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Mathematical Problems in Engineering
Volume 2015, Article ID 404868, 13 pages
Research Article

A Two-Phase Heuristic Algorithm for the Common Frequency Routing Problem with Vehicle Type Choice in the Milk Run

College of Management & Economics, Tianjin University, 92 Weijin Road, Nankai District, Tianjin 300072, China

Received 12 August 2015; Revised 23 September 2015; Accepted 27 September 2015

Academic Editor: Yuri Vladimirovich Mikhlin

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.


High frequency and small lot size are characteristics of milk runs and are often used to implement the just-in-time (JIT) strategy in logistical systems. The common frequency problem, which simultaneously involves planning of the route and frequency, has been extensively researched in milk run systems. In addition, vehicle type choice in the milk run system also has a significant influence on the operating cost. Therefore, in this paper, we simultaneously consider vehicle routing planning, frequency planning, and vehicle type choice in order to optimize the sum of the cost of transportation, inventory, and dispatch. To this end, we develop a mathematical model to describe the common frequency problem with vehicle type choice. Since the problem is NP hard, we develop a two-phase heuristic algorithm to solve the model. More specifically, an initial satisfactory solution is first generated through a greedy heuristic algorithm to maximize the ratio of the superior arc frequency to the inferior arc frequency. Following this, a tabu search (TS) with limited search scope is used to improve the initial satisfactory solution. Numerical examples with different sizes establish the efficacy of our model and our proposed algorithm.