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This paper presents a bi-objective model for the design and optimization of a sustainable hierarchical multi-modal hub network. The proposed model focuses on sustainability by considering economic, environmental, and social aspects of the decisions in a hierarchical network. A case of Turkish network for freight transportation is used to validate the proposed model. To solve the small-sized problems, the augmented epsilon constraint method version 2 (AUGMECON2) is applied. It can be inferred from the Pareto-optimal set obtained by AUGMECON2 that the effect of increasing the number of hubs after a threshold is marginal. The current contribution proposes two multi-objective genetic algorithms (NSGA-II and NRGA), which incorporate LP solving and Dijkstra algorithm. The results show the superiority of NRGA compared to NSGA-II in terms of solution time. Also, we present an alternative, more efficient formulation to the problem. Based on the alternative formulation, in addition to AUGMECON2, we use two exact methods, including Torabi and Hassini (TH) method and augmented weighted Tchebycheff procedure (AWTP), to find Pareto-optimal solutions for small, medium, and large-sized problems (including the case study). The performance of the proposed solution methods is measured using some multi-objective indicators. The results show the superiority of AUGMECON2. [ABSTRACT FROM AUTHOR]

In the vehicle routing problem with cross-docking (VRPCD), it is assumed that the selected suppliers and the quantity of the products purchased from each supplier are known. This paper presents an MILP model which incorporates supplier selection and order allocation into the VRPCD in a multi-cross-dock system minimising the total costs, including purchasing, transportation, cross-docking, inventory and early/tardy delivery penalty costs. The sensitivity of the model on the key parameters of the objective function is analysed and the supply decisions are evaluated when the coefficients of the distribution cost are changed. A two-stage solution algorithm (TSSA) is proposed and the results of the TSSA for small-sized instances are compared with the exact solutions. Finally, a large-sized real case of an urban freight transport is solved using the TSSA. [ABSTRACT FROM AUTHOR]