A polynomial-time algorithm for sailing speed optimization with containership resource sharing

•We formulate the containership sailing speed optimization problem as a mathematical programming model from the perspective of shipping lines.•We develop a polynomial-time algorithm to solve the problem based on bi-section search methods.•We test our algorithm with numerical experiments.

The sailing speed optimization problem aims to determine the optimal cruising speeds of ships by balancing the number of ships required on services, the fuel consumption, and the level of service provided for customers. The level of service can be incorporated into a sailing speed optimization model from the perspective of supply chain management or from the perspective of shipping lines. We design a polynomial-time algorithm workable to solve the two models based on bi-section search methods. The novelties of the algorithm include constructing a new parameter on which the bi-section search will be executed and deriving a near-optimal solution by taking advantage of the problem structure. We also provide theoretical results that guarantee the validity of the polynomial-time algorithm.