A multi-commodity two-Echelon capacitated vehicle routing problem with time windows: Model formulations and solution approach - Dellaert, Nico; Van Woensel, Tom; Crainic, Teodor Gabriel; Dashty Saridarq, Fardin (Computers & operations research, 2021)
•The MC-2E-VRPTW model formulations involve a combined arc-path based model.•We obtain better lower bound estimates and new capacity constraints in the 2-path formulation.•The numerical evaluation demonstrates the power of the developed models and solution methods. This paper studies the multi-commodity two-echelon capacitated vehicle routing problem with time windows. Specifically, we take customer-specific origin to destination, non-substitutable demands into account. The main components are: (i) first echelon tours, (ii) second echelon tours and (iii) movement of commodities from first echelon to second echelon, considering route connection and synchronization. Exploiting the structure of the problem, we propose a decomposition scheme which decouples the first and second echelon routing problems, by deleting the third component, and re-couples them by using constraints ensuring movement of commodities between the two echelons. Based on this decomposition, we present (i) a number of model formulations for the MC-2E-VRPTW, and (ii) develop an exact solution approach for this real-life problem. A computational study on a comprehensive set of instances shows the effectiveness in terms of computational effort and solution quality.