Abstract
In this paper, we consider a variety of models for dealing with demand uncertainty for a joint dynamic pricing and inventory control problem in a make-to-stock manufacturing system. We consider a multi-product capacitated, dynamic setting, where demand depends linearly on the price. Our goal is to address demand uncertainty using various robust and stochastic optimization approaches. For each of these approaches, we first introduce closed-loop formulations (adjustable robust and dynamic programming), where decisions for a given time period are made at the beginning of the time period, and uncertainty unfolds as time evolves. We then describe models in an open-loop setting, where decisions for the entire time horizon must be made at time zero. We conclude that the affine adjustable robust approach performs well (when compared to the other approaches such as dynamic programming, stochastic programming and robust open loop approaches) in terms of realized profits and protection against constraint violation while at the same time it is computationally tractable. Furthermore, we compare the complexity of these models and discuss some insights on a numerical example.
Similar content being viewed by others
References
Adida, E. (2006). Dynamic pricing and inventory control with no backorder under uncertainty and competition. PhD dissertation, Massachusetts Institute of Technology, Operations Research Center, June 2006.
Adida, E., & Perakis, G. (2006a). A robust optimization approach to dynamic pricing and inventory control with no backorders. Mathematical Programming, 107(1–2), 97–129.
Adida, E., & Perakis, G. (2006b). Dynamic pricing and inventory control: Uncertainty and competition. Operations Research, forthcoming.
Araman, V. F., & Caldentey, R. (2009). Dynamic pricing for nonperishable products with demand learning. Operations Research, 57(5), 1169–1188.
Axsäter, S., & Juntti, L. (1996). Comparison of echelon stock and installation stock policies for two-level inventory systems. International Journal of Production Economics, 45, 303–310.
Balashevich, N. V., Gabasov, R., & Kirillova, F. M. (2001). Numerical methods for open-loop and closed-loop optimization of piecewise linear systems. Computational Mathematics and Mathematical Physics, 41(11), 1578–1593.
Ben-Daya, M., & Raouf, A. (1994). Inventory models involving lead time as a decision variable. The Journal of the Operational Research Society, 45(5), 579–582.
Ben-Tal, A., & Nemirovski, A. (1998). Robust convex optimization. Mathematics of Operations Research, 23, 769–805.
Ben-Tal, A., Goryashko, A., Guslitzer, E., & Nemirovski, A. (2004). Adjustable robust solutions of uncertain linear programs. Mathematical Programming, 99(2), 351–376.
Bertsekas, D. P., & Tsitsiklis, J. N. (1996). Neuro-dynamic programming. Belmont: Athena Scientific.
Bertsimas, D., & de Boer, S. (2005). Dynamic pricing and inventory control for multiple products. Journal of Revenue and Pricing Management, 3(4), 303–319.
Bertsimas, D., & Mersereau, A. (2007). A learning approach for interactive marketing to a customer segment. Operations Research, 55(6), 1120–1135.
Bertsimas, D., & Paschalidis, I. Ch. (2001). Probabilistic service level guarantees in make-to-stock manufacturing systems. Operations Research, 49(1), 119–133.
Bertsimas, D., & Sim, M. (2004). The price of robustness. Operations Research, 52(1), 35–53.
Bertsimas, D., & Thiele, A. (2006). A robust optimization approach to supply chain management. Operations Research, 54(1).
Biller, S., Chan, L. M. A., Simchi-Levi, D., & Swann, J. (2005). Dynamic pricing and the direct-to-customer model in the automotive industry. Electronic Commerce Research, 5(2), 309–334.
Birge, J. R., & Louveaux, F. V. (1997). Introduction to stochastic programming. New York: Springer.
Bitran, G., & Caldentey, R. (2003). An overview of pricing models and revenue management. Manufacturing and Service Operations Management, 5(3), 203–229.
Caro, F., & Gallien, J. (2007). Dynamic assortment with demand learning for seasonal consumer goods. Management Science, 53(2), 276–292.
Chen, L., & Plambeck, E. L. (2008). Dynamic inventory management with learning about the demand distribution and substitution probability. Manufacturing and Service Operations Management, 10(2), 236–256.
Chen, X., & Simchi-Levi, D. (2004a). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case. Operations Research, 52(6), 887–896.
Chen, X., & Simchi-Levi, D. (2004b). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case. Mathematics of Operations Research, 29(3), 698–723.
Chen, X., Sim, M., & Sun, P. (2007). A robust optimization perspective of stochastic programming. Operations Research, 55(6), 1058–1071.
Clark, A. J., & Scarf, H. (1960). Optimal policies for a multiechelon inventory problem. Management Science, 6, 475–490.
Dupačová, J. (1991). On statistical sensitivity analysis in stochastic programming. Annals of Operations Research, 30, 199–214.
El-Ghaoui, L., Oustry, F., & Lebret, H. (1999). Robust solutions to uncertain semidefinite programs. SIAM Journal of Optimization, 9(1), 33–52.
Elmaghraby, W., & Keskinocak, P. (2003). Dynamic pricing: Research overview, current practices and future directions. Management Science, 49, 1287–1309.
Eppen, G. D. (1979). Effects of centralization on expected costs in a multi-location newsboy problem. Management Science, 25(5), 498–501.
Federgruen, A., & Heching, A. (1999). Combined pricing and inventory control under uncertainty. Operations Research, 47, 454–475.
Gilbert, S. M. (2000). Coordination of pricing and multiple-period production across multiple constant priced goods. Management Science, 46(12), 1602–1616.
Guslitzer, E. (2002). Uncertainty-immunized solutions in linear programming. Master’s of science, Technion, Minerva Optimization Center, Faculty of Industrial Engineering and Management, Haifa, Israel, June 2002.
Holt, C. C., Modigliani, F., Muth, J., & Simon, H. A. (1960). Planning production, inventories, and work force. Englewood Cliffs: Prentice-Hall.
Kachani, S., & Perakis, G. (2002). A fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems. Working paper, Operations Research Center, Massachusetts Institute of Technology.
Kachani, S., Perakis, G., & Simon, C. (2007). Modeling the transient nature of dynamic pricing with demand learning in a competitive environment. In Friesz, T. L., (Ed.), Network science, nonlinear science and infrastructure systems (pp. 223–267). Berlin: Springer.
Liao, C.-J., & Shyu, C.-H. (1991). An analytical determination of lead time with normal demand. International Journal of Operations and Production Management, 11(9).
Maglaras, C., & Meissner, J. (2006). Dynamic pricing strategies for multi-product revenue management problems. Manufacturing and Service Operations Management, 8(2), 136–148.
Paschalidis, I. Ch., & Liu, Y. (2002). Pricing in multiservice loss networks: Static pricing, asymptotic optimality, and demand substitution effects. IEEE/ACM Transactions On Networking, 10(3), 425–438.
Pekelman, D. (1973). Simultaneous price-production decisions. Operations Research, 22, 788–794.
Pindyck, R. (1990). Inventories and the short-run dynamics of commodity prices. Working paper, Massachusetts Institute of Technology.
Porteus, E. L. (1990). Stochastic inventory theory. In Heyman, D. P., & Sobel, M. J. (Eds.): Vol. 2. Handbooks in OR and MS Amsterdam: Elsevier.
Römisch, W., & Schultz, R. (1991). Distribution sensitivity in stochastic programming. Mathematical Programming, 50, 197–226.
Rudi, N., Kapur, S., & Pyke, D. F. (2001). A two-location inventory model with transshipment and local decision making. Management Science, 47(12), 1668–1680.
Sahinidis, N. V. (2004). Optimization under uncertainty: State-of-the-art and opportunities. Computers and Chemical Engineering, 28, 971–983.
Senhadji, A., & Montenegro, C. (1999). Time series analysis of export demand equations: A cross-country analysis. IMF Staff Papers, 46, 259–273.
Sethi, S. P., Suo, W., Taksar, M., & Yan, H. (1998). Optimal production planning in a multi-product stochastic manufacturing system with long-run average cost. Discrete Event Dynamic Systems: Theory and Applications, 8, 37–54.
Slaughter, M. (2001). International trade and labor-demand elasticities. Journal of International Economics, 54, 27–56.
Soyster, A. (1973). Convex programming with set-inclusive constraints and applications to inexact linear programming. Operations Research, 21, 1154–1157.
Talluri, K., & van Ryzin, G. (2004). The theory and practice of revenue management. Dordrecht: Kluwer.
van Hessem, D. H., & Bosgra, O. H. (2002). Closed-loop stochastic dynamic process optimization under input and state constraints. In Proceedings of the 2002 American control conference.
Zimmerman, H.-J. (1991). Fuzzy set theory and its application (2nd edn.). Boston: Kluwer.
Zipkin, P. H. (2000). Foundations of inventory management. New York: McGraw-Hill.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Adida, E., Perakis, G. Dynamic pricing and inventory control: robust vs. stochastic uncertainty models—a computational study. Ann Oper Res 181, 125–157 (2010). https://doi.org/10.1007/s10479-010-0706-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10479-010-0706-1