Schedule design for liner services under vessel speed reduction incentive programs

Abstract

Proof. We apply the Karush-Kuhn-Tucker (KKT) conditions to analyze the properties of the optimal sailing speed for each leg of route r without considering the speed limit constraints (4).Let µ and ν l be the Lagrangian multipliers associated with constraints (3) and (5), respectively.

Promoting Liquefied Natural Gas (LNG) Bunkering for Maritime Transportation: Should Ports or Ships Be Subsidized?

“…In practice, governments and nonprofit organizations are the policy makers, but the shipping industry, including the ports and shipping companies, are the ones that determine the outcome of the regulations. Given the hierarchical structure, multi-level optimization models have been used in studies regarding various ship emission regulations, including Energy Efficiency Design Index (EEDI) [33,34], the Emission Control Areas (ECAs) [35], the Vessel Speed Reduction Incentive Program (VSRIP) [36,37], and the carbon tax [38,39].…”

A joint liner ship path, speed and deployment problem under emission reduction measures

“…In our instances, each VSRIP has one or two VSRZs, whose radii can be 20 or 40 nm and speed limit is 12 knots. The dockage refunds per ship visit for 20 nm and 40 nm VSRZs are generated randomly between 1,000 and 2,000 USD and between 2,000 and 3,000 USD, respectively (Zhuge et al, 2020).…”

“…Extensive recent studies have focused on ship routing, schedule design, and fleet deployment, such as Andersson et al (2015), Karsten et al (2018), Ng and Lin (2018), Tan et al (2018), Ng (2019), Wang et al (2019), Zhen et al (2019), Dong et al (2020a), andDong et al (2020b), most of which can also been seen in the surveys, including Meng et al (2014), Meng (2017), andZis et al (2020). Further, many research works on the shipping network design problem take into account one or two of the three emission reduction measures, i.e., sulfur emission regulations (Cariou et al, 2018;Zhen et al, 2018;Sheng et al, 2019;Zhao et al, 2019;Ma et al, 2020a,b;Reinhardt et al, 2020;Zhen et al, 2020b), carbon tax (Wang and Chen, 2017;Xin et al, 2019), and VSRIPs (Zhuge et al, 2020).…”

Optimal subsidy design for shore power usage in ship berthing operations

“…Economic subsidies are promising methods to promote the shore power usage, and they have been used by the government in other incentive programs under government policies. For example, Zhuge et al (2019Zhuge et al ( , 2020 presented nonlinear models for designing subsidy for ships that slow down within a certain distance from ports to reduce the air emissions near the port; Yi et al (2021) proposed an innovative bi-level programming model to design an optimal subsidy for promoting intermodal transport of prefabricated construction products. Hence, the introduction of subsidies that can make shore power more economical and increase the usage rate of existing shore power facilities is a pressing need (Chen et al, 2019;Radwan et al, 2019;Ship Technology, 2017).…”