A Heuristic Algorithm and a Lower Bound for the Two-Echelon Location-Routing Problem with Soft Time Window Constraints

The location-routing problem is one of the most important location problems for designing integrated logistics systems. In the last three decades, various types of objective function and constraints have been considered for this problem. However, time window constraints have received little attention, despite their numerous real-life applications. In this article, a new 4-index mathematical model, an e cient and fast heuristic and a lower bound for the two-echelon location-routing problems with soft time window constraints are presented. The proposed heuristic tries to solve the problem via creating an initial solution, then improving it by searching on six neighborhoods of the solution, and using the Or-opt heuristic. At the end, computational results show the e ciency of the proposed heuristic, using the proposed lower bound.