Joint Design and Pricing of Intermodal Port - Hinterland Network Services : Considering Economies of Scale and Service Time Constraints

Maritime container terminal operating companies have extended their role from node operators to that of multimodal transport network operators. They have extended the gates of their seaport terminals to the gates of inland terminals in their network by means of frequent services of high capacity transport modes such as river vessels (barges) and trains. These network operators face the following three interrelated decisions: (1) determine which inland terminals act as extended gates of the seaport terminal, (2) determine capacities of the corridors, i.e. capacity of the transport means and frequency of service, and (3) set the prices for the transport services on the network. We propose a bi-level programming model to jointly design and price extended gate network services for profit maximization. The network operator does so while anticipating the decisions of the customers who choose minimum cost paths to their final destinations, and who always have the option to choose direct trucking offered by the competition. The model in this paper extends existing bi-level models in a multimodal format by including service time constraints and economies of scale. Considering the special structure of our problem, we propose a heuristic that provides near optimal solutions to our problem in substantially less time. Through experimental results in some realistic instances, we study optimal network designs while comparing sea port-to-door and sea port to inland port services and situations where transit time requirements do and do not apply. Our results show that when demand is relatively low, there are significant differences in the optimal network design for port-to-door versus port-to-port services. In the case of port-to-door services, the prices of services are determined by the competition and not by the design of the network, so the network is designed against minimum costs, and economies of scale are achieved by consolidating flows through a limited number of extended gates. The case of port-to-port services is different, i.e. revenues are enhanced not so much by reducing costs through the exploitation of economies of scale, but by exploiting the possibilities to dedicate extended gates to market segments for which the competition leaves room for higher port-to-port tariffs