Download presentation

Presentation is loading. Please wait.

Published byAlina Massingale Modified over 2 years ago

1
1 Robust Newsvendor Competition Houyuan Jiang (Cambridge Judge Business School) Serguei Netessine (The Wharton School of Business) Sergei Savin (Columbia Graduate School of Business)

2
2 Outline Newsvendor problem and robust optimization Maximin/worst-case criterion Absolute regret criterion Relative regret criterion Computational comparisons

3
3 Newsvendor competition (Netessine-Rudi, 03) p i : Unit price c i : Unit cost D i : Demand random variable F i : CDF for D i Q i : Production quantity o ij: : Overflow rate from newsvendor j to newsvendor i

4
4 What demand information is available Moments: Mean, standard deviation, etc Shape: Support, symmetry, uni-modality, etc We assume that we only know demand supports

5
5 Robust approaches Maximin/worst-case: Scarf (58), Gallego-Moon (93), Bental-Nemirovsky (99), Bertsimas- Sim (04), Aghassi-Bertsimas (06) Absolute regret: Savage (51), Kasugi-Kasegai (61), Variraktarakis (00), Perakis-Roels (05), Perakis-Roels (06), Perakis-Roels (07), Yue et al (07) Relative regret/competitive ratio: Ball-Queyranne (05), Lan et al (06), Zhu et al (06) Maximum entropy: Jaynes (57), Eren-Maglaras (06)

6
6 Maximin criterion Monopoly: Optimal quantity order for newsvendor i is the lower bound of their demand support, A i Competition: Optimal quantity order for newsvendor i is still the lower bound of their demand support, A i

7
7 Absolute regret: Definition

8
8 Absolute regret: Results 1. There exists a Nash equilibrium and the response function is 2. There exists a unique Nash equilibrium if 3. There exists one newsvendor such that its quantity order does not exceed the upper bound of its demand support 4. There exists a unique Nash equilibrium for a symmetric game:

9
9 Absolute regret: Results (N = 2) There exists a unique closed-form Nash equilibrium Which is

10
10 Relative regret: Definition

11
11 Regret regret: Results 1. There exists a Nash equilibrium and the response function is 2. There exists a unique Nash equilibrium if 3. There exists one newsvendor such that its quantity order does not exceed the upper bound of its demand support 4. There exists a unique Nash equilibrium for a symmetric game:

12
12 Relative regret: Results (N = 2) There exists a closed-form Nash equilibrium Which is unique Which is unique for some cases

13
13 Symmetric game: Support sensitivity Basic data: N = 2 [A,B]=[20,70] p=20 c=10 o=0.5

14
14 Symmetric game: Price sensitivity

15
15 Symmetric game: Overflow sensitivity

16
16 Asymmetric game: Support sensitivity

17
17 Symmetric game: Price sensitivity

18
18 Symmetric game: Overflow sensitivity

19
19 Ex-ante and ex-post versions Ex-ante: Evaluate performance measures before demand realization is known Ex-post: Evaluate performance measures after demand realization is known

20
20 Conclusions and future research Ex-ante and ex-post versions are equivalent when only demand supports are available We obtained closed-form response functions and some closed-form Nash equilibrium Absolute regret criterion is most robust Robust games with additional information Robust games with asymmetric information

21
21 Thank you

22
22 Maximin criterion: Definition Ex-ante Ex-post

23
23 Absolute regret: Definition Ex-ante Ex-post

24
24 Relative regret: Definition Ex-ante Ex-post

Similar presentations

OK

BART VANLUYTEN, JAN C. WILLEMS, BART DE MOOR 44 th IEEE Conference on Decision and Control 12-15 December 2005 Model Reduction of Systems with Symmetries.

BART VANLUYTEN, JAN C. WILLEMS, BART DE MOOR 44 th IEEE Conference on Decision and Control 12-15 December 2005 Model Reduction of Systems with Symmetries.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google