Abstract
We consider a purchase/inventory control problem in which the purchase price and demand are stochastic, a common situation encountered by firms that replenish in a foreign currency or from commodity markets. More specifically, we assume that the demand follows a Poisson arrival process and that the log-price evolves according to a general Wiener process. Under these circumstances, the optimal policy is a state dependent base-stock policy that can be described as a series of threshold prices. An iterative procedure for determining the optimal thresholds has been derived earlier but, even for the simplest price process, the solution quickly becomes numerically intractable. To deal with this, we propose an approximation that allows us to derive simple heuristics for finding thresholds that are close to optimal. For certain price processes the heuristics are just a series of closed-form expressions. The computational complexity is reduced significantly, and the numerical study shows that the new heuristics perform considerably better than earlier suggested heuristics.
Similar content being viewed by others
References
Axsäter S (1990) Simple solution procedures for a class of two-echelon inventory problems. Oper Res 38(1):64–69
Berling P, Martínez-de-Albéniz V (2011) Optimal inventory policies when purchase price and demand are stochastic. Oper Res 59(1):109–124
Bertsekas DP (2000) Dynamic programming and optimal control. Athena Scientific, Belmont
Brennan M, Schwartz E (1985) Evaluating natural resource investments. J Bus 58(2):135–157
Dixit AK, Pindyck RS (1994) Investment under uncertainty. Princeton University Press, Princeton
Doege J, Schiltknecht P, Lüthi H-J (2006) Risk management of power portfolios and valuation of flexibility. OR Spect 28(2):267–287
Fabian T, Fisher J, Sasieni M, Yardeni A (1959) Purchasing raw material on a fluctuating market. Oper Res 7(1):107–122
Feng Y, Sun J (2001) Computing the optimal replenishment policy for inventory systems with random discount opportunities. Oper Res 49(5):790–795
Kalymon BA (1971) Stochastic prices in a single-item inventory purchasing model. Oper Res 19(6):1434–1458
Goel A, Gutierrez GJ (2011) Multiechelon procurement and distribution policies for traded commodities. Manag Sci 57(12):2228–2244
Goel A, Gutierrez G (2011) Effect of term structure model of futures price on procurement policies (October 18, 2011). McCombs research paper series no. IROM-06-11. Available at SSRN: http://ssrn.com/abstract=1945770 or http://dx.doi.org/10.2139/ssrn.1945770
Goel A, Gutierrez G (2012) Integrating commodity markets in the optimal procurement policies of a stochastic inventory system. Working paper, University of Texas at Austin, Austin
Goel A, Tanrisever F (2011) Integrated options and spot procurement for commodity processors (December 10, 2011). Available at SSRN: http://ssrn.com/abstract=1898866 or http://dx.doi.org/10.2139/ssrn.1898866
Golabi K (1985) Optimal inventory policies when ordering prices are random. Oper Res 33(3):575–588
Haksöz Seshadri S (2007) Supply chain operations in the presence of a spot market: a review with discussion. J Oper Res Soc 58(11):1412–1429
Hull J (2006) Options, futures and other derivatives, 6th edn. Pearson Prentice Hall, Upper Saddle River
Jain A, Groenevelt H, Rudi N (2010) Continuous review inventory model with dynamic choice of two freight modes with fixed costs. Manuf Serv Oper Manag 12(1):120–139
Marklund J (2011) Inventory control in divergent supply chains with time-based dispatching and shipment consolidation. Nav Res Logist 58(1):59–71
Martínez-de-Albéniz V, Simchi-Levi D (2005) A portfolio approach to procurement contracts. Prod Oper Manag 14(1):90–114
Moinzadeh K (1997) Replenishment and stocking policies for inventory systems with random deal offerings. Manag Sci 43(3):334–342
Muharremoglu A, Tsitsiklis JN (2008) A single-unit decomposition approach to multiechelon inventory systems. Oper Res 56(5):1089–1103
Özekici S, Parlar M (1999) Inventory models with unreliable suppliers in a random environment. Ann Oper Res 91(1):123–136
Schwartz E (1997) The stochastic behavior of commodity prices: implications for valuation and hedging. J Fin 52(3):923–973
Secomandi N (2010) Optimal commodity trading with a capacitated storage asset. Manag Sci 56(3):449467
Song JS, Zipkin P (1993) Inventory control in a fluctuating demand environment. Oper Res 41(2):351–370
Spinler S, Huchzermeier A, Kleindorfer P (2003) Risk hedging via options contracts for physical delivery. OR Spect 25(3):379–395
Yi J, Scheller-Wolf A (2003) Dual sourcing from a regular supplier and a spot market. Working paper, Tepper School of Business, Carnegie Mellon University
Zhao Y (2008) Evaluation and optimization of installation base-stock policies in supply chains with compound Poisson demand. Oper Res 56(2):437452
Zheng YS (1994) Optimal control policy for stochastic inventory systems with Markovian discount opportunities. Oper Res 42(4):721–738
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Berling, P., Xie, Z. Approximation algorithms for optimal purchase/inventory policy when purchase price and demand are stochastic. OR Spectrum 36, 1077–1095 (2014). https://doi.org/10.1007/s00291-014-0369-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00291-014-0369-4