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Dynamic Carbon Intensity Indicator (CII) Management in Stochastic Tramp Shipping Market

Hanyu Cheng, Liangqi Cheng, Xiwen Bai

TL;DR

The paper addresses long-term tramp fleet deployment under market uncertainty and the IMO Carbon Intensity Indicator ($CII$) by developing a $2$-stage stochastic programming model that jointly optimizes routing, cargo allocation, and sailing speed while enforcing annual $CII$ constraints. A novel heuristic accelerates solution finding and achieves a $5%$-level optimality gap, enabling practical planning under uncertainty. Key findings include the emergence of a $CII$ paradox under Supply-based $CII$ and the substantial value of incorporating future information (EVPI and VSS) for profitability and emissions planning. The work informs policy design and strategic fleet management by showing how regulatory design and information availability shape emission outcomes and economic performance in tramp shipping.

Abstract

In the maritime sector, tramp shipping companies manage fleets to maximize profit while navigating market uncertainties. The International Maritime Organization (IMO) recently introduced the Carbon Intensity Indicator (CII) to reduce greenhouse gas emissions, further complicating deployment decisions. This paper introduces a novel two-stage stochastic programming model for long-term fleet deployment under market uncertainty and CII regulation. It is the first to integrate key operational uncertainties such as fuel prices, freight rates, and cargo demand into a unified tactical planning framework under CII regulation, simultaneously optimizing routing, cargo allocation, and speed. Furthermore, we develop an novel efficient heuristic algorithm that reliably converges to solutions within a 5\% optimality gap, enabling practical decision-support under uncertainty. Numerical analysis highlights two key findings based on our model: (1) It uncovers the ``CII paradox,'' a critical counterintuitive phenomenon where the present Supply-based CII regulation may increase total emissions significantly and drastically reduce profits. This challenges the conventional wisdom that stricter carbon-intensity rules invariably reduce emissions. (2) It demonstrates the advantage of stochastic modeling, showing that accounting for future uncertainties significantly narrows the revenue gap with perfect-foresight solutions, thereby offering superior economic performance over deterministic approaches. Collectively, these results deepen the understanding of environmental regulation's operational impacts and pave the way for more effective and sustainable fleet management strategies.

Dynamic Carbon Intensity Indicator (CII) Management in Stochastic Tramp Shipping Market

TL;DR

The paper addresses long-term tramp fleet deployment under market uncertainty and the IMO Carbon Intensity Indicator () by developing a -stage stochastic programming model that jointly optimizes routing, cargo allocation, and sailing speed while enforcing annual constraints. A novel heuristic accelerates solution finding and achieves a -level optimality gap, enabling practical planning under uncertainty. Key findings include the emergence of a paradox under Supply-based and the substantial value of incorporating future information (EVPI and VSS) for profitability and emissions planning. The work informs policy design and strategic fleet management by showing how regulatory design and information availability shape emission outcomes and economic performance in tramp shipping.

Abstract

In the maritime sector, tramp shipping companies manage fleets to maximize profit while navigating market uncertainties. The International Maritime Organization (IMO) recently introduced the Carbon Intensity Indicator (CII) to reduce greenhouse gas emissions, further complicating deployment decisions. This paper introduces a novel two-stage stochastic programming model for long-term fleet deployment under market uncertainty and CII regulation. It is the first to integrate key operational uncertainties such as fuel prices, freight rates, and cargo demand into a unified tactical planning framework under CII regulation, simultaneously optimizing routing, cargo allocation, and speed. Furthermore, we develop an novel efficient heuristic algorithm that reliably converges to solutions within a 5\% optimality gap, enabling practical decision-support under uncertainty. Numerical analysis highlights two key findings based on our model: (1) It uncovers the ``CII paradox,'' a critical counterintuitive phenomenon where the present Supply-based CII regulation may increase total emissions significantly and drastically reduce profits. This challenges the conventional wisdom that stricter carbon-intensity rules invariably reduce emissions. (2) It demonstrates the advantage of stochastic modeling, showing that accounting for future uncertainties significantly narrows the revenue gap with perfect-foresight solutions, thereby offering superior economic performance over deterministic approaches. Collectively, these results deepen the understanding of environmental regulation's operational impacts and pave the way for more effective and sustainable fleet management strategies.

Paper Structure

This paper contains 27 sections, 2 theorems, 53 equations, 13 figures, 11 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature review
  3. Problem description
  4. Tramp shipping market operation
  5. Tactical planning in tramp shipping deployment problems
  6. Introduction of CII to fleet deployment
  7. Model formulation
  8. Model setup
  9. Mathematical formulation
  10. Solution method
  11. Numerical analysis
  12. Instance generation
  13. Algorithm performance
  14. Results under two CII forms
  15. Effect of stochastic scenarios
  16. ...and 12 more sections

Key Result

Proposition 1

Under Assumptions (A1)-(A4), if a ship is initially compliant with a Supply-based CII standard $\mathrm{CII}_0$ and the standard is tightened to $(1-p)\mathrm{CII}_0$ for some $p \in (0,1)$, then the ship can achieve compliance with the new standard by substituting port time for additional ballast s

Figures (13)

  • Figure 1: Results changing with CII standards
  • Figure 2: Illustration of the deployment problem
  • Figure 3: Route transition during P-1 and P-2
  • Figure 4: Difference of (a) average objective values and (b) running time of two solution methods under different trade lane quantities.
  • Figure 5: Normalized deviation between heuristic route search algorithm and exact solver ($N$=2, 3, 4 and 5)
  • ...and 8 more figures

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2: Non-negativity of EVPI and VSS
  • proof