerged in SC management: the well-being of employees, SC sustainability, and competition between SCs for limited resources. In this paper, we create a game-theoretic SC network model that incorporates together non-cooperative SC competition, employee productivity and engagement, and green investing. Each competing firm within the network seeks to maximise its profit by determining an optimal flow of products and allocation of green investments across the SC according to a predetermined budget. A carbon tax on emissions and consumer sustainability preferences are also included in the model. The model is solved using a Variational Inequality reformulation. The illustrative numerical examples presented in this paper have been inspired by the Maltese dairy industry and demonstrate the applicability of the model to real-world problems. The results highlight the significance of the employee engagement factor in enabling firms to adopt and realise more sustainable SC practices.