The direct and cross effects in a supply chain with consumers sensitive to both carbon emissions and delivery time

In this paper, we study a supply chain consisting of an upstream manufacturer who faces carbon tax regulation from the government, and a downstream retailer who sells the product to consumers via an online channel. The consumers are sensitive to the product's carbon emission as well as its delivery time. Building Stackelberg game models, we explore how consumers’ dual sensitivities to carbon emission and delivery time impact the two firms’ optimal decisions and profits. Our major findings are as follow. First, as expected, there are “direct effects” of consumer's dual sensitivities: the retailer's optimal delivery time decreases as consumers’ sensitivity to delivery time increases; the manufacturer's optimal carbon emission reduction effort level increases as consumers’ sensitivity to carbon emissions increases. Second and more importantly, there are distinct “cross effects” of consumers’ dual sensitivities: when the sensitivity to delivery time increases, the manufacturer's optimal carbon emission reduction effort level first decreases and then increases; if carbon tax rate increases, the retailer's optimal delivery time first increases and then decreases; if the sensitivity to the product's carbon emissions increases, the retailer's optimal delivery time always decreases. To address the potential free riding problem due to these “cross effects”, we propose a two-way cost sharing contract for the supply chain, where each firm shares a certain proportion of the other's investment cost. We show that this contract can achieve Pareto improvement for the supply chain.