Complexity of sales effort and carbon emission reduction effort in a two-parallel household appliance supply chain model

Abstract

• A two-parallel household appliance SC model considering pricing, carbon emission reduction and sale effort was proposed. • The research framework about a dynamic Stackelberg game with respect to five variables was provided. • The complexity and profit of the two-parallel household appliance SCs under VN, TS, and LCS game models were investigated. • A phenomenon that the TS game system evolved into chaos from the two-cycle state via a six-cycle state was discovered. This paper studies the complexity of sales effort and carbon emission reduction effort in a Bertrand household appliance supply chain system. A two-parallel model consisting of a traditional supply chain without any carbon emission reduction effort and a low-carbon supply chain with carbon emission reduction effort is established. The chain to chain competition is analyzed in three scenarios, one of which is a horizontal Nash game, and the others are the traditional supply chain Stackelberg game and the low-carbon supply chain Stackelberg game. The optimal solutions of the horizontal Nash game and the Stackelberg game are obtained and three models’ dynamic evolutions based on the bounded rationality are investigated. A dynamic Stackelberg game model with respect to five variables is proposed and investigated via the stable region, the bifurcation, and the maximum Lyapunov exponent. The profits of the two-parallel household appliance supply chains are compared in three dynamic game structures. An interesting phenomenon that the system will enter a six-cycle state after the two-cycle state and fall into chaos directly is discovered in the traditional supply chain Stackelberg game. Our results suggest that the adjustments of price would affect the stability and profits much more than the sales effort and carbon emission reduction effort in all three game structures. Every supply chain should take the suitable adjustment speeds for the price and sales effort to keep the system in the stable state. Each adjustment should not exceed the domain of attraction.