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The economic ship speed under time charter contract: a cash flow approach

The economic ship speed under time charter contract: a cash flow approach
The economic ship speed under time charter contract: a cash flow approach
Various deterministic models for economic ship speed optimisation exist in the literature, but none considered the time charter contract, and in particular the influence of the redelivery time. This paper studies the economic optimal speed of a ship on a (time) charter contract through the development of an Operational Research (OR) optimisation model. The ship charterer’s objective is to maximise the Net Present Value (NPV) of a cash-flow function of the ship’s activities over a relevant future horizon H, where H can be interpreted as any possible day within the redelivery time window as specified in the time charter clause. We develop a general time charter contract model PM(H), and three special cases P1, P∞ and PM(H → ∞), each model mapping onto different contractual contexts, and present algorithms to each of these models for finding optimal ship speeds for any journey structure. While ships on time charter contracts may travel to any series of ports during the charter contract, examining the models’ behaviour when the ship repeatedly executes a roundtrip journey allows us to reach some important general insights about the impact of contract type for any journey structure. In particular, economic speeds in PM(H) follow a very different pattern than those in the classic models from the literature, as well as in the recent class of NPV models P(n, m,Go) from Ge et al. (2021). We prove that P1 and P∞ map quite generally to the classes P(1, n, 0) and P(∞, n,−), respectively, while P(n, m, 0) shows behaviour in approximation equal to the special case PM(H → ∞). We prove that two main strands of speed optimisation models from the literature, which did not consider the contract type nor used the NPV approach, show equivalence under mild conditions to P1 and P∞, respectively. These results facilitate matching models to contract types. None of these models, however, matches the general time charter contract model PM(H) introduced in this paper. In general, the paper demonstrates how optimal economic speed is dependent on the (time) charter contract type, and that this should thus be reflected in the speed optimisation model developed.
Bulk Cargo Shipping, Charter Contract, Maritime speed optimisation, Tanker Shipping, Bulk cargo shipping, Charter contract, Tanker shipping
1366-5545
Beullens, Patrick
893ad2e2-0617-47d6-910b-3d5f81964a9c
Ge, Fangsheng
631f19cf-c813-4291-bea0-a41542fe36e9
Hudson, Dominic
3814e08b-1993-4e78-b5a4-2598c40af8e7
Beullens, Patrick
893ad2e2-0617-47d6-910b-3d5f81964a9c
Ge, Fangsheng
631f19cf-c813-4291-bea0-a41542fe36e9
Hudson, Dominic
3814e08b-1993-4e78-b5a4-2598c40af8e7

Beullens, Patrick, Ge, Fangsheng and Hudson, Dominic (2023) The economic ship speed under time charter contract: a cash flow approach. Transportation Research Part E: Logistics and Transportation Review, 170, [102996]. (doi:10.1016/j.tre.2022.102996).

Record type: Article

Abstract

Various deterministic models for economic ship speed optimisation exist in the literature, but none considered the time charter contract, and in particular the influence of the redelivery time. This paper studies the economic optimal speed of a ship on a (time) charter contract through the development of an Operational Research (OR) optimisation model. The ship charterer’s objective is to maximise the Net Present Value (NPV) of a cash-flow function of the ship’s activities over a relevant future horizon H, where H can be interpreted as any possible day within the redelivery time window as specified in the time charter clause. We develop a general time charter contract model PM(H), and three special cases P1, P∞ and PM(H → ∞), each model mapping onto different contractual contexts, and present algorithms to each of these models for finding optimal ship speeds for any journey structure. While ships on time charter contracts may travel to any series of ports during the charter contract, examining the models’ behaviour when the ship repeatedly executes a roundtrip journey allows us to reach some important general insights about the impact of contract type for any journey structure. In particular, economic speeds in PM(H) follow a very different pattern than those in the classic models from the literature, as well as in the recent class of NPV models P(n, m,Go) from Ge et al. (2021). We prove that P1 and P∞ map quite generally to the classes P(1, n, 0) and P(∞, n,−), respectively, while P(n, m, 0) shows behaviour in approximation equal to the special case PM(H → ∞). We prove that two main strands of speed optimisation models from the literature, which did not consider the contract type nor used the NPV approach, show equivalence under mild conditions to P1 and P∞, respectively. These results facilitate matching models to contract types. None of these models, however, matches the general time charter contract model PM(H) introduced in this paper. In general, the paper demonstrates how optimal economic speed is dependent on the (time) charter contract type, and that this should thus be reflected in the speed optimisation model developed.

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More information

Accepted/In Press date: 17 December 2022
e-pub ahead of print date: 11 January 2023
Published date: 1 February 2023
Additional Information: Funding Information: Dr. Fangsheng Ge is supported by a PhD scholarship from the Southampton Marine and Maritime Institute (SMMI), United Kingdom . We thank Shell International Trading and Shipping Company Ltd for constructive feedback during the development of our modelling efforts. Publisher Copyright: © 2022 The Authors
Keywords: Bulk Cargo Shipping, Charter Contract, Maritime speed optimisation, Tanker Shipping, Bulk cargo shipping, Charter contract, Tanker shipping

Identifiers

Local EPrints ID: 473971
URI: http://eprints.soton.ac.uk/id/eprint/473971
ISSN: 1366-5545
PURE UUID: 705a20fc-3a9e-43c9-af17-a8b780be2032
ORCID for Patrick Beullens: ORCID iD orcid.org/0000-0001-6156-3550
ORCID for Fangsheng Ge: ORCID iD orcid.org/0000-0003-4344-0121
ORCID for Dominic Hudson: ORCID iD orcid.org/0000-0002-2012-6255

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Date deposited: 07 Feb 2023 17:31
Last modified: 17 Mar 2024 04:11

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