Open Journal Systems

Solving Hub Network Problem Using Genetic Algorithm

Mursyid Hasan Basri

Abstract


This paper addresses a network problem that described as follows. There are n ports that interact, and p of those will be designated as hubs. All hubs are fully interconnected. Each spoke will be allocated to only one of available hubs. Direct connection between two spokes is allowed only if they are allocated to the same hub. The latter is a distinct characteristic that differs it from pure hub-and-spoke system. In case of pure hub-and-spoke system, direct connection between two spokes is not allowed. The problem is where to locate hub ports and to which hub a spoke should be allocated so that total transportation cost is minimum. In the first model, there are some additional aspects are taken into consideration in order to achieve a better representation of the problem. The first, weekly service should be accomplished. Secondly, various vessel types should be considered. The last, a concept of inter-hub discount factor is introduced. Regarding the last aspect, it represents cost reduction factor at hub ports due to economies of scale. In practice, it is common that the cost rate for inter-hub movement is less than the cost rate for movement between hub and origin/destination. In this first model, inter-hub discount factor is assumed independent with amount of flows on inter-hub links (denoted as flow-independent discount policy). The results indicated that the patterns of enlargement of container ship size, to some degree, are similar with those in Kurokawa study. However, with regard to hub locations, the results have not represented the real practice. In the proposed model, unsatisfactory result on hub locations is addressed. One aspect that could possibly be improved to find better hub locations is inter-hub discount factor. Then inter-hub discount factor is assumed to depend on amount of inter-hub flows (denoted as flow-dependent discount policy). There are two discount functions examined in this paper. Both functions are characterized by non-linearity, so there is no guarantee to find the optimal solution. Moreover, it has generated a great number of variables. Therefore, a heuristic method is required to find near optimal solution with reasonable computation time. For this reason, a genetic algorithm (GA)-based procedure is proposed. The proposed procedure then is applied to the same problem as discussed in the basic model. The results indicated that there is significant improvement on hub locations. Flows are successfully consolidated to several big ports as expected. With regards to spoke allocations, however, spokes are not fairly allocated.

Keywords: Hub and Spoke Model; Marine Transportation; Genetic Algorithm


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