Optimal operating strategy for a long-haul liner service route

This paper proposes an optimal operating strategy problem arising in liner shipping industry that aims to determine service frequency, containership fleet deployment plan, and sailing speed for a long-haul liner service route. The problem is formulated as a mixed-integer nonlinear programming model that cannot be solved efficiently by the existing solution algorithms. In view of some unique characteristics of the liner shipping operations, this paper proposes an efficient and exact branch-and-bound based ε-optimal algorithm. In particular, a mixed-integer nonlinear model is first developed for a given service frequency and ship type; two linearization techniques are subsequently presented to approximate this model with a mixed-integer linear program; and the branch-and-bound approach controls the approximation error below a specified tolerance. This paper further demonstrates that the branch-and-bound based ε-optimal algorithm obtains a globally optimal solution with the predetermined relative optimality tolerance ε in a finite number of iterations. The case study based on an existing long-haul liner service route shows the effectiveness and efficiency of the proposed solution method.