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The purpose of this paper is to present a stable and efficient numerical technique based on modified trigonometric cubic B-spline functions for solving the time-fractional diffusion equation (TFDE). The TFDE has numerous applications to model many real objects and processes.

The time-fractional derivative is used in the Caputo sense. A modification is made in trigonometric cubic B-spline (TCB) functions for handling the Dirichlet boundary conditions. The modified TCB functions have been used to discretize the space derivatives. The stability of the technique is also discussed.

The obtained results are compared with those reported earlier showing that the present technique gives highly accurate results. The stability analysis shows that the method is unconditionally stable. Furthermore, this technique is efficient and requires less storage.

The current work is novel for solving TFDE. This technique is unconditionally stable and gives better results than existing results (Ford et al., 2011; Sayevand et al., 2016; Ghanbari and Atangana, 2020).

The purpose of this paper is to improve the tactical planning of the stakeholders of the midstream liquefied natural gas (LNG) supply chain, using an optimisation approach. The results can contribute to enhance the proactivity on significant investment decisions.

A decision support tool (DST) is proposed to minimise the operational cost of a fleet of vessels. Mixed integer linear programming (MILP) used to perform contract assignment combined with a genetic algorithm solution are the foundations of the DST. The aforementioned methods present a formulation of the maritime transportation problem from the scope of tramp shipping companies.

The validation of the DST through a realistic case study illustrates its potential in generating quantitative data about the cost of the midstream LNG supply chain and the annual operations schedule for a fleet of LNG vessels.

The LNG transportation scenarios included assumptions, which were required for resource reasons, such as omission of stochasticity. Notwithstanding the assumptions made, it is to the authors’ belief that the paper meets its objectives as described above.

Potential practitioners may exploit the results to make informed decisions on the operation of LNG vessels, charter rate quotes and/or redeployment of existing fleet.

The research has a novel approach as it combines the creation of practical management tool, with a comprehensive mathematical modelling, for the midstream LNG supply chain. Quantifying future fleet costs is an alternative approach, which may improve the planning procedure of a tramp shipping company.