Supply chain equilibrium among companies with offline and online selling channels

Abstract

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.

Optimal production strategies of competitive firms considering product innovation

“…Yu and Nagurney [57] used variational inequality theory to solve a network-based supply chain problem considering different consumer demands. Yu et al [58] developed a supply chain system model considering the preferences of consumers for offline and online selling channels. Based on the discussion of consumers' demand preferences, product innovation design features were classified by Kano model, then Yang et al [53] proposed Non-dominated Sorting Genetic Algorithm to solve the model.…”

Optimal production for manufacturers considering consumer environmental awareness and green subsidies

“…We assume that the cost is continuously differentiable, and convex with respect to ; 0,1, , ; 1, , (Nagurney et al, 2002;Yu and Nagurney, 2013;Yu et al, 2015), if the binary variables…”

“…In addition, it also provides us an approach for developing algorithms with analysis in convergence. On this basis, variational inequality theory has been extensively used in obtaining equilibrium solutions in a large number of literature (Zhang, 2006;Nagurney and Yu, 2012;Masoumi et al, 2012;Yu et al, 2015). Nagurney et al (2002) developed a supply chain network model and established a finite dimensional variational inequality formulation, which was then extended.…”

La Nueva Cadena de Suministro en la Era de los E-Retailers: Una Revisión Bibliográfica Actualizada

“…Un aspecto que marca la diferencia notablemente entre ambos canales es la diferencia de coste entre uno y otro. Yu et al (2015) demuestran que el coste de la venta online puede ser menor que el offline por causa de las diferencias entre los costes de transporte y procesamiento. Dicha reducción del coste ha animado a ciertos proveedores a integrarse verticalmente tratando de alcanzar el mercado minorista directamente, llegando a convertirse en competidores de sus propios clientes.…”