Stackelberg Game Design and Operation of a Non-Cooperative Bi-Level H2 Supply Chain Under Cournot Equilibrium

Abstract

In the pathway toward decarbonization, hydrogen is presented as a great option as it can be produced from a wide variety of feedstock using multiple production, storage and transportation options for diverse applications. Although H 2 could provide flexibility and sector coupling to energy systems, the design and management of the hydrogen supply chain (HSC) is also identified as a challenging task. Until now, most of the HSC designs are treated as problems with single or multiple objectives without any hierarchical conflict. This paper proposes a mixed-integer bi-level programming (MIBLP) approach as a mathematical model of the Stackelberg game. The solution strategy considers the MIBLP as a multi-parametric problem: if the feasible set of the lower level optimization problem (LLP) of the bi-level programming problem (BLPP) is parametric in terms of the optimization variables of the upper level problem (ULP), each level can be solved with a different approach. Consequently, to handle continuous and discrete variables at both levels, we propose a hybrid method involving Differential Evolution (DE) for the ULP and an Integer Linear Programming Solver (ILPS) for the LLP. The developed hybrid evolutionary-deterministic strategy evaluates the performance of two HSC study cases combining Steam Methane Reforming and Electrolysis processes for H 2 production: a classical Stackelberg game design vs. a Stackelberg one leader - multi followers under Cournot competition. In both scenarios, the ULP objective is to minimize the distribution cost while the LLP objective tries to minimize the production cost of a given producer. The experimental results obtained show that the solution method is efficient and promising for dealing with one-leader multi-objective / multi-follower single objective optimization cases.