Fleet Sizing and Scheduling Model of Container Carriers between Two Ports

by Elyamak, Alaa Mustapha

Globalization and containerization have changed the shipping industry and carriers are challenged to reshape their operational planning in order to maintain their market share. The objective of this paper is to formulate a model to determine the optimal fleet size and sailing frequency that minimizes total shipping and inventory (wait) costs for a container shipping company. The proposed model assumes an arrival process that follows a Poisson rate. We first consider unlimited ship capacity and propose a solution to determine the required fleet size and the optimal sailing frequency. We then extend the work to consider limited ship capacity. Furthermore, we introduce a cost component associated with outsourcing shipments due to insufficient capacity. The outsourced shipment is utilized when the number of containers at a port exceeds the available capacity. In the general case, a closed form solution could not be derived. Therefore, a simulation study is undertaken to analyze optimal fleet sizing, scheduling, and outsourcing policies under varying paramaters. Our study investigates the trade-off between building capacity and outsourcing in the context of cargo shipment. The model proves to be a reliable tool to determine optimal delay time at ports and optimal fleet size.