A stochastic programming framework for Nash bargaining in oligopolistic industrial gas markets with customer contracts

Abstract

Mature industries, such as the industrial gases sector, often evolve into oligopolistic markets, which can amplify their susceptibility to market uncertainties. In this work, we propose a two-stage stochastic Nash bargaining in industrial gases market oligopolies, accounting for electricity price and demand uncertainties. A multi-period model is developed considering the fair customer and contract type allocation (first-stage decisions) and the optimal supply chain planning (second-stage decisions) as a mixed integer linear program. The stochastic customer allocation results in a preference for longer duration contracts while minimizing the customer mobility between firms. The two-stage approach increases supply chain resilience, allowing for higher operational flexibility in the examined case studies. Under different uncertainty realizations, the stochastic allocation succeeds in satisfying the contracted demand primarily by sales, i.e., more than 90% for the duopoly and 99% for the oligopoly, and the remaining demand is covered by swaps between firms without relying on outsourcing.