Journal of Combinatorial Optimization

, Volume 35, Issue 1, pp 266–292 | Cite as

Closed-loop supply chain inventory management with recovery information of reusable containers

  • Tianji Yang
  • Chao Fu
  • Xinbao LiuEmail author
  • Jun Pei
  • Lin Liu
  • Panos M. Pardalos


This paper considers a closed-loop supply chain consisting of one-manufacturer and one-retailer. This supply chain provides single-kind products with reusable containers. The main purpose of this study is to explore and evaluate the value of recovery information captured by embedded sensors in the environment of internet of things. The recovery information of containers dynamically monitors recovery status and provides a reliable estimation of return quantity. The value of information is measured by the cost saving performances with full, partial or no recovery information. When the full or partial recovery information is available, the decisions are made based on the known quantities of the usable or total return flow. When no recovery information is available, the decisions are made based on the stationary distribution of the return flow. A periodic inventory model is built with uncertainties of forward and reverse flows. Then, a myopic order policy is proposed for the different levels of information utilization. Through the optimality analysis, we introduce a farsighted inventory control policy. Using the general result of Markov decision processes, the performance of heuristic policies is displayed. The farsighted policy performs better than the myopic policy. In addition, the farsighted policy helps to lessen the convex impact of utilization rate on the expected cost. Afterwards, we extend the model with the selective disposal behavior. A simulation study is used to depict sensitivity and robustness of the farsighted policy. Finally, we extend the simulation experiment with uniformly distributed in-use time for a more general applicability.


Closed-loop supply chain Reusable containers Internet of things Value of information 



Closed-loop supply chain


Radio frequency identification


Internet of things


Geographic information system


Returnable transportation items


“Event, agent, location, equipment, and thing” ontology model


Value of information




Markov decision process


Discrete-time Markov decision process


Virtual inventory of products


Expected cost


Value of full information


Value of partial information



This work was supported by the National Natural Science Foundation of China (Nos. 71231004, 71171071, 71521001), Anhui Province Natural Science Foundation (No. 1608085QG167), and the Fundamental Research Funds for the Central Universities (Nos. JZ2015HGBZ0116, JZ2015HGBZ0117). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026). In this paper, Tianji Yang is responsible for the numerical example and coding work. The detailed results attached with manuscript are uploaded to the submission system. Thanks for the valuable suggestions from the anonymous reviewers.

Supplementary material

10878_2015_9987_MOESM1_ESM.pdf (318 kb)
Supplementary material 1 (pdf 318 KB)


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Tianji Yang
    • 1
    • 2
  • Chao Fu
    • 1
    • 2
  • Xinbao Liu
    • 1
    • 2
    Email author
  • Jun Pei
    • 1
    • 2
  • Lin Liu
    • 1
    • 2
  • Panos M. Pardalos
    • 3
  1. 1.School of ManagementHefei University of TechnologyHefeiChina
  2. 2.Key Laboratory of Process Optimization and Intelligent Decision-making of Ministry of EducationHefeiChina
  3. 3.Department of Industrial and Systems Engineering, Center for Applied OptimizationUniversity of FloridaGainesvilleUSA

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