Optimal Pricing Strategy in a Two-Echelon Supply Chain with Admissible Advanced and Delayed Payments

  • B. C. GiriEmail author
  • R. Bhattacharjee
  • T. Maiti
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


In the traditional economic order quantity model, the purchasing cost of an order is paid at the time of its receipt. However, in reality, installment payment of purchasing cost is very common and many distributors pay the purchasing cost to the manufacturers in installments (upstream partial prepayment). In a similar manner, distributors allow retailers to pay the purchasing cost after the goods are received (downstream partial delay payment). This article develops a two-echelon supply chain model with a single-manufacturer and a single-retailer in which the manufacturer adopts a lot-for-lot policy for meeting the demand of the retailer under admissible advanced and delayed payment options. The market demand at the retailer is assumed to be linearly dependent on the selling price. The effect of advanced/delayed payment on the optimal payment time is analyzed. The optimal results of the developed model and sensitivity analysis are presented for a numerical example. It is revealed that the supply chain’s average profit attains the maximum when the optimal cycle time is longer than the optimal payment time.


Supply chain Lot-for-lot policy Price-dependent demand Advanced/delayed payment 


  1. 1.
    Goyal, S.K.: Economic order quantity under conditions of permissible delay in payment. J. Oper. Res. Soc. 36, 335–338 (1985)CrossRefGoogle Scholar
  2. 2.
    Jamal, A.M.M., Sarker, B.R., Wang, S.: Optimal payment time for a retailer under permitted delay of payment by the wholesaler. Int. J. Prod. Econ. 66, 59–66 (2000)CrossRefGoogle Scholar
  3. 3.
    Teng, J.T., Chang, C.T., Goyal, S.K.: Optimal pricing and ordering policy under permissible delay in payments. Int. J. Prod. Econ. 97, 121–129 (2005)CrossRefGoogle Scholar
  4. 4.
    Cheng, M.C., Lou, K.R., Ouyang, L.Y., Chiang, Y.H.: The optimal ordering policy with trade credit under two different payment methods. TOP 18, 413–428 (2010)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chung, K.J.: The correct proofs for the optimal ordering policy with trade credit under two different payment methods in a supply chain system. TOP 20, 768–776 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Huang, Y.F.: Economic order quantity under conditionally permissible delay in payments. Eur. J. Oper. Res. 176, 911–924 (2007)CrossRefGoogle Scholar
  7. 7.
    Giri, B.C., Maiti, T.: Supply chain model with price- and trade credit-sensitive demand under two-level permissible delay in payments. Int. J. Syst. Sci. 44, 937–948 (2013)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Giri, B.C., Sharma, S.: Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing. Oper. Res. 16, 25–50 (2016)Google Scholar
  9. 9.
    Yang, C.T.: The optimal order and payment policies for deteriorating items in discount cash flows analysis under the alternatives of conditionally permissible delay in payments and cash discount. TOP 18, 429–443 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Sarker, B.R., Jamal, A.M.M., Wang, S.: Optimal payment time under permissible delay in payment for products with deterioration. Prod. Plan. Control 11, 380–390 (2000)CrossRefGoogle Scholar
  11. 11.
    Liao, H.C., Chen, Y.K.: Optimal payment time for retailer’s inventory system. Int. J. Syst. Sci. 34, 245–253 (2003)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Huang, Y.F.: Buyer’s optimal ordering policy and payment policy under supplier credit. Int. J. Syst. Sci. 36, 801–807 (2005)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Chang, C.T., Wu, S.J., Chen, L.C.: Optimal payment time with deteriorating items under inflation and permissible delay in payments. Int. J. Syst. Sci. 40, 985–993 (2009)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Maiti, A.K., Maiti, M.K., Maiti, M.: Inventory model with stochastic lead-time and price dependent demand incorporating advance payment. Appl. Math. Model. 33, 2433–2443 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Giri, B.C., Bhattacharjee, R., Maiti, T.: Optimal payment time in a two-echelon supply chain with price-dependent demand under trade credit financing. Int. J. Syst. Sci. Oper. Logist. 5(4), 374–392 (2018)Google Scholar
  16. 16.
    Li, R., Chan, Y.L., Chang, C.T., Barron, L.E.C.: Pricing and lot-sizing policies for perishable products with advance-cash-credit payments by a discounted cash-flow analysis. Int. J. Prod. Econ. 193, 578–589 (2017)CrossRefGoogle Scholar
  17. 17.
    Teng, J.T., Barron, L.E.C., Chang, H.J., Wu, J., Hu, Y.: Inventory lot-size policies for deteriorating items with expiration dates and advance payments. Appl. Math. Model. 40, 8605–8616 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Zhang, Q., Zhang, D., Tsao, Y.C., Luo, J.: Optimal ordering policy in a two-stage supply chain with advance payment for stable supply capacity. Int. J. Prod. Econ. 177, 34–43 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia
  2. 2.Department of MathematicsJIS College of EngineeringKalyaniIndia

Personalised recommendations