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Mathematical Problems in Engineering
Volume 2014, Article ID 537409, 14 pages
Research Article

Integrated Inventory Routing Problem with Quality Time Windows and Loading Cost for Deteriorating Items under Discrete Time

Tao Jia,1,2 Xiaofan Li,1,2 Nengmin Wang,1,2 and Ran Li1,2

1School of Management, Xi’an JiaoTong University, No. 28 Xianning Road, Xi’an, Shaanxi 710049, China
2The Key Lab of the Ministry of Education for Process Control and Efficiency Engineering, No. 28 Xianning Road, Xi’an, Shaanxi 710049, China

Received 21 September 2013; Revised 26 November 2013; Accepted 26 November 2013; Published 29 January 2014

Academic Editor: Yunqiang Yin

Copyright © 2014 Tao Jia 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.


We investigate an integrated inventory routing problem (IRP) in which one supplier with limited production capacity distributes a single item to a set of retailers using homogeneous vehicles. In the objective function we consider a loading cost which is often neglected in previous research. Considering the deterioration in the products, we set a soft time window during the transportation stage and a hard time window during the sales stage, and to prevent jams and waiting cost, the time interval of two successive vehicles returning to the supplier’s facilities is required not to be overly short. Combining all of these factors, a two-echelon supply chain mixed integer programming model under discrete time is proposed, and a two-phase algorithm is developed. The first phase uses tabu search to obtain the retailers’ ordering matrix. The second phase is to generate production scheduling and distribution routing, adopting a saving algorithm and a neighbourhood search, respectively. Computational experiments are conducted to illustrate the effectiveness of the proposed model and algorithm.