Reza Rahmati

This article proposes a two-stage stochastic profit-maximizing hub location problem (HLP) with uncertain demand. Additionally, the model incorporates several carbon regulations, such as carbon tax policy (CTP), carbon cap-and-trade policy (CCTP), carbon cap policy (CCP), and carbon offset policy (COP). In the proposed models, an enhanced sample average approximation (ESAA) method was used to obtain a suitable number of scenarios. To cluster similar samples, k-means clustering and self-organizing map (SOM) clustering algorithms were embedded in the ESAA. The L-shaped algorithm was employed to solve the model inside the ESAA method more efficiently. The proposed models were analyzed using the well-known Australian Post (AP) data set. Computational experiments showed that all of the carbon regulations could reduce overall carbon emissions. Among carbon policies, CCTP could achieve better economic results for the transportation sector. The results also demonstrated that the SOM clustering algorithm within the ESAA method was superior to both k-means inside ESAA and classical SAA algorithms according to the %gap and standard deviation measures. In addition, the results showed that the L-shaped algorithm performed better than the commercial solver in large-scale instances.

In this paper, a two-stage robust optimisation is presented for an uncapacitated hub location problem in which demand is uncertain and the level of conservatism is controlled by an uncertainty budget. In the first stage, locations for establishing hub facilities were determined, and allocation decisions were made in the second stage. An accelerated Benders decomposition algorithm was used to solve the problem. Computational experiments showed better results in terms of number of iterations and computation time for Benders decomposition with Pareto-optimal cuts in comparison with the classical Benders decomposition algorithm. According to numerical analysis, it was concluded that increasing the uncertainty budget also increased total costs for more established hubs. To determine the uncertainty budget in an appropriate manner, a new expected aggregate function was introduced. The numerical studies demonstrated the usefulness of the proposed method in defining the appropriate uncertainty budget in the presence of uncertainty.