Using game theory to solve a competitive supply chain network model with green investments and labour

Abstract

In light of the recent severe Supply Chain (SC) disruptions that have occurred across multiple industries around the globe, three essential themes have emerged in SC management: the well-being of employees, the sustainability of SC practices and the competition between SCs for limited resources. Moreover, these three themes are linked, with an increasing number of employees demanding sustainability from the firms they work with, as well as an increasing competition amongst firms to find talent. Taking into consideration the above, this dissertation aims to create a SC network model that incorporates together SC competition, labour productivity and green investing. Each competing firm within the network seeks to maximise its profit by determining the optimal flow of products between manufacturing facilities, distribution centres, storage facilities and the eventual sales to demand markets, as well as how best to invest in green initiatives across the SC according to a predetermined budget. Factors such as the introduction of a carbon tax on emissions, consumer preferences and employee engagement are also included in the model. Game Theory is used to formulate a Nash Equilibrium solution to the model, such that no firm would be able to individually improve its profits by deviating from this solution. Numerical examples for various scenarios inspired by the Maltese dairy industry are solved using a Variational Inequality reformulation and the Extragradient algorithm, and sensitivity analysis is also carried out. The results highlight the importance of the three aforementioned themes on SC profitability and the close relationship between them.