Integrated and sequential algorithms for the robust two-echelon location-routing problem under demand uncertainty

This paper addresses the two-echelon capacitated location-routing problem (2E-CLRP) when faced with demand uncertainty. We assume that the customer’s demands at the second echelon are uncertain and design a two-echelon distribution network where open satellites, served from a single depot, have sufficient capacities to handle the variation in demand. At the same time, the planned routes must remain feasible for all values of demand within an uncertainty set. We propose a robust counterpart for an integrated model of the 2E-CLRP and solve it using an adaptive large neighborhood search heuristic and a branch-and-cut algorithm. We also design four non-integrated solution approaches based on the robust counterparts for the 2E-CLRP subproblems, including the vehicle routing problem (VRP), the facility location problem (FLP), the location-routing problem (LRP), and the two-echelon FLP (2E-FLP). The importance of an integrated approach to 2E-CLRP is demonstrated by comparing it to non-integrated approaches. Results show that early integration of location and routing decisions leads to better location and total costs. We also evaluate the price of robustness and the trade-off between conservative and riskier robust solutions using a Monte Carlo simulation. We perform a series of computational experiments to validate the proposed algorithms using benchmark instances for the deterministic 2E-CLRP, LRP and robust VRP.