IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v257y2017i1d10.1007_s10479-016-2195-3.html
   My bibliography  Save this article

Effect of two-echelon trade credit on pricing-inventory policy of non-instantaneous deteriorating products with probabilistic demand and deterioration functions

Author

Listed:
  • Reza Maihami

    (Amirkabir University of Technology)

  • Behrooz Karimi

    (Amirkabir University of Technology)

  • Seyyed Mohammad Taghi Fatemi Ghomi

    (Amirkabir University of Technology)

Abstract

Usually, the profit of companies will increase if they employ trade credit financing policy to encourage customer to purchase more. This paper develops a model for pricing and inventory control of non-instantaneous deteriorating items under two-echelon trade credit in which the vendor provides a credit period to the retailer and the retailer in turn offers a delay in payment to his/her customer. The price-dependent probabilistic demand function and partially backlogged shortages are adopted. Also, deterioration is shown by three different probability distribution function including (1) uniform distribution, (2) triangular distribution, and (3) beta distribution. The theoretical results are designed to determine the optimal selling price and the optimal inventory control variables so that the retailer’s total profit is maximized. Also, the necessary and sufficient conditions to prove the existence and uniqueness of the optimal solution are provided. Moreover, an algorithm is extended to describe the solution procedure. Numerical example, sensitivity analysis, and a simulation approach are presented to illustrate the performance of the algorithm and the theoretical results. Several managerial insights are also driven from computational results. The results indicate that the retailer’s total profit increases by considering the non-instantaneous deteriorating phenomenon and the trade credit policy.

Suggested Citation

  • Reza Maihami & Behrooz Karimi & Seyyed Mohammad Taghi Fatemi Ghomi, 2017. "Effect of two-echelon trade credit on pricing-inventory policy of non-instantaneous deteriorating products with probabilistic demand and deterioration functions," Annals of Operations Research, Springer, vol. 257(1), pages 237-273, October.
    • Handle: RePEc:spr:annopr:v:257:y:2017:i:1:d:10.1007_s10479-016-2195-3
    DOI: 10.1007/s10479-016-2195-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-016-2195-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-016-2195-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Teng, Jinn-Tsair & Chang, Chun-Tao & Goyal, Suresh Kumar, 2005. "Optimal pricing and ordering policy under permissible delay in payments," International Journal of Production Economics, Elsevier, vol. 97(2), pages 121-129, August.
    2. Wu, Kun-Shan & Ouyang, Liang-Yuh & Yang, Chih-Te, 2006. "An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging," International Journal of Production Economics, Elsevier, vol. 101(2), pages 369-384, June.
    3. Chen, Jen-Ming & Chen, Tsung-Hui, 2007. "The profit-maximization model for a multi-item distribution channel," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(4), pages 338-354, July.
    4. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Infinite Horizon Case," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 698-723, August.
    5. 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.
    6. Dye, Chung-Yuan, 2007. "Joint pricing and ordering policy for a deteriorating inventory with partial backlogging," Omega, Elsevier, vol. 35(2), pages 184-189, April.
    7. Dye, Chung-Yuan, 2013. "The effect of preservation technology investment on a non-instantaneous deteriorating inventory model," Omega, Elsevier, vol. 41(5), pages 872-880.
    8. Chang, Horng-Jinh & Teng, Jinn-Tsair & Ouyang, Liang-Yuh & Dye, Chung-Yuan, 2006. "Retailer's optimal pricing and lot-sizing policies for deteriorating items with partial backlogging," European Journal of Operational Research, Elsevier, vol. 168(1), pages 51-64, January.
    9. Abdelsalam, Hisham M. & Elassal, Magy M., 2014. "Joint economic lot sizing problem for a three—Layer supply chain with stochastic demand," International Journal of Production Economics, Elsevier, vol. 155(C), pages 272-283.
    10. Maihami, Reza & Nakhai Kamalabadi, Isa, 2012. "Joint pricing and inventory control for non-instantaneous deteriorating items with partial backlogging and time and price dependent demand," International Journal of Production Economics, Elsevier, vol. 136(1), pages 116-122.
    11. Chang, Chun-Tao & Teng, Jinn-Tsair & Goyal, Suresh Kumar, 2010. "Optimal replenishment policies for non-instantaneous deteriorating items with stock-dependent demand," International Journal of Production Economics, Elsevier, vol. 123(1), pages 62-68, January.
    12. Pahl, Julia & Voß, Stefan, 2014. "Integrating deterioration and lifetime constraints in production and supply chain planning: A survey," European Journal of Operational Research, Elsevier, vol. 238(3), pages 654-674.
    13. Shah, Nita H & Soni, Hardik N & Patel, Kamlesh A, 2013. "Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates," Omega, Elsevier, vol. 41(2), pages 421-430.
    14. Roya Tat & Ata Allah Taleizadeh & Maryam Esmaeili, 2015. "Developing economic order quantity model for non-instantaneous deteriorating items in vendor-managed inventory (VMI) system," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(7), pages 1257-1268, May.
    15. Ankit Prakash Tyagi & Rama Kant Pandey & Shivraj Singh, 2014. "An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and variable holding cost," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 21(4), pages 466-488.
    16. Govindan, Kannan, 2015. "The optimal replenishment policy for time-varying stochastic demand under vendor managed inventory," European Journal of Operational Research, Elsevier, vol. 242(2), pages 402-423.
    17. Goyal, S. K. & Giri, B. C., 2001. "Recent trends in modeling of deteriorating inventory," European Journal of Operational Research, Elsevier, vol. 134(1), pages 1-16, October.
    18. Nicholas C. Petruzzi & Maqbool Dada, 1999. "Pricing and the Newsvendor Problem: A Review with Extensions," Operations Research, INFORMS, vol. 47(2), pages 183-194, April.
    19. Charles W. Haley & Robert C. Higgins, 1973. "Inventory Policy and Trade Credit Financing," Management Science, INFORMS, vol. 20(4-Part-I), pages 464-471, December.
    20. M. Palanivel & R. Uthayakumar, 2015. "Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1762-1773, July.
    21. Liao, Jui-Jung & Chung, Kun-Jen & Huang, Kuo-Nan, 2013. "A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system," International Journal of Production Economics, Elsevier, vol. 146(2), pages 557-565.
    22. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    23. Awi Federgruen & Aliza Heching, 1999. "Combined Pricing and Inventory Control Under Uncertainty," Operations Research, INFORMS, vol. 47(3), pages 454-475, June.
    24. Shilpy Tayal & S.R. Singh & Rajendra Sharma & Anubhav Pratap Singh, 2015. "An EPQ model for non-instantaneous deteriorating item with time dependent holding cost and exponential demand rate," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 23(2), pages 145-162.
    25. Zhu, Stuart X., 2012. "Joint pricing and inventory replenishment decisions with returns and expediting," European Journal of Operational Research, Elsevier, vol. 216(1), pages 105-112.
    26. Chang, Chun-Tao, 2004. "An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity," International Journal of Production Economics, Elsevier, vol. 88(3), pages 307-316, April.
    27. P. L. Abad, 1996. "Optimal Pricing and Lot-Sizing Under Conditions of Perishability and Partial Backordering," Management Science, INFORMS, vol. 42(8), pages 1093-1104, August.
    28. Chung, Kun-Jen & Huang, Tien-Shou, 2007. "The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing," International Journal of Production Economics, Elsevier, vol. 106(1), pages 127-145, March.
    29. Xin Chen & David Simchi-Levi, 2004. "Coordinating Inventory Control and Pricing Strategies with Random Demand and Fixed Ordering Cost: The Finite Horizon Case," Operations Research, INFORMS, vol. 52(6), pages 887-896, December.
    30. Liao, Hung-Chang & Tsai, Chih-Hung & Su, Chao-Ton, 2000. "An inventory model with deteriorating items under inflation when a delay in payment is permissible," International Journal of Production Economics, Elsevier, vol. 63(2), pages 207-214, January.
    31. Yu-Chung Tsao, 2016. "Joint location, inventory, and preservation decisions for non-instantaneous deterioration items under delay in payments," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(3), pages 572-585, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kuan Zeng & Xianhao Xu & Pin Zhou & Qingguo Bai, 2024. "Financing the newsvendor with vendor credit line," Operations Management Research, Springer, vol. 17(3), pages 833-849, September.
    2. Hardik N. Soni & Dipali N. Suthar, 2020. "Optimal pricing and replenishment policy for non-instantaneous deteriorating items with varying rate of demand and partial backlogging," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 986-1021, September.
    3. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.
    4. Leyla Aliabadi & Seyed Hessameddin Zegordi & Ali Husseinzadeh Kashan & Mohammad Ali Rastegar, 2024. "A sustainable supply chain model for time-varying deteriorating items under the promotional cost-sharing policy and three-level trade credit financing," Operational Research, Springer, vol. 24(2), pages 1-59, June.
    5. Ata Allah Taleizadeh & Sara Tavassoli & Arijit Bhattacharya, 2020. "Inventory ordering policies for mixed sale of products under inspection policy, multiple prepayment, partial trade credit, payments linked to order quantity and full backordering," Annals of Operations Research, Springer, vol. 287(1), pages 403-437, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Janssen, Larissa & Claus, Thorsten & Sauer, Jürgen, 2016. "Literature review of deteriorating inventory models by key topics from 2012 to 2015," International Journal of Production Economics, Elsevier, vol. 182(C), pages 86-112.
    2. Chandra K. Jaggi & Sunil Tiwari & Satish K. Goel, 2017. "Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities," Annals of Operations Research, Springer, vol. 248(1), pages 253-280, January.
    3. Dye, Chung-Yuan, 2013. "The effect of preservation technology investment on a non-instantaneous deteriorating inventory model," Omega, Elsevier, vol. 41(5), pages 872-880.
    4. Bakker, Monique & Riezebos, Jan & Teunter, Ruud H., 2012. "Review of inventory systems with deterioration since 2001," European Journal of Operational Research, Elsevier, vol. 221(2), pages 275-284.
    5. Chaitanyakumar N. Rapolu & Deepa H. Kandpal, 2020. "Joint pricing, advertisement, preservation technology investment and inventory policies for non-instantaneous deteriorating items under trade credit," OPSEARCH, Springer;Operational Research Society of India, vol. 57(2), pages 274-300, June.
    6. Maryam Ghoreishi & Gerhard-Wilhelm Weber & Abolfazl Mirzazadeh, 2015. "An inventory model for non-instantaneous deteriorating items with partial backlogging, permissible delay in payments, inflation- and selling price-dependent demand and customer returns," Annals of Operations Research, Springer, vol. 226(1), pages 221-238, March.
    7. Li, Guiping & He, Xiuli & Zhou, Jing & Wu, Hao, 2019. "Pricing, replenishment and preservation technology investment decisions for non-instantaneous deteriorating items," Omega, Elsevier, vol. 84(C), pages 114-126.
    8. Tiwari, Sunil & Cárdenas-Barrón, Leopoldo Eduardo & Khanna, Aditi & Jaggi, Chandra K., 2016. "Impact of trade credit and inflation on retailer's ordering policies for non-instantaneous deteriorating items in a two-warehouse environment," International Journal of Production Economics, Elsevier, vol. 176(C), pages 154-169.
    9. Chandan Mahato & Gour Chandra Mahata, 2023. "Optimal Pricing and Inventory Decisions for Perishable Products with Multivariate Demand Function Under Trade Credit," SN Operations Research Forum, Springer, vol. 4(2), pages 1-26, June.
    10. M. Palanivel & R. Uthayakumar, 2016. "Two-warehouse inventory model for non-instantaneous deteriorating items with partial backlogging and inflation over a finite time horizon," OPSEARCH, Springer;Operational Research Society of India, vol. 53(2), pages 278-302, June.
    11. M. Palanivel & R. Uthayakumar, 2015. "Finite horizon EOQ model for non-instantaneous deteriorating items with price and advertisement dependent demand and partial backlogging under inflation," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(10), pages 1762-1773, July.
    12. R. Sundara rajan & R. Uthayakumar, 2017. "Comprehensive solution procedure for optimizing replenishment policies of instantaneous deteriorating items with stock-dependent demand under partial trade credit linked to order quantity," 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. 8(2), pages 1343-1373, November.
    13. Qin, Yiyan & Wang, Jianjun & Wei, Caimin, 2014. "Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously," International Journal of Production Economics, Elsevier, vol. 152(C), pages 42-48.
    14. Maihami, Reza & Govindan, Kannan & Fattahi, Mohammad, 2019. "The inventory and pricing decisions in a three-echelon supply chain of deteriorating items under probabilistic environment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 118-138.
    15. Prashant Chintapalli, 2015. "Simultaneous pricing and inventory management of deteriorating perishable products," Annals of Operations Research, Springer, vol. 229(1), pages 287-301, June.
    16. Zhang, Jianxiong & Wang, Yu & Lu, Lihao & Tang, Wansheng, 2015. "Optimal dynamic pricing and replenishment cycle for non-instantaneous deterioration items with inventory-level-dependent demand," International Journal of Production Economics, Elsevier, vol. 170(PA), pages 136-145.
    17. Shah, Nita H & Soni, Hardik N & Patel, Kamlesh A, 2013. "Optimizing inventory and marketing policy for non-instantaneous deteriorating items with generalized type deterioration and holding cost rates," Omega, Elsevier, vol. 41(2), pages 421-430.
    18. Chen, Jing & Dong, Ming & Rong, Ying & Yang, Liang, 2018. "Dynamic pricing for deteriorating products with menu cost," Omega, Elsevier, vol. 75(C), pages 13-26.
    19. Chung, Kun-Jen & Huang, Tien-Shou, 2007. "The optimal retailer's ordering policies for deteriorating items with limited storage capacity under trade credit financing," International Journal of Production Economics, Elsevier, vol. 106(1), pages 127-145, March.
    20. Madhukar Nagare & Pankaj Dutta & Pravin Suryawanshi, 2020. "Optimal procurement and discount pricing for single-period non-instantaneous deteriorating products with promotional efforts," Operational Research, Springer, vol. 20(1), pages 89-117, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:257:y:2017:i:1:d:10.1007_s10479-016-2195-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.