Closed-Form Solutions for the EPQ-Based Inventory Model for Exponentially Deteriorating Items Under Retailer Partial Trade Credit Policy in Supply Chain

  • Ali Akbar Shaikh
  • Leopoldo Eduardo Cárdenas-Barrón
  • Sunil Tiwari
Technical Note


Mahata (Expert Syst Appl 39(3):3537–3550, 2012) developed an economic production quantity (EPQ) inventory model for exponentially deteriorating items under permissible delay in payments considering that both demand and production are constant and known. This paper, applying well-known approximation mathematical expressions, derives closed-form formulas for the time at which the production ends, the cycle length and the total cost of inventory system. Moreover, this work presents a comparison of the solutions to the numerical examples by approximation closed-form formulas and Mahata (2012)’s method. The approximated method works properly because the percent of penalty is negligible less than 0.09%.


Inventory EPQ Partial trade credit Supply chain Exponentially deteriorating items 



We thank the editor and anonymous reviewers for their constructive feedback on earlier draft of this paper. The Tecnológico de Monterrey Research Group in Industrial Engineering and Numerical Methods 0822B01006 supported the first and second authors.


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Copyright information

© Springer (India) Private Ltd., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe University of BurdwanBurdwanIndia
  2. 2.School of Engineering and SciencesTecnológico de MonterreyMonterreyMexico
  3. 3.The Logistics Institute-Asia PacificNational University of SingaporeSingaporeSingapore

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