A multi-objective optimization model for the problems of sustainable collaborative hub location and cost sharing

This paper addresses the problems of distribution network design and gain sharing in a collaborative context. We propose mathematical models to compare the performance of three scenarios based on several sustainability indicators: logistics costs, CO₂ emissions, created job opportunities, noise level, and accident risk. The scenarios assume multi-period transportation planning, performed by a heterogeneous fleet of vehicles. Mathematical models are used to determine the number of hubs, their capacities, and their locations, as well as the links between network nodes, the quantities transported, the quantities delayed, the inventory level, and the number and type of vehicles used in each period. Single-objective optimization is performed in an exact manner for small instances, while the genetic algorithm is used to solve large instances. Multi-objective resolution is performed using the ε-constraint method for small instances and the non-dominated sorting genetic algorithm II for large instances. We use a distribution network located in France for our numerical experiments. The costs of collaboration were shared by three approaches: egalitarian approach, volume method, and Shapley value. Experimental results and sensitivity analysis reveal some interesting findings: (1) it is always beneficial to design a collaborative distribution network; (2) relaxing delivery times and increasing the number of available vehicles further improve collaborative performance; and (3) cooperative game-theoretic approaches are most appropriate for sharing costs.