Sharif University of Technology Scientia Iranica 1026-3098 17 1 2010 06 01 A Heuristic Algorithm and a Lower Bound for the Two-Echelon Location-Routing Problem with Soft Time Window Constraints 3323 EN S.H. Zegordi Department of Industrial Engineering,Tarbiat Modares University E. Nikbakhsh Department of Industrial Engineering,Tarbiat Modares University Journal Article 2010 07 21 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. https://scientiairanica.sharif.edu/article_3323_914c872ce83884ecb171cbce20a7717b.pdf