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It is necessary to implement green supply chains. But green development needs to be gradual and coexist with ordinary products in the market. This paper aims to study the green and ordinary product pricing and green decision-making under chain-to-chain competition.

This paper considers consumers' multiple preferences and takes two competitive supply chains with asymmetric channels as the research object. Through the construction of the game models involving different competitive situations, this paper studies the pricing, green decision-making and the supply chains' profits, and discusses the impact of consumer green preference, channel preference, green investment and competition on the decision-making and performance. Finally, this paper further studies the impact of the decision structure on the environmental and economic benefits of supply chains.

The results show that consumer green preference has an incentive effect on the green supply chain and also provides an opportunity for the regular supply chain to increase revenue. Specifically, consumers' preference for green online channels improves the product greenness, but its impact on the green retailer and regular supply chain depends on the green investment cost. Moreover, competition not only fosters product sustainability, but also improves supply chain performance. This paper also points out that the decentralization of the regular supply chain is conducive to the environmental attributes of the green product, while the environment-friendly structure of the green supply chain is different under different conditions. In addition, the profit of a supply chain under centralized decision is not always higher than that under decentralized decision.

The novelty of this paper is that it investigates the pricing of two heterogeneous alternative products and green decision-making for the green product under the competition between two supply chains with asymmetric channels, in which the green supply chain adopts dual channels and the regular supply chain adopts a single retail channel.

The purpose of this paper is to present a semi-analytical solution to one-dimensional (1D) consolidation induced by a constant inner point sink in viscoelastic saturated soils.

Based on the Kelvin–Voigt constitutive law and 1D consolidation equation of saturated soils subject to an inner sink, the analytical solutions of the effective stress, the pore pressure and the surface settlement in Laplace domain were derived by using Laplace transform. Then, the semi-analytical solutions of the pore pressure and the surface settlement in physical domain were obtained by implementing Laplace numerical inversion via Crump method.

As for the case of linear elasticity, it is shown that the simplified form of the presented solution in this study is the same as the available analytical solution in the literature. This to some degree depicts that the proposed solution in this paper is reliable. Finally, parameter studies were conducted to investigate the effects of the relevant parameters on the consolidation settlement of saturated soils. The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils.

The presented solution and method are of great benefit to provide deep insights into the 1D consolidation behavior of viscoelastic saturated soils. Consolidation behavior of viscoelastic saturated soils could be reasonably predicted by using the proposed solution with considering variations of both flux and depth because of inner point sink.