Supply chain equilibrium among companies with offline and online selling channels

This study proposes a supply chain system model containing Nash game companies that compete in a common market. Each company adopts a vertical integration strategy and runs offline and online selling channels. To maximise profits, the companies determine optimal production quantities and prices. Using theory of finite-dimensional variational inequality, we prove the existence and uniqueness of the equilibrium pattern and develop a converged algorithm. Numerically, we compute the equilibrium production quantities and prices, and subsequently generate three findings through sensitivity analyses. By changing the transportation cost, we demonstrate that the offline price is conditionally higher than the online price with different transportation and processing costs. All equilibrium prices and profits decrease when substitution intensity is increased, and thus companies should differentiate their products. Altering consumer preference for online purchasing shows that consumer preference significantly influences the production quantities and profits. Online selling is not positively affected by consumer preference for online purchasing but is affected by the complex relationship between consumer preference and its variable cost.