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Mathematical Problems in Engineering
Volume 2015, Article ID 428925, 22 pages
Research Article

A Two-Stage Simulated Annealing Algorithm for the Many-to-Many Milk-Run Routing Problem with Pipeline Inventory Cost

1College of Management & Economics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, China
2Simon Business School, University of Rochester, 304 University Park, Rochester, NY 14620, USA

Received 20 March 2015; Revised 21 July 2015; Accepted 22 July 2015

Academic Editor: Antonios Tsourdos

Copyright © 2015 Yu Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In recent years, logistics systems with multiple suppliers and plants in neighboring regions have been flourishing worldwide. However, high logistics costs remain a problem for such systems due to lack of information sharing and cooperation. This paper proposes an extended mathematical model that minimizes transportation and pipeline inventory costs via the many-to-many Milk-run routing mode. Because the problem is NP hard, a two-stage heuristic algorithm is developed by comprehensively considering its characteristics. More specifically, an initial satisfactory solution is generated in the first stage through a greedy heuristic algorithm to minimize the total number of vehicle service nodes and the best insertion heuristic algorithm to determine each vehicle’s route. Then, a simulated annealing algorithm (SA) with limited search scope is used to improve the initial satisfactory solution. Thirty numerical examples are employed to test the proposed algorithms. The experiment results demonstrate the effectiveness of this algorithm. Further, the superiority of the many-to-many transportation mode over other modes is demonstrated via two case studies.