American Institute of Mathematical Sciences

Advanced
April  2009, 5(2): 391-402. doi: 10.3934/jimo.2009.5.391

Censored newsvendor model revisited with unnormalized probabilities

Alain Bensoussan 1, , Metin Çakanyildirim 2, and  Suresh P. Sethi 3,

1. 

International Center for Decision and Risk Analysis, School of Management, P.O.Box 830688, SM 30, University of Texas at Dallas, Richardson, TX 75083-0688, United States
2. 

School of Management, P.O.Box 830688, SM 30, University of Texas at Dallas, Richardson, TX 75083-0688, United States
3. 

Center for Intelligent Supply Networks, School of Management, P.O.Box 830688, SM 30, University of Texas at Dallas, Richardson, TX 75083-0688, United States

Received  April 2008 Revised  October 2008 Published  April 2009

This paper revisits the model of the censored newsvendor presented by Ding, Puterman and Bisi [8], We analyze that model in an infinite-horizon context by using the interesting concept of unnormalized probabilities. The unnormalized probabilities considerably simplify the dynamic programming equation and facilitate the proof of the existence of an optimal policy. They can also be used to give a simple, alternative proof to Ding et al.'s claim that the myopic order quantity is always less than or equal to the optimal order quantity. Importantly, the concept of unnormalized probabilities can be used to treat other important operations research problems with partial observations.
Keywords: Unnormalized probabilities, unobserved unmet demand, newsvendor problem..
Mathematics Subject Classification: Primary: 93C41, 93C41; Secondary: 49L2.
Citation: Alain Bensoussan, Metin Çakanyildirim, Suresh P. Sethi. Censored newsvendor model revisited with unnormalized probabilities. Journal of Industrial & Management Optimization, 2009, 5 (2) : 391-402. doi: 10.3934/jimo.2009.5.391
[1]

Reza Lotfi, Gerhard-Wilhelm Weber, S. Mehdi Sajadifar, Nooshin Mardani. Interdependent demand in the two-period newsvendor problem. Journal of Industrial & Management Optimization, 2020, 16 (1) : 117-140. doi: 10.3934/jimo.2018143
[2]

Yuwei Shen, Jinxing Xie, Tingting Li. The risk-averse newsvendor game with competition on demand. Journal of Industrial & Management Optimization, 2016, 12 (3) : 931-947. doi: 10.3934/jimo.2016.12.931
[3]

Rafał Kamocki, Marek Majewski. On the continuous dependence of solutions to a fractional Dirichlet problem. The case of saddle points. Discrete & Continuous Dynamical Systems - B, 2014, 19 (8) : 2557-2568. doi: 10.3934/dcdsb.2014.19.2557
[4]

Gabriella Pinzari. Global Kolmogorov tori in the planetary $\boldsymbol N$-body problem. Announcement of result. Electronic Research Announcements, 2015, 22: 55-75. doi: 10.3934/era.2015.22.55
[5]

Wei Liu, Shiji Song, Ying Qiao, Han Zhao. The loss-averse newsvendor problem with random supply capacity. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1417-1429. doi: 10.3934/jimo.2016080
[6]

Yong Zhang, Huifen Zhong, Yue Liu, Menghu Huang. Online ordering strategy for the discrete newsvendor problem with order value-based free-shipping. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1617-1630. doi: 10.3934/jimo.2018114
[7]

Paulina Ávila-Torres, Fernando López-Irarragorri, Rafael Caballero, Yasmín Ríos-Solís. The multimodal and multiperiod urban transportation integrated timetable construction problem with demand uncertainty. Journal of Industrial & Management Optimization, 2018, 14 (2) : 447-472. doi: 10.3934/jimo.2017055
[8]

Ming Chen, Chongchao Huang. A power penalty method for the general traffic assignment problem with elastic demand. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1019-1030. doi: 10.3934/jimo.2014.10.1019
[9]

Shouyu Ma, Zied Jemai, Evren Sahin, Yves Dallery. Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts. Journal of Industrial & Management Optimization, 2018, 14 (3) : 931-951. doi: 10.3934/jimo.2017083
[10]

Jia Shu, Zhengyi Li, Weijun Zhong. A market selection and inventory ordering problem under demand uncertainty. Journal of Industrial & Management Optimization, 2011, 7 (2) : 425-434. doi: 10.3934/jimo.2011.7.425
[11]

Drew Fudenberg, David K. Levine. Tail probabilities for triangular arrays. Journal of Dynamics & Games, 2014, 1 (1) : 45-56. doi: 10.3934/jdg.2014.1.45
[12]

Hajnal R. Tóth. Infinite Bernoulli convolutions with different probabilities. Discrete & Continuous Dynamical Systems - A, 2008, 21 (2) : 595-600. doi: 10.3934/dcds.2008.21.595
[13]

Adrian Tudorascu. On absolutely continuous curves of probabilities on the line. Discrete & Continuous Dynamical Systems - A, 2019, 39 (9) : 5105-5124. doi: 10.3934/dcds.2019207
[14]

Ido Polak, Nicolas Privault. A stochastic newsvendor game with dynamic retail prices. Journal of Industrial & Management Optimization, 2018, 14 (2) : 731-742. doi: 10.3934/jimo.2017072
[15]

Artur O. Lopes, Elismar R. Oliveira. Entropy and variational principles for holonomic probabilities of IFS. Discrete & Continuous Dynamical Systems - A, 2009, 23 (3) : 937-955. doi: 10.3934/dcds.2009.23.937
[16]

Fabio Camilli, Lars Grüne. Characterizing attraction probabilities via the stochastic Zubov equation. Discrete & Continuous Dynamical Systems - B, 2003, 3 (3) : 457-468. doi: 10.3934/dcdsb.2003.3.457
[17]

Leandro Cioletti, Artur O. Lopes. Interactions, specifications, DLR probabilities and the Ruelle operator in the one-dimensional lattice. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6139-6152. doi: 10.3934/dcds.2017264
[18]

Ángel Arroyo, Joonas Heino, Mikko Parviainen. Tug-of-war games with varying probabilities and the normalized p(x)-laplacian. Communications on Pure & Applied Analysis, 2017, 16 (3) : 915-944. doi: 10.3934/cpaa.2017044
[19]

Feng Zhang, Jinting Wang, Bin Liu. Equilibrium joining probabilities in observable queues with general service and setup times. Journal of Industrial & Management Optimization, 2013, 9 (4) : 901-917. doi: 10.3934/jimo.2013.9.901
[20]

Zhenwei Luo, Jinting Wang. The optimal price discount, order quantity and minimum quantity in newsvendor model with group purchase. Journal of Industrial & Management Optimization, 2015, 11 (1) : 1-11. doi: 10.3934/jimo.2015.11.1

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (26)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences