Coordination of a three-level supply chain with variable demand and order size dependent trade credit in healthcare industries

  • S. K. KaruppasamyEmail author
  • R. Uthayakumar
Original Article


In a traditional inventory model, the customer who purchases the goods is expected to pay the seller immediately. However, in many practical situations, the seller will give the customer a reasonable postpone period when the customer’s request amount surpasses a given limit. Now-a-days, the time-dependent demand plays a vital role in the healthcare industries. This paper, we generalized an order linked trade credit approach in three-level supply chain system, including the pharmaceutical manufacturer, the wholesaler and, the hospitals are involved. The pharmaceutical manufacturer gives a permissible delay period to the wholesaler and, the wholesaler likewise gives an order linked trade credit policy on the hospital. This entire investigation is examined in a pharmaceutical stock model for time-dependent production and time-dependent demand of healthcare industries. We outline the pharmaceutical model of three-level supply chain system with cost minimization to decide the optimal cycle time. Further, we decide the optimal cycle time, optimal order quantity and optimal payment time. The model is solved analytically by minimizing the total annual inventory cost of the centralized supply chain model. To delineate the pharmaceutical inventory models the numerical examples are provided. The sensitivity analysis is carried out for parameters and, the managerial implications are also obtained.


Pharmaceutical products Supply chain Time-dependent demand Trade credit 

Mathematics Subject Classification




We would like to sincerely thank the editor and three anonymous referees for their most valuable, constructive, innovative comments and suggestions that have encouraged the authors to make significant improvements in this paper. This research is supported by the Council of Scientific and Industrial Research, Government of India under the Scheme of CSIR Research Project with CSIR/No. 25(0218)/13/EMR-II/Dated 05.09.2013.


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Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2019

Authors and Affiliations

  1. 1.Department of MathematicsThe Gandhigram Rural Institute (Deemed to be University)GandhigramIndia

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