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Optimization of Extended Hub-and-spoke Regional Port Transportation Networks with Interval Cost Parameters Wang Chuanxu School of Economy and Management, Shanghai Maritime University, P.R.China, 200135 Abstract: In regional port transportation networks, the ports are connected by direct transports or via a transshipment port. This has led to the formation of hub-and-spoke networks in regional port transportation industry. Cargoes from original ports are usually consolidated at hub port and shipped to different destination ports. Hub-and-spoke transportation can be classified into two types: pure and extended. The pure hub-and-spoke transportation network is characterized by transshipment in which direct transport between ports is excluded and all cargoes have to be transported through a hub port. The extended hub-and–spoke transportation network consists of direct transportation between ports and transshipment via the hub port. Based on extended hub-and-spoke regional port transportation network, a model is introduced for regional port transportation network optimization problem where the cost coefficients of the objective functions are expressed as interval values. The proposed model aims at minimizing the total costs including the transportation cost between two ports and handling cost occurring at ports. Meanwhile it optimizes the following factors: cargo transportation volume and corresponding transportation capacity via a hub port from an original port to a destination port, cargo transportation volume and corresponding transportation capacity directly from an original port to a destination port. Based on preference relations between intervals, the proposed model can be solved by transforming it into an equivalent deterministic two-objective linear programming model that can be solved by goal programming or fuzzy programming. At last, a numerical example is given to demonstrate the effectiveness of the proposed model. Key Words: Hub-and-spoke, Optimization, Port transportation network

1 Introduction
In regional port transportation networks, the sizes and types of ships calling at every port are different because individual port’s natural condition and capacity are different. The route selection is important in regional port transportation network optimization. The port condition and economy of scale in ship transportation should be considered to select the routes from original ports to destination ports. In regional port transportation networks, the ports are connected by direct transports or via a transshipment port. This has led to the formation of hub-and-spoke networks in regional port transportation industry. Cargoes from original ports are usually consolidated at hub port and shipped to

Hub port

Port

Port

Figure1 Structure of an extended hub-and-spoke system

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troP

troP troP

Port

different destination ports. Hub-and-spoke transportation can be classified into two types: pure and extended. The pure hub-and-spoke transportation network is characterized by transshipment in which direct transport between ports is excluded and all cargoes have to be transported through a hub port. The extended hub-and–spoke transportation network consists of direct transportation between ports and transshipment via the hub port (Fig. 1)[1]. In this paper, based on extended hub-and-spoke port transportation system, a decision model is developed to determine the following factors: cargo transportation volume and corresponding transportation capacity via a hub port from an original port to a destination port, cargo transportation volume and corresponding transportation capacity directly from an original port to a destination port. The decision problem of hub-and-spoke systems has received many attentions in academic literature. Some researchers solved it as the location –allocation problem that determines locations of hubs and a...