Partial linked-to-order delayed payment and life time effects on decaying items ordering

  • Ata Allah Taleizadeh
  • Nadia Pourmohammad-Zia
  • Ioannis KonstantarasEmail author
Original paper


Trade-credit is an influential implementation in financial transactions. This paper proposes an inventory model for decaying items with lifetime under linked-to-order partial delay in payments. More precisely, the items are gradually deteriorating and also have a known maximum lifetime. The payment scheme is structured as follows: if the order quantity reaches a particular level, fully permissible trade credit is possible, otherwise the partial trade credit is offered. To the best of our knowledge, this is the first research incorporating the “Linked-to-order Trade Credit Financing” scheme for deteriorating items with lifetime. Selling price and purchasing costs are not considered equal and there is no need for the interest charged in stocks to be larger than the interest earned on investment. Theoretical results are developed to obtain the optimum solutions of the problem. The authenticity and pertinence of the model and solution procedure are illustrated through numerical results. Finally, sensitivity analysis and managerial insights are provided.


Inventory Partial trade credit Linked to order trade credit Deterioration Life time 

Mathematics Subject Classification




  1. Aggarwal SP, Jaggi CK (1995) Ordering policies of deteriorating items under permissible delay in payments. J Oper Res Soc 46:658–662CrossRefGoogle Scholar
  2. Annadurai K, Uthayakumar R (2015) Decaying inventory model with stock-dependent demand and shortages under two-level trade credit. Int J Adv Manuf Technol 77:525–543CrossRefGoogle Scholar
  3. Banu A, Mondal SK (2018) Analyzing an inventory model with two-level trade credit period including the effect of customers’ credit on the demand function using q-fuzzy number. Oper Res 1–29Google Scholar
  4. Cárdenas-Barrón LE, Treviño-Garza G (2014) An optimal solution to a three echelon supply chain network with multi-product and multi-period. Appl Math Model 38:1911–1918CrossRefGoogle Scholar
  5. Chang CT (2004) An EOQ model with deteriorating items under inflation when supplier credits linked to order quantity. Int J Prod Econ 88:307–316CrossRefGoogle Scholar
  6. Chang CT, Ouyang LY, Teng JT (2003) An EOQ model for deteriorating items under supplier credits linked to ordering quantity. Appl Math Model 27:983–996CrossRefGoogle Scholar
  7. Chen SC, Teng JT, Skouri K (2013) Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit. Int J Prod Econ 155:302–309CrossRefGoogle Scholar
  8. Chung KJ, Huang TS (2007) The optimal retailer’s ordering policies for deteriorating items with limited storage capacity under trade credit financing. Int J Prod Econ 106:127–145CrossRefGoogle Scholar
  9. Chung KJ, Lin SD, Srivastava HM (2013) The inventory models under conditional trade credit in a supply chain system. Appl Math Model 37:10036–10052CrossRefGoogle Scholar
  10. Das BC, Das B, Mondal SK (2013) Integrated supply chain model for a deteriorating item with procurement cost dependant credit period. Comput Ind Eng 64:788–796CrossRefGoogle Scholar
  11. Dye CY, Yang CT (2015) Sustainable trade credit and replenishment decisions with credit-linked demand under carbon emission constraints. Eur J Oper Res 244:187–200CrossRefGoogle Scholar
  12. Giri BC, Sharma S (2016) Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing. Oper Res Int J 16:25–50CrossRefGoogle Scholar
  13. Goyal SK (1985) Economic order quantity under conditions of permissible delay in payments. J Oper Res Soc 35:335–338CrossRefGoogle Scholar
  14. Huang YF (2007) Economic order quantity under conditionally permissible delay in payments. Eur J Oper Res 176:911–924CrossRefGoogle Scholar
  15. Huang YF, Hsu KH (2008) An EOQ model under retailer partial trade credit policy in supply chain. Int J Prod Econ 112:655–664CrossRefGoogle Scholar
  16. Jaggi CK, Aggarwal KK, Goel SK (2007) Retailer’s optimal ordering policy under two stage TCF. Adv Model Optim 9:67–80Google Scholar
  17. Jaggi CK, Cárdenas-Barrón LE, Tiwari S, Shafi AA (2017) Two-warehouse inventory model for deteriorating items with imperfect quality under the conditions of permissible delay in payments. Sci Iran Trans E Ind Eng 24:390Google Scholar
  18. Khouja M, Mehrez A (1996) Optimal inventory policy under different supplier credit policies. J Manuf Syst 15:334–339CrossRefGoogle Scholar
  19. Liao JJ (2008) An EOQ model with non-instantaneous receipt and exponentially deteriorating items under two-level trade credit. Int J Prod Econ 113:852–861CrossRefGoogle Scholar
  20. Liao JJ, Chung KJ, Huang KN (2013) A deterministic inventory model for deteriorating items with two warehouses and trade credit in a supply chain system. Int J Prod Econ 146:557–565CrossRefGoogle Scholar
  21. Mishra U, Tijerina-Aguilera J, Tiwari S, Cárdenas-Barrón LE (2018) Retailer’s joint ordering, pricing, and preservation technology investment policies for a deteriorating item under permissible delay in payments. Math Probl Eng 2018:6962417CrossRefGoogle Scholar
  22. Ouyang LY, Ho CH, Su CH (2008) Optimal strategy for an integrated system with variable production rate when the freight rate and trade credit are both linked to the order quantity. Int J Prod Econ 115:151–162CrossRefGoogle Scholar
  23. Ouyang LY, Teng JT, Goyal SK, Yang CT (2009) An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity. Eur J Oper Res 194(2):418–431CrossRefGoogle Scholar
  24. Seifert D, Seifert RW, Protopappa-Sieke M (2013) A review of trade credit literature: opportunities for research in operations. Eur J Oper Res 231:245–256CrossRefGoogle Scholar
  25. Shah NH (2015) Retailer’s replenishment and credit policies for deteriorating inventory under credit period-dependent demand and bad-debt loss. TOP 23(1):298–312CrossRefGoogle Scholar
  26. Shah NH, Cárdenas-Barrón LE (2015) Retailer’s decision for ordering and credit policies for deteriorating items when a supplier offers order-linked credit period or cash discount. Appl Math Comput 259:569–578Google Scholar
  27. Shaikh AA, Bhunia AK, Cárdenas-Barrón LE, Sahoo L, Tiwari S (2018) A fuzzy inventory model for a deteriorating item with variable demand, permissible delay in payments and partial backlogging with Shortage Follows Inventory (SFI) Policy. Int J Fuzzy Syst 20:1606–1623CrossRefGoogle Scholar
  28. Taleizadeh AA, Noori-Daryan M (2015) Pricing, manufacturing and inventory policies for raw material in a three-level supply chain. Int J Syst Sci 47(4):919–931CrossRefGoogle Scholar
  29. Taleizadeh AA, Wee HM, Jolai F (2013) Revisiting fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math Comput Model 57(5–6):1466–1479CrossRefGoogle Scholar
  30. Taleizadeh AA, Kalantary SS, Cárdenas-Barrón LE (2015) Determining optimal price, replenishment lot size and number of shipment for an EPQ model with rework and multiple shipments. J Ind Manag Optim 11(4):1059–1071CrossRefGoogle Scholar
  31. Tat R, Taleizadeh AA, Esmaeili M (2015) Developing EOQ model with non-instantaneous deteriorating items in vendor-managed inventory (VMI) system. Int J Syst Sci 46(7):1257–1268CrossRefGoogle Scholar
  32. Teng JT, Lou KR, Wang L (2014) Optimal trade credit and lot size policies in economic production quantity models with learning curve production costs. Int J Prod Econ 155:318–323CrossRefGoogle Scholar
  33. Tiwari S, Cárdenas-Barrón LE, Goh M, Shaikh AA (2018) Joint pricing and inventory model for deteriorating items with expiration dates and partial backlogging under two-level partial trade credits in supply chain. Int J Prod Econ 200:16–36CrossRefGoogle Scholar
  34. Tsao YC (2010) Two-phase pricing and inventory management for deteriorating and fashion goods under trade credit. Math Methods Oper Res 72:107–127CrossRefGoogle Scholar
  35. Wang WC, Teng JT, Lou KR (2014) Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime. Eur J Oper Res 232:315–321CrossRefGoogle Scholar
  36. Wu J, Chan YL (2014) Lot-sizing policies for deteriorating items with expiration dates and partial trade credit to credit-risk customers. Int J Prod Econ 155:292–301CrossRefGoogle Scholar
  37. Wu J, Ouyang LY, Cárdenas-Barrón LE, Goyal SK (2014) Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing. Eur J Oper Res 237:898–908CrossRefGoogle Scholar
  38. Zhang Q, Dong M, Luo J, Segerstedt A (2014) Supply chain coordination with trade credit and quantity discount incorporating default risk. Int J Prod Econ 152:352–360CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Industrial Engineering, College of EngineeringUniversity of TehranTehranIran
  2. 2.School of Industrial Engineering and SystemsAmirkabir University of TechnologyTehranIran
  3. 3.Department of Business Administration, School of Business AdministrationUniversity of MacedoniaThessalonikiGreece

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