The impact of loading restrictions on the two-echelon location routing problem

Abstract

The two-echelon location routing problem (2E-LRP) arises in freight distribution when goods available at different origins are delivered to their respective destinations via intermediate facilities. The literature concerning the 2E-LRP considers freight capacities of vehicles to be scalars, while customer demands are additive volumes of individual items. However, ignoring the real dimensions of items and vehicles can lead to infeasible load plans in practice. Further investigation is thus required to study the impact of realistic loading restrictions on the 2E-LRP, algorithms for the problem and the quality of the solutions produced by those algorithms. This paper introduces a generalized 2E-LRP with two-dimensional loading restrictions (2E-LRP2L). To investigate how exactly one should handle these restrictions we introduce a heuristic optimization method combined with different loading strategies and evaluate their performance on instances derived from real-world data. Given that we are introducing a new problem, the quality of our heuristic is assessed by comparing it against state-of-the-art 2E-LRP methods on benchmark instances. The results indicate that the proposed method is highly competitive, finding most best-known solutions as well as providing some new ones.