Bi-objective optimisation model and its exact solution method of profit and market share of novel repair-and-support ships based on game theory

Abstract

Novel repair-and-support ships could provide spot systemic maintenance and repair (MR) services for damaged offshore platforms on a deep sea, competing against shipyards. Therefore, to wisely decide the optimal strategy for the repair-and-support ship to enter the MR market of offshore platforms, comparative and competition analyses are made between the repair-and-support ship and shipyard when providing MR services for damaged offshore platforms on a deep sea. Thereafter, a bi-objective optimisation model of profit and market share of the repair-and-support ship based on game theory is formulated, considering the characteristics of the repair-and-support ship as a compound player and its mixed motives in competition. In this model, dispatching and repair prices of the repair-and-support ship and the repair price of the shipyard are considered decision variables. Therefore, focusing on the particularity of this model, a solution method combining pricing game and bi-objective optimisation is designed to obtain a continuous and exact Pareto front, and its proof is provided. A closed-form expression of the Pareto front for profit and market share of the repair-and-support ship is derived. This solution method is compared with a decomposition-based weighted sum method and augmented e-constraint method. The results show that this solution method has advantages in Pareto front size and running time. Finally, some management insights are obtained through numerical simulation. The research results of this study are conducive to the operator of the repair-and-support ship to make wiser decisions on the trade-off between profit and market share.