Liner ship route capacity utilization estimation with a bounded polyhedral container shipment demand pattern

This paper aims to estimate capacity utilization of a liner ship route with a bounded polyhedral container shipment demand pattern, arising in the liner container shipping industry. The proposed maximum and minimum liner ship route capacity utilization problems are formulated as a linear programming model and a min–max model, respectively. We examine two fundamental properties of the min–max model. These two nice properties enable us to develop two ε-optimal global optimization algorithms for solving the min–max model, which find a globally ε-optimal solution by iteratively cutting off the bounded polyhedral container shipment demand set with a cut. The latter algorithm overcomes non-convexity of the remaining feasible demand set generated by the former algorithm via a novel hyperplane cut. Each hyperplane cut can assure that the current vertex of the polyhedral demand set is cut off, whereas solutions that may improve the current one by more than a factor of ε are retained. Extensive numerical experiments for problems larger than those encountered in real applications demonstrate the computational efficacy of the latter algorithm.