Maritime transport is now regarded as one of the main contributors to global climate change by virtue of its CO2 emissions. Meanwhile, slow steaming, i.e., slower ship speed, has become a common practice in the maritime industry so as to lower CO2 emissions and reduce bunker fuel consumption. The practice raised various operational decision issues in terms of shipping companies: how much ship speed is, how much to bunker the fuel, and at which port to bunker. In this context, this study addresses an operation problem in a shipping companies, which is the problem of determining the ship speed, bunkering ports, and bunkering amount at the ports over a given ship route to minimize the bunker fuel and ship time costs as well as the carbon tax which is a regulatory measure aiming at reducing CO2 emissions. The ship time cost is included in the problem because slow steaming increases transit times, which implies increased in-transit inventory costs in terms of shippers. We formulate the problem as a nonlinear lot-sizing model and suggest a Lagrangian heuristic to solve the problem. The performance of the heuristic algorithm is evaluated using the data obtained from reliable sources. Although the problem is an operational problem, the heuristic algorithm is used to address various strategic issues facing shipping companies, including the effects of bunker prices, carbon taxes, and ship time costs on the ship speed, bunkering amount and number of bunkering ports. For this, we conduct sensitivity analyses of these factors and finally discuss study findings.

1. Introduction
 2. Problem Description
 3. Solution Algorithm
 4. Numerical Studies
 5. Concluding Remarks
 Acknowledgement
 References

• Hwa-Joong Kim(Asia Pacific School of Logistics, Inha University) | 김화중
• Jae-Gon Kim(Department of Industrial and Management Engineering, Incheon National University) | 김재곤 Corresponding Author