##
**Optimal dynamic pricing of perishable products with stochastic demand and a finite set of prices.**
*(English)*
Zbl 0967.90003

Summary: Consider a continuous-time inventory problem in which a retailer sets the price on a fixed number of a perishable asset that must be sold prior to the time at which it perishes. The retailer can dynamically adjust the price between any of a finite number of allowable prices. Demand for the product is Poisson with an intensity that is inversely related to the price. The optimal policy is piecewise-constant. The maximum expected revenue is nondecreasing and concave in both the remaining inventory and the time-to-go. For a given inventory level the optimal price declines as the time at which the products perish approaches. At any given time the optimal price is nonincreasing in the number of items remaining unsold. These results are extended to (i) the case in which the prices and corresponding demand intensities depend on the time-to-go; and (ii) the case in which the retailer can restock to meet demand at a unit cost after the initial inventory has been sold.

### MSC:

90B05 | Inventory, storage, reservoirs |

90C59 | Approximation methods and heuristics in mathematical programming |

91B24 | Microeconomic theory (price theory and economic markets) |

PDF
BibTeX
XML
Cite

\textit{R. E. Chatwin}, Eur. J. Oper. Res. 125, No. 1, 149--174 (2000; Zbl 0967.90003)

Full Text:
DOI

### References:

[1] | Bass, F., The relationship between diffusion rates, experience curves and demand elasticities for consumer durable technical innovations, Journal of business, 53, 551-567, (1980) |

[2] | Belobaba, P.P., Airline yield management: an overview of seat inventory control, Transportation science, 21, 63-73, (1987) |

[3] | Belobaba, P.P., 1987. Origin – destination seat inventory control, Abstract, TIMS/ORSA Joint National Meeting Bulletin, St. Louis, MI, October |

[4] | Belobaba, P.P., Application of a probabilistic decision model to airline seat inventory control, Operations research, 37, 183-197, (1989) |

[5] | Bitran, G.R.; Caldentey, R.; Mondschein, S.V., Coordinating clearance markdown sales of seasonal products in retail chains, Operations research, 46, 609-624, (1998) · Zbl 0996.90006 |

[6] | Bitran, G.R.; Mondschein, S.V., Periodic pricing of seasonal products in retailing, Management science, 43, 64-79, (1997) · Zbl 0888.90026 |

[7] | Bitran, G.R., Wadhwa, H.K., 1996a. Some structural properties of the seasonal product pricing problem, Working Paper #3897-96, MIT Sloan School of Management, Cambridge, MA |

[8] | Bitran, G.R., Wadhwa, H.K., 1996b. A methodology for demand learning with an application to the optimal pricing of seasonal products, Working Paper #3898-96, MIT Sloan School of Management, Cambridge, MA |

[9] | Brumelle, S.L.; McGill, J.I., Airline seat allocation with multiple nested fare classes, Operations research, 41, 127-137, (1993) · Zbl 0775.90148 |

[10] | Chatwin, R.E., 1993. Optimal airline overbooking, Ph.D. Dissertation, Department of Operations Research, Stanford University, CA |

[11] | Chatwin, R.E., Optimal control of continuous-time terminal-value birth-and-death processes and airline overbooking, Naval research logistics, 43, 159-168, (1996) · Zbl 0862.60091 |

[12] | Chatwin, R.E., Multi-period airline overbooking with a single fare class, Operations research, 46, 805-819, (1998) · Zbl 0987.90503 |

[13] | Chatwin, R.E., 1999. Continuous-time airline overbooking with time-dependent fares and refunds. Transportation Science 33, 182-191 · Zbl 1002.90525 |

[14] | Colville, G., Phillips, R.L., 1992. Dynamic O & D yield management, Abstract, ORSA/TIMS Joint National Meeting Bulletin, San Francisco, CA, November |

[15] | Curry, R.E., Optimal airline seat allocation with fare classes nested by origins and destinations, Transportation science, 24, 193-204, (1990) |

[16] | Dror, M.; Trudeau, P.; Ladany, S.P., Network models for seat allocation of flights, Transportation research B, 22, 239-250, (1988) |

[17] | Feng, Y.; Gallego, G., Optimal starting times for end-of-season sales and optimal stopping times for promotional fares, Management science, 41, 1371-1391, (1995) · Zbl 0859.90024 |

[18] | Feng, Y.; Gallego, G., Perishable asset revenue management with Markovian time dependent demand intensities, (1996), Department of Industrial Engineering and Operational Research Columbia University, New York · Zbl 1231.91271 |

[19] | Gallego, G.; van Ryzin, G., Optimal dynamic pricing of inventories with stochastic demand over finite horizons, Management science, 40, 999-1020, (1994) · Zbl 0816.90054 |

[20] | Gallego, G.; van Ryzin, G., A multiproduct dynamic pricing problem and its application to network yield management, Operations research, 45, 24-41, (1997) · Zbl 0889.90052 |

[21] | Glover, F.; Glover, R.; Lorenzo, J.; McMillan, C., The passenger-mix problem in the scheduled airlines, Interfaces, 12, 73-79, (1982) |

[22] | Karlin, S., Total positivity, (1968), Stanford University Press Stanford, CA |

[23] | Kincaid, W.M.; Darling, D.A., An inventory pricing problem, Journal of mathematical analysis and applications, 7, 183-208, (1963) · Zbl 0202.49103 |

[24] | Lee, T.C.; Hersh, M., A model for dynamic airline seat inventory control with multiple seat bookings, Transportation science, 27, 252-265, (1993) |

[25] | Lippman, S.A., Applying a new device in the optimization of exponential queuing systems, Operations research, 23, 687-710, (1975) · Zbl 0312.60048 |

[26] | Lippman, S.A., Countable-state, continuous-time dynamic programming with structure, Operations research, 24, 477-490, (1976) · Zbl 0353.90092 |

[27] | Littlewood, K., 1972. Forecasting and control of passengers. In: Proceedings of the Twelfth AGIFORS Symposium, pp. 95-128 |

[28] | McGill, J.I., 1989. Optimization and estimation problems in airline yield management, Ph.D. Dissertation, Commerce and Business Administration Program, University of British Columbia, Canada |

[29] | Mamer, J.W., Successive approximations for finite horizon, semi-Markov decision processes with application to asset liquidation, Operations research, 34, 638-644, (1986) · Zbl 0622.90089 |

[30] | Miller, B.L., Finite state continuous time Markov decision processes with a finite planning horizon, SIAM journal of control, 6, 266-280, (1968) · Zbl 0162.23302 |

[31] | Nair, S.K., Bapna, R., Lin, B., 1997. An application of yield management for internet service providers. Manufacturing and Services Operations Management, Department of Operations and Information Management, University of Connecticut, Storrs, CT, (to appear) |

[32] | Phillips, R.L., 1994. A marginal value approach to airline origin and destination revenue management. In: Henry, J., Yvon, J.P. (Eds.), Proceedings of the Sixteenth IFIP Conference on System Modeling and Optimization, Springer, New York · Zbl 0925.90248 |

[33] | Robinson, L.W., Optimal and approximate control policies for airline booking with sequential fare classes, Operations research, 43, 252-263, (1995) · Zbl 0832.90072 |

[34] | Rothstein, M., An airline overbooking model, Transportation science, 5, 180-192, (1971) |

[35] | Rothstein, M., O.R. and the airline overbooking problem, Operations research, 33, 237-248, (1985) |

[36] | Smith, B.C., 1993a. Market based yield management: it’s profitable and practical. In: Proceedings of the 1993 AGIFORS General Symposium |

[37] | Smith, B.C., 1993b. Continuous nesting. In: Proceedings of the IATA’s 5th Revenue Management Conference and Technical Briefing, Montreal, Canada, October, pp. 425-465 |

[38] | Smith, B.C.; Leimkuhler, J.F.; Darrow, R.M., Yield management at American airlines, Interfaces, 22, 8-31, (1992) |

[39] | Smith, S.A.; Achabal, D.D., Clearance pricing and inventory policies for retail chains, Management science, 44, 285-300, (1998) · Zbl 0989.90098 |

[40] | Soumis, F.; Nagurney, A., A stochastic, multiclass airline network equilibrium model, Operations research, 41, 721-730, (1993) · Zbl 0800.90409 |

[41] | Stadje, W., A full information pricing problem for the Sale of several identical commodities, Zeitschrift für operations research, 34, 161-181, (1990) · Zbl 0704.90007 |

[42] | Swan, B., 1994. Bid price methodology. In: Proceedings of the IATA’s Sixth Revenue Management Conference and Technical Briefing, Barcelona, Spain, October |

[43] | Talluri, K.; van Ryzin, G., An analysis of bid price controls for network revenue management, Management science, 44, 1577-1593, (1998) · Zbl 1004.90042 |

[44] | Wang, K., 1983. Optimum seat allocation for multi-leg flights with multiple fare types. In: Proceedings of the AGIFORS 23rd Annual Symposium, pp. 225-246 |

[45] | Weatherford, L.R.; Bodily, S.E., A taxonomy and research overview of perishable-asset revenue management: yield management, overbooking and pricing, Operations research, 40, 831-844, (1992) |

[46] | Williamson, E.L., 1992. Airline network seat control, Ph.D. Dissertation, MIT, Cambridge, MA |

[47] | Wollmer, R.D., An airline seat management model for a single leg route when lower fare classes book first, Operations research, 40, 26-37, (1992) · Zbl 0825.90664 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.