, Volume 56, Issue 3, pp 945–964 | Cite as

Ordering policies under currency risk sharing agreements: a Markov chain approach

  • Suresha KharviEmail author
  • T. P. M. Pakkala
  • G. Srinivasan
Application Article


If an exporter or a wholesaler sells goods at a fixed price to be paid in the currency of the seller’s country, then the purchase price of the importer depends upon the prevailing exchange rate of their respective currencies. Ideally, in a floating exchange rate system, the purchase price has to change according to shifts in the exchange rate. In such a scenario the entire exchange rate risk is borne by the importer/buyer. However, in international trade, it is customary for the parties to enter into a risk-sharing agreement, under which the buyer does not pay the seller on the basis of the prevailing exchange rate, but pays a mutually agreed upon price that falls within a range of fluctuating exchange rates. In this manner, the profit or loss due to fluctuations in the exchange rate would be shared by both the parties. These stochastic variations in purchase prices are modeled through a Markov chain. In this article, the resulting purchase and inventory problem is analyzed by identifying a regenerative cycle. An optimal selling price that maximizes the expected profit per unit time is also discussed. Further, optimal ordering policies under no stock-out conditions are derived with an optimal uniform demand corresponding to the optimal selling price. Through sensitivity analyses, differences in profit function with respect to carrying cost fraction, setup costs, and purchase prices are also shown. An investigation into the possible loss if this model solution is not implemented is also made through numerical illustrations. A discussion of a special case of two-purchase price scenario gives additional insight into the problem.


Inventory Risk-sharing Variable price Markov chain Regenerative cycle Exchange rate Optimal selling price Optimal policy Price-dependent demand Two-price inventory problem 



  1. 1.
    Moffett, M.H., Stonehill, A.I., Eiteman, D.K.: Fundamentals of Multinational Finance, 6th edn. NY Pearson, New York (2018)Google Scholar
  2. 2.
    Kim, K.K., Park, K.S.: Transferring and sharing exchange-rate risk in a risk-averse supply chain of a multinational firm. Eur. J. Oper. Res. 237(2), 634–648 (2014)CrossRefGoogle Scholar
  3. 3.
    Naddor, E.: Inventory Systems. Wiley, New York (1966)Google Scholar
  4. 4.
    Goyal, S.K.: An inventory model for a product for which price fluctuates. Oper. Res. 3(2), 112–117 (1975)Google Scholar
  5. 5.
    Buzacott, J.A.: Economic order quantities with inflation. Oper. Res. Q. 26(3), 553–558 (1975)CrossRefGoogle Scholar
  6. 6.
    Lev, B., Soyster, A.L.: An inventory model with finite horizon and price changes. J. Oper. Res. Soc. 30(1), 43–53 (1979)CrossRefGoogle Scholar
  7. 7.
    Goyal, S.K.: A note on the paper: an inventory model with finite horizon and price changes. J. Oper. Res. Soc. 30(9), 839–840 (1980)CrossRefGoogle Scholar
  8. 8.
    Taylor, S.G., Bradley, C.E.: Optimal ordering strategies for announced price increases. Oper. Res. 33(2), 312–325 (1985)CrossRefGoogle Scholar
  9. 9.
    Lev, B., Weiss, H.J.: Inventory models with cost changes. Oper. Res. 38(1), 53–63 (1990)CrossRefGoogle Scholar
  10. 10.
    Gascon, A.: On the finite horizon EOQ model with cost changes. Oper. Res. 43(4), 716–717 (1995)CrossRefGoogle Scholar
  11. 11.
    Ghosh, A.K.: On some inventory models involving shortages under an announced. Int. J. Syst. Sci. 34(2), 129–137 (2003)CrossRefGoogle Scholar
  12. 12.
    Huang, W., Kulkarni, V.G.: Optimal EOQ for announced price increases in infinite horizon. Oper. Res. 51(2), 336–339 (2003)CrossRefGoogle Scholar
  13. 13.
    Taleizadeh, A.A., Pentico, D.W.: An economic order quantity model with a known price increase and partial backordering. Eur. J. Oper. Res. 228(3), 516–525 (2013)CrossRefGoogle Scholar
  14. 14.
    Arcelus, F.J., Pakkala, T.P.M., Srinivasan, G.: On the interaction between retailer’s inventory policies and manufacturer trade deals in response to supply-uncertainty occurrences. Ann. Oper. Res. 143, 45–58 (2006)CrossRefGoogle Scholar
  15. 15.
    Arcelus, F.J., Pakkala, T.P.M., Srinivasan, G.: A retailer’s decision process when anticipating a vendor’s temporary discount offer. Comput. Ind. Eng. 57, 253–260 (2009)CrossRefGoogle Scholar
  16. 16.
    Arcelus, F.J., Pakkala, T.P.M., Srinivasan, G.: A purchasing framework for B2B pricing decisions and risk-sharing in supply chains. J. Decis. Sci. Inst. 33(4), 645–672 (2002)CrossRefGoogle Scholar
  17. 17.
    Pegels, C.C., Jelmert, A.E.: An evaluation of blood-inventory policies: a Markov chain application. Oper. Res. 18(6), 1087–1098 (1970)CrossRefGoogle Scholar
  18. 18.
    Arcelus, F.J., Pakkala, T.P.M., Srinivasan, G.: Retailer’s response to repetitive special sales under uncertainty. Int. J. Quant. Prod. Manag. 6, 137–149 (2000)Google Scholar
  19. 19.
    Abboud, N.E.: A discrete-time Markov production-inventory model with machine breakdowns. Comput. Eng. 39, 95–107 (2001)Google Scholar
  20. 20.
    Chen, F., Song, J.S.: Optimal policies for multiechelon inventory problems with Markov—modulated demand. Oper. Res. 49(2), 226–234 (2001)CrossRefGoogle Scholar
  21. 21.
    Hekimoglu, M., van der Laan, E., Dekker, R.: Markov-modulated analysis of a spare parts system with random lead times and disruption risks. Eur. J. Oper. Res. 269(3), 909–922 (2018)CrossRefGoogle Scholar
  22. 22.
    Emmons, H., Gilbert, S.M.: The role of returns policies in pricing and inventory decisions for catalogue goods. Manag. Sci. 44, 276–283 (1998)CrossRefGoogle Scholar
  23. 23.
    Lau, A.H.L., Lau, H.S.: Effects of a demand-curve’s shape on the optimal solutions of a multi-echelon inventory/pricing model. Eur. J. Oper. Res. 147, 530–548 (2003)CrossRefGoogle Scholar
  24. 24.
    Lau, A.H.L., Lau, H.S.: Some two-echelon supply-chain games: improving from deterministic-symmetric-information to stochastic-asymmetric-information models. Eur. J. Oper. Res. 161(1), 203–223 (2005)CrossRefGoogle Scholar
  25. 25.
    Petruzzi, N.C., Dada, M.: Pricing and the newsvendor problem: a review with extensions. Oper. Res. 47(2), 183–194 (1999)CrossRefGoogle Scholar
  26. 26.
    Weng, Z.K.: Modeling quantity discounts under general price-sensitive demand functions: optimal policies and relationships. Eur. J. Oper. Res. 86, 300–314 (1995)CrossRefGoogle Scholar
  27. 27.
    Ross, S.: Stochastic Processes. Wiley, New York (1983)Google Scholar
  28. 28.
  29. 29.

Copyright information

© Operational Research Society of India 2019

Authors and Affiliations

  1. 1.Mangalore UniversityMangalagangotriIndia
  2. 2.Justice K. S. Hegde Institute of ManagementNitteIndia
  3. 3.Faculty of AdministrationUniversity of New BrunswickFrederictonCanada

Personalised recommendations