Abstract
In the highly competitive environment in which companies operate today, it is crucial that the supporting processes such as inventory management are as efficient as possible. In particular, a trade-off between inventory costs and service levels needs to be assessed. In this paper, we determine an optimal batch ordering policy accounting for both demand and market price fluctuations such that the long-term discounted cost is minimised. This means that future costs are reduced by a constant factor as we need to take inflation and other factors into account. To this end, the inventory system is modelled as a Markovian queueing system with finite capacity in a random environment. Assuming phase-type distributed lead times, Markovian demand and price fluctuations, the optimal ordering strategy is determined by a Markov decision process (MDP) approach. To illustrate our results, we analyse the ordering policy under several price fluctuation scenarios by some numerical examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bellman, R.: A Markovian decision process. Journal of Mathematics and Mechanics 6(4), 679–684 (1957)
Hillier, F.S., Lieberman, G.: Introduction to Operations Research, ch. 19. McGraw-Hill, Singapore (2010)
Hopp, W., Spearman, M.: Factory Physics, Inventory Control: From EOQ to RDP. McGraw-Hill (2008)
Howard, R.: Dynamic programming and Markov processes. The M.I.T. Press (1960)
Miller, G.: Aggregate inventory management. PROACTION (2006)
Puterman, M., Shin, M.: Modified policy iteration algorithms for discounted Markov decision problems. Management Science 24 (1978)
Sutton, R.: On the significance of Markov decision processes. In: Gerstner, W., Hasler, M., Germond, A., Nicoud, J.-D. (eds.) ICANN 1997. LNCS, vol. 1327, pp. 273–282. Springer, Heidelberg (1997)
Sutton, R., Barto, A.: Reinforcement learning: An introduction. IEEE Transactions on Neural Networks 9(5), 1054 (1998)
Teng, J.T., Chern, M.S., Chan, Y.L.: Deterministic inventory lot-size models with shortages for fluctuating demand and unit purchase cost. International Transactions in Operational Research 12(1), 83–100 (2005)
Tijms, H.C.: Stochastic modelling and analysis: A computational approach, Markovian decision processes and their application. John Wiley & Sons Inc., New York (1986)
Yan, K., Kulkarni, V.: Optimal inventory policies under stochastic production and demand rates. Stochastic Models 24(2), 173–190 (2008)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Cuypere, E., De Turck, K., Bruneel, H., Fiems, D. (2013). Optimal Inventory Management in a Fluctuating Market. In: Dudin, A., De Turck, K. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2013. Lecture Notes in Computer Science, vol 7984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39408-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-39408-9_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39407-2
Online ISBN: 978-3-642-39408-9
eBook Packages: Computer ScienceComputer Science (R0)