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The algorithm for the optimal cycle time and pricing decisions for an integrated inventory system with order-size dependent trade credit in supply chain management

Author

Listed:
  • Chung, Kun-Jen
  • Liao, Jui-Jung
  • Ting, Pin-Shou
  • Lin, Shy-Der
  • Srivastava, H.M.

Abstract

A given inventory problem consists of two parts: (1) the modeling part and (2) the solution procedure part. The modeling part can provide insight into the solution of the inventory problem and the solution procedure part involves the implementation of the inventory model. Both the modeling part and the solution procedure part of the inventory problem are equally important. Recently, Ouyang et al. [17] developed an integrated inventory model with a price-sensitive demand rate and determined both the economic lot size of the buyer’s ordering and the supplier’s production batch in order to maximize the total profit per unit time. Basically, their modeling is correct and interesting. They developed an algorithm based upon the first-order condition and the second-order condition to locate the optimal solution. However, the fundamentals of mathematics and the numerical examples which are considered in this paper illustrate that their algorithm based upon the first-order condition and the second-order condition to locate the optimal solution has several shortcomings. These shortcomings are shown here to influence the accuracy of the implementation of the inventory model. Since there exist reasons and motivations to present the correct solution procedures to the targeted readers, the main purpose of this paper is to adopt the rigorous methods of mathematical analysis in order to develop the complete solution procedures to locate the optimal solution for removing shortcomings in the earlier investigation by Ouyang et al. [17].

Suggested Citation

  • Chung, Kun-Jen & Liao, Jui-Jung & Ting, Pin-Shou & Lin, Shy-Der & Srivastava, H.M., 2015. "The algorithm for the optimal cycle time and pricing decisions for an integrated inventory system with order-size dependent trade credit in supply chain management," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 322-333.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:322-333
    DOI: 10.1016/j.amc.2015.06.039
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    References listed on IDEAS

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    1. Lu, Lu, 1995. "A one-vendor multi-buyer integrated inventory model," European Journal of Operational Research, Elsevier, vol. 81(2), pages 312-323, March.
    2. Chung, Kun-Jen, 1994. "An algorithm for computing the economically optimal -control chart for a process with multiple assignable causes," European Journal of Operational Research, Elsevier, vol. 72(2), pages 350-363, January.
    3. Chen, Sheng-Chih & Cárdenas-Barrón, Leopoldo Eduardo & Teng, Jinn-Tsair, 2014. "Retailer’s economic order quantity when the supplier offers conditionally permissible delay in payments link to order quantity," International Journal of Production Economics, Elsevier, vol. 155(C), pages 284-291.
    4. Soni, Hardik N, 2013. "Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment," International Journal of Production Economics, Elsevier, vol. 146(1), pages 259-268.
    5. Chen, Liang-Hsuan & Kang, Fu-Sen, 2007. "Integrated vendor-buyer cooperative inventory models with variant permissible delay in payments," European Journal of Operational Research, Elsevier, vol. 183(2), pages 658-673, December.
    6. Chung, Kun-Jen & Eduardo Cárdenas-Barrón, Leopoldo & Ting, Pin-Shou, 2014. "An inventory model with non-instantaneous receipt and exponentially deteriorating items for an integrated three layer supply chain system under two levels of trade credit," International Journal of Production Economics, Elsevier, vol. 155(C), pages 310-317.
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    Cited by:

    1. Sudip Adak & G. S. Mahapatra, 2021. "Effect of inspection and rework of probabilistic defective production on two-layer supply chain incorporating deterioration and reliability dependent demand," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(3), pages 565-578, June.
    2. Anil K. Agrawal & Amit Ambar Gupta & Manu K. Vora, 2021. "Optimal pricing and lot-sizing policies under promotional expense for some Veblen products," OPSEARCH, Springer;Operational Research Society of India, vol. 58(1), pages 83-108, March.
    3. A.K. Agrawal & A.A. Gupta & M.K. Vora, 2020. "Pricing and lot-sizing policies for products with demand under Veblen effect," Operations Management Research, Springer, vol. 13(1), pages 85-93, June.
    4. Beatrice Marchi & Lucio E. Zavanella & Simone Zanoni, 2023. "Supply chain finance for ameliorating and deteriorating products: a systematic literature review," Journal of Business Economics, Springer, vol. 93(3), pages 359-388, April.

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