Profit-oriented fixed-charge network design with elastic demand

This paper extends classic fixed-charge multicommodity network design by explicitly considering demand elasticity with respect to routing cost in a profit maximization context with service commitments. Demand quantity is determined by a spatial interaction model that accounts for routing costs, thus capturing the trade-off between infrastructure investment, efficient routing, and increased revenue. A numerical example is presented to demonstrate the added value of incorporating demand elasticity in profit-oriented network design problems. An arc-based and a path-based formulation, both with the flexibility of incorporating O/D pair selection by means of network and data transformations, are presented. The arc-based formulation is solved using state-of-the-art global optimization software while the path-based formulation serves as the basis for a hybrid matheuristic that combines a slope scaling metaheuristic and column generation. Computational experience shows the hybrid matheuristic to be superior in terms of solution quality and computation time.