Mathematical Modelling for Hub and Spoke Technology

In this chapter we speak about the differences and characteristics of the 6 proposed single-assignment models.

In the model number 1 the distances will be calculated by the triangle of inequality and this is a difference among this model and all the other 5 models. There are no congestion cost like in the model number 3 and there is just one optimized criterion while in the model number 4 there are two optimization criteria. The model number 1 considers as solution the genetic algorithm method like in the model number 6.

In the model number 2 there are factors for collect, transfer among hubs and distribution to the final customer and this is a difference between this model and the model number 1. In this model we do not have the congestion cost like the model number 3 and we have just one optimized criterion while in the model number 4 there are two optimized criteria. The solution of the model number 2 will be found thanks to a hybrid heuristic solution while in the fifth and model number 6 will be used the genetic algorithm.

In the model number 3 there are congestion cost and the delay function of traffic flow of goods at the places this is the main difference among this model and all the other 5 models. This model has also just one optimized criterion as difference with the model number 4 in which there are two optimized criteria. We do not consider as solution the genetic algorithm like in the models number 5 and 6.

In the model number 4 two optimized criteria were used and this is the difference among this model and all the other 5 models. The first optimized criterion is the minimization of the total transportation cost and the second one is minimization of the service time of hubs. Other difference among this model and the other 5 models is that in this model there is fixed time to start the service at the hub, as further difference between this model and the model number 3 we do not have in this model the congestion cost.

The model number 5 does not consider the triangle of inequality for calculating distances so this is one difference between this model and the model number 1. The solution is possible thanks to genetic algorithm and this is the difference between this model and the model number 2. The model number 5 does not consider the congestion cost like we have in the model number 3. This model has just one optimized criterion and this is the difference between this model and the model number 4. In the model number 5 does not optimize the fixed cost for building hubs and this is the difference between this model and the model number 6.

The model number 6 is different from the first four models for the same reasons the model number 5 is different from them too. The main difference between this model and the 5 other model is that this model optimizes the fixed cost for building hubs.