Effects of variable production rate on quality of products in a single-vendor multi-buyer supply chain management

  • Biswajit Sarkar
  • Arunava Majumder
  • Mitali Sarkar
  • Namhun KimEmail author
  • Mehran Ullah


A supply chain with multiple buyers leads to a hike in demand and for satisfying them, a high standard production manufacturing system is required. A predetermined production rate in a supply chain model with economic production lot size is quite inappropriate for this type of situation as production rate can be changed in some cases to fulfill demand of customers. Rate of production has an impact in maintaining process quality. Manufacturing quality deteriorates with an increasing rate of production. In this context, this paper develops a single-vendor multi-buyer supply chain model with variable production rate and imperfect quality of products. The unit production cost is considered as a function of the production rate. Three different production functions are established to relate process quality and production rate. Due to huge demand by multi-buyer, the lead time demand is considered as random variable and it follows a normal distribution. The objective of this study is to analyze how the flexibility of the production rate affects the product quality as well as entire supply chain cost under a single-setup multiple-delivery policy. A classical optimization technique is employed to obtain the global optimum solution. An illustrative algorithm is established to obtain the numerical results. Numerical examples and graphical interpretations, and sensitivity analysis are given to illustrate the model. Numerical study proves that the variable production rate effects a lot on the total cost of supply chain model.


Supply chain management Flexible production rate Quality management Controllable lead time Single-setup-multi-delivery policy 


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This work was supported by the ‘Development of 3D Printing-based Smart Manufacturing Core Technology’ Research Fund (1.180032.01) of UNIST (Ulsan National Institute of Science & Technology).


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Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Biswajit Sarkar
    • 1
  • Arunava Majumder
    • 2
  • Mitali Sarkar
    • 1
  • Namhun Kim
    • 3
    Email author
  • Mehran Ullah
    • 1
  1. 1.Production Engineering & Operations Management Laboratory, Department of Industrial & Management EngineeringHanyang UniversityAnsan Gyeonggi-doSouth Korea
  2. 2.Department of Mathematics, School of Chemical Engineering and Physical SciencesLovely Professional UniversityPhagwaraIndia
  3. 3.School of Mechanical, Aerospace and Nuclear EngineeringUlsan National Institute of Science & TechnologyUlsanSouth Korea

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