Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T17:11:47.575Z Has data issue: false hasContentIssue false
  • English
  • Français

PRICING PERISHABLE PRODUCTS WITH COMPOUND POISSON DEMANDS

Published online by Cambridge University Press:  17 May 2011

Pengfei Guo ,
Zhaotong Lian  and
Yulan Wang
Pengfei Guo
Affiliation:
Department of Logistics and Maritime Studies, Hong Kong Polytechnic University, Hong Kong E-mail: lgtpguo@polyu.edu.hk
Zhaotong Lian
Affiliation:
Faculty of Business Administration, University of Macau, Macau E-mail: lianzt@umac.mo
Yulan Wang
Affiliation:
Institute of Textiles and Clothing, Hong Kong Polytechnic University, Hong Kong E-mail: yulan.wang@inet.polyu.edu.hk
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider the dynamic pricing problem of perishable products in a system with a constant production rate. Potential demands arrive according to a compound Poisson process, and are price-sensitive. We carry out the sample path analysis of the inventory process and by using level-crossing method, we derive its stationary distribution given a pricing function. Based on the distribution, we express the average profit function. By a stochastic comparison approach, we characterize the pricing strategy given different customers willingness-to-pay functions. Finally, we provide an approximation algorithm to calculate the optimal pricing function.

Keywords

revenue managementdynamic pricingperishable inventorylevel-crossing
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 25 , Issue 3 , July 2011 , pp. 289 - 306
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Ata, B. & Shneorson, S. (2006). Dynamic control of an M/M/1 service system with adjustable arrival and service rates. Management Science 52: 1778–1791.CrossRefGoogle Scholar
2.Aydin, G. & Ziya, S. (2008). Pricing promotional products under upselling. Manufacturing and Service Operations Management 10: 360–376.CrossRefGoogle Scholar
3.Bar-Lev, S., David, P. & Stadje, W. (2005). Control policies for inventory systems with perishable items: Outsourcing and urgency classes. Probability in the Engineering and Informational Sciences 19: 309–326.CrossRefGoogle Scholar
4.Bertsekas, D. (1995). Dynamic programming and optimal control, Vol. 1. Belmont, MA: Athena Scientific.Google Scholar
5.Bitran, G. & Caldentey, R. (2003). An overview of pricing models for revenue management. Manufacturing and Service Operations Management 5: 203–229.CrossRefGoogle Scholar
6.Brill, H. & Posner, M. (1977). Level crossings in point processes applied to queues: Single server case. Operations Research 25: 662–673.CrossRefGoogle Scholar
7.Cooper, W. & Gupta, D. (2006). Stochastic comparisons in airline revenue management. Manufacturing and Service Operations Management 8: 221–234.CrossRefGoogle Scholar
8.Elmaghraby, W., Gulcu, A. & Keskinocak, P. (2004). Optimal markdown mechanisms in the presence of rational customers with multi-unit demands. Working Paper, Georgia Insitute of Technology, School of Industrial and Systems Engineering.Google Scholar
9.Elmaghraby, W. & Keskinocak, P. (2003). Dynamic pricing in the presence of inventory considerations: Research overview, current practices and future directions. Management Science 49: 1287–1309.CrossRefGoogle Scholar
10.Fries, B. (1975). Optimal ordering policy for a perishable commodity with fixed lifetime. Operations Research 23: 46–61.CrossRefGoogle Scholar
11.Gallego, G. & van Ryzin, G. (1994). Optimal dynamic pricing of inventories with stochastic demand over finite horizions. Management Science 40: 999–1020.CrossRefGoogle Scholar
12.Graves, S. (1982). The application of queueing theory to continuous perishable inventory systems. Management Science 28: 400–406.CrossRefGoogle Scholar
13.Guo, P. & Zipkin, P. (2009). The effects of information on a queue with balking and phase-type service times. Naval Research Logistics 55: 406–411.CrossRefGoogle Scholar
14.Kaspi, H. & Perry, D. (1983). Inventory system on perishable commodities. Advances in Applied Probability 15: 674–685.CrossRefGoogle Scholar
15.Lariviere, M. (2006). A note on probability distributions with increasing generalized failure rates. Operations Research 54: 602–604.CrossRefGoogle Scholar
16.Lian, Z. & Liu, L. (2001). An (s, S) continuous review perishable inventory system: Models and heuristics. IIE Transactions 33: 809–822.CrossRefGoogle Scholar
17.Liu, L. & Lian, Z. (1999). An (s, S) continuous review model for perishable inventory. Operations Research 47: 150–158.CrossRefGoogle Scholar
18.Nahmias, S. (1975). Optimal ordering policies for perishable inventory—II. Operations Research 23: 735–749.CrossRefGoogle Scholar
19.Nahmias, S. (1982). Approximation techniques for several stochastic inventory models, Computers and Operations Research 30: 141–158.Google Scholar
20.Nahmias, S., Perry, D. & Stafje, W. (2004). Acturial valuation of perishable inventory systems. Probability in the Engineering and Information Sciences 18: 219–232.CrossRefGoogle Scholar
21.Nahmias, S., Perry, D. & Stafje, W. (2004). Perishable inventory systems with variable input and demand rates. Mathematical Methods of Operations Research 60: 155–162.CrossRefGoogle Scholar
22.Neuts, M. (1981). Matrix-geometric solutions in stochastic models: An algorthmic approach. New York: Dover.Google Scholar
23.Perry, D. (1999). Analysis of a sampling control scheme for a perishable inventory system. Operations Research 47: 966–973.CrossRefGoogle Scholar
24.Perry, D. & Stadje, W. (2001). Disaters in Markovian inventory systems for perishable items. Advances in Applied Probability 33: 61–75.CrossRefGoogle Scholar
25.Ravichandran, N.Stochastic analysis of a continuous review perishable inventory system with positive lead time and Poisson demand. ( 1995). European Journal of Operational Research 84: 444–457.CrossRefGoogle Scholar
26.Schmidt, C. & Nahmias, S. (1985). Policies for perishable inventory. Management Science 31: 719–728.CrossRefGoogle Scholar
27.Shaked, M. & Shanthikumar, J. (2006). Stochastic orders. New York: Springer-Verlag.Google Scholar
28.Stidham, S. & Weber, R. (1989). Monotonic and insensitive optimal policies for control of queues with undiscounted costs. Operations Research 87: 611–625.CrossRefGoogle Scholar
29.Topkis, D. (1998). Supermodularity and complementarity. Princeton, NJ: Princeton University Press.Google Scholar
30.Weiss, H. (1980). Optimal ordering policies for continuous review perishable inventory models. Operations Research 28: 365–374.CrossRefGoogle ScholarPubMed
31.Yossi, A. & Pazgal, A. (2008). Optimal pricing of seasonal products in the presence of forward-looking consumers. Manufacturing and Service Operations Management, 10: 339–359.Google Scholar
32.Zhang, D. & Cooper, W. (2005). Revenue management for parallel flights with customer choice behavior. Operations Research 53: 415–431.CrossRefGoogle Scholar
33.Ziya, S., Ayhan, H. & Foley, R. (2004). Relationships among three assumptions in revenue management. Operations Research 52: 804–809.CrossRefGoogle Scholar