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


Department of Industrial Engineering,Tarbiat Modares University


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
ecient 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 eciency of the proposed heuristic, using
the proposed lower bound.