Sequential and Dynamic Decisions on Sales Price and Accepting the Customer’s Demand by Markov Decision Process

Document Type : Research Paper


Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran


In this article, decisions about price and stock allocation for a seller with multiple customer classes are analyzed. With each customer arrival, the seller needs to decide about accepting or rejecting the customer’s demand by considering the stock on hand. In the case of acceptance, one needs to decide about the selling price. After any change in the inventory level, decision about continuing or stopping the production is needed. The seller faces a sequential and dynamic decision making problem, which is modeled by the Markov decision process and the optimal policy is determined. Finally, the impact of optimal policy on the seller’s profit is investigated by a numerical analysis.


Main Subjects

1 -  McGill, J.I. and VanRyzin, G.J. (1999). “Revenue Management: Research Overview and Prospects.” Transportation Science, Vol. 33, No. 2, PP. 233–256.
2 -  Gans, N. and Savin, S. (2007). “Pricing and Capacity Rationing for Rentals with Uncertain Durations.” Management Science, Vol. 53, No. 3, PP. 390-407.
3 -  Yang, C. T., Pan, Q., Ouyang, L.Y. and Teng, J. T. (2013). “Retailer's Optimal Order and Credit Policies When a Supplier Offers Either a Cash Discount or a Delay Payment Linked to Order Quantity.” European Journal of Industrial Engineering, Vol. 7, No. 3, PP. 370-392.
4 -  Frank, K. C., Zhang, R. Q. and Duenyas, I. (2003). “Optimal Policies for Inventory Systems with Priority Demand Classes.” Operations Research, Vol. 51, No. 6, PP. 993-1002.
5 -  Deshpande, V., Cohen, M. A. and Donohue, K. (2003). “A Threshold Inventory Rationing Policy for Service-Differentiated Demand Classes.” Management Science, Vol. 49, No. 6, PP. 683-703.
6 -  Arslan, H., Graves, S. C. and Roemer, T. A. (2007). “A Single-Product Inventory Model for Multiple Demand Classes.” Management Science, Vol.53, No. 9, PP. 1486-1500.
7 -  Teunter, R. H. and Haneveld, W. K. K. (2008). “Dynamic Inventory Rationing Strategies for Inventory Systems with Two Demand Classes, Poisson Demand and Backordering.” European Journal of Operational Research, Vol. 190, PP. 156-178.
8 -  Fadiloglu, M. M. and Bulut, O. (2010). “A Dynamic Rationing Policy for Continuous-review Inventory Systems.” European Journal of Operational Research, Vol. 202, PP. 675-685.
9 -  Ha, A. Y. (1997a). “Inventory Rationing in a Make-to-Stock Production System with Several Demand Classes and Lost Sales.” Management Science, Vol. 43, No. 8, PP. 1093-1103.
10 -  Ha, A. Y. (1997b). “Stock-Rationing Policy for a Make-to-Stock Production System with Two Priority Classes and Backordering.” Naval Research Logistics, Vol. 44, PP. 457-472.
11 -  De Vericourt, F., Karaesmen, F., Dallery, Y. (2001). “Assessing the Benefits of Different Stock-Allocation Policies for a Make-to-Stock Production System.” Manufacturing and Service Operations Management, Vol 3, No. 2, PP. 105-121.
12 -  DeVericourt, F., Karaesmen, F. and Dallery, Y. (2002). “Optimal Stock Allocation for a Capacitated Supply System.” Management Science, Vol. 48, No. 11, PP. 1486-1501.
13 -  Huang, B. and Iravani, S. M. R. (2008). “A Make-to-Stock System with Multiple Customer Classes and Batch Ordering.” Operations Research, Vol.56, No. 5, PP. 1312-1320.
14 -  Li, Q. and Atkins, D. (2002). “Coordinating Replenishment and Pricing in a Firm.” Manufacturing and service Operations Management, Vol. 4, No. 4, PP. 241–257.
15 -  Zhang, M. and Bell, P. C. (2007). “The Effect of Market Segmentation with Demand Leakage between Market Segments on a Firm’s Price and Inventory Decisions.” European Journal of Operational Research, Vol. 182, PP. 738-754.
16 -  Petruzzi, N. C. and Dada, M. (1999). “Pricing and the Newsvendor Problem: A Review with Extensions.” Operations Research, Vol. 47, PP. 183-194.
17 -  Chen, X. and Simchi-Levi, D. (2006). “Coordinating Inventory Control and Pricing Strategies; The Continuous Review Model.” Operations Research Letters, Vol.34, PP. 323–332.
18 -  Gallego, G. and Van Ryzin, G. (1994). “Optimal Dynamic Pricing of Inventories with Stochastic Demand over Finite Horizons.” Management Science, Vol. 40, No. 8, PP. 999-1020.
19 -  Chew, E. P., Lee, C. and Liu R. (2009). “Joint Inventory Allocation and Pricing Decisions for Perishable Products.” International Journal of Production Economics, Vol. 120, PP. 139-150.
20 -  Ahmadi, M. and Shavandi, H. (2014). “Joint Pricing and Rationing in a Production System with Two Demand Classes.” European Journal of Industrial Engineering, Vol. 8, No. 6, PP. 836-860
21 -  Ahmadi, M. and Shavandi, H. (2014). “Dynamic Pricing in a Production System with Multiple Demand Classes.” Applied Mathematical Modeling, Accepted
22 -  Puterman, M.L. (2005). Markov Decision Processes, Discrete Stochastic Dynamic Programming, Wiley, New Jersey.
23 -  Lippman, S. A. (1975). “Applying a New Device in the Optimization of Exponential Queuing Systems.” Operations Research, Vol.23, No. 4, PP. 687-710.