Journal of Global Optimization

, Volume 68, Issue 4, pp 851–878 | Cite as

A stochastic production planning problem in hybrid manufacturing and remanufacturing systems with resource capacity planning

  • Chang Fang
  • Xinbao Liu
  • Panos M. Pardalos
  • Jianyu Long
  • Jun Pei
  • Chao Zuo


Hybrid manufacturing and remanufacturing systems have become a topic of considerable interest in the advanced manufacturing industry due in part to the profit and cost saving by reusing remaufacturable parts in the end-of-use products. In this paper, we investigate a production planning problem in such a hybrid system with the integration of resource capacity planning that is shared by both manufacturing and remanufacturing processes. Due to the uncertain nature in practice, both new and remanufactured product demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the historical data, we formulate the stochastic aggregate production planning problem as a mixed integer linear programming (MILP) model. Based on the Lagrangian relaxation (LR) technique, the MILP model is decomposed into four sets of sub-problems. For these sub-problems, four heuristic procedures are developed, respectively. Then, a LR based heuristic for the main problem is proposed and further tested on a large set of problem instances. The results show that the algorithm generates solutions very close to optimums in an acceptable time. At last, the impact of demands uncertainty on the solution is analyzed by the sensitivity analysis on a number of scenarios.


Stochastic production planning Hybrid manufacturing and remanufacturing system Scenario based approach Resource capacity planning Lagrangian relaxation MILP 



This work is supported by the Social Sciences Foundation of Anhui Province (No. AHSKQ2016D28), the First Major Project in Anhui Normal University (FRZD201302), the Public Projects of Zhejiang Province (No. 2017C31069), the Natural Science Foundation of Anhui Province (No. 1608085QG167, 1608085MG152), the National Natural Science Foundation of China (No. 71601065, 71231004, 71501058) and the Humanities and Social Sciences Foundation of the Chinese Ministry of Education (No. 15YJC630097). Panos M. Pardalos is partially supported by the project of “Distinguished International Professor by the Chinese Ministry of Education” (MS2014HFGY026).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Chang Fang
    • 1
    • 2
  • Xinbao Liu
    • 4
  • Panos M. Pardalos
    • 2
  • Jianyu Long
    • 2
    • 3
  • Jun Pei
    • 2
    • 4
  • Chao Zuo
    • 5
  1. 1.School of Economics and ManagementAnhui Normal UniversityWuhuChina
  2. 2.Center for Applied Optimization, Department of Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  3. 3.Department of Metallurgical Engineering, School of Materials Science and EngineeringChongqing UniversityChongqingChina
  4. 4.School of ManagementHefei University of TechnologyHefeiChina
  5. 5.Department of Logistics Management and EngineeringZhejiang Gongshang UniversityHangzhouChina

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