
-
Previous Article
A class of descent four–term extension of the Dai–Liao conjugate gradient method based on the scaled memoryless BFGS update
- JIMO Home
- This Issue
-
Next Article
Parametric solutions to the regulator-conjugate matrix equations
Distribution-free solutions to the extended multi-period newsboy problem
1. | School of Management, Guangdong University of Technology, Guangzhou 510520, China |
2. | School of Business Administration, Guangdong University of Finance & Economics, Guangzhou 510320, China |
This paper concerns the distribution-free, multi-period newsboy problem in which the newsboy has to decide the order quantity of the newspaper in the subsequent period without knowing the distribution of the demand. The Weak Aggregating Algorithm (WAA) developed in learning and prediction with expert advices makes decision only based on historical information and provides theoretical guarantee for the decision-making method. Based on the advantage of WAA and stationary expert advices, this paper continues providing distribution-free methods for the extended multi-period newsboy problems in which the shortage cost and the integral order quantities are considered. In particular, we provide an alternative proof for the theoretical result which guarantees the cumulative gain our proposed method achieves is as large as that of the best stationary expert advice. Numerical examples are provided to illustrate the effectiveness of our proposed methods.
References:
[1] |
S. Al-Binali,
A risk-reward framework for the competitive analysis of financial games, Algorithmica, 25 (1999), 99-115.
doi: 10.1007/PL00009285. |
[2] |
H. K. Alfares and H. H. Elmorra,
The distribution-free newsboy problem: extension to the shortage penalty case, International Journal of Production Economics, 93-94 (2005), 465-477.
doi: 10.1016/j.ijpe.2004.06.043. |
[3] |
O. Besbes and A. Muharremoglu, On implications of demand censoring in the newsvendor problem, Management Science, 59 (2013), 1407-1424. Google Scholar |
[4] |
A. Burnetas and C. Smith,
Adaptive ordering and pricing for perishable products, Operations Research, 48 (2000), 436-443.
doi: 10.1287/opre.48.3.436.12437. |
[5] |
N. Cesa-Bianchi and G. Lugosi,
Prediction, Learning, and Games, Cambridge University Press, Cambridge, 2006.
doi: 10.1017/CBO9780511546921. |
[6] |
L. L. Ding, X. M. Liu and Y. F. Xu,
Competitive risk management for online Bahncard problem, Journal of Industrial and Management Optimization, 6 (2010), 1-14.
doi: 10.3934/jimo.2010.6.1. |
[7] |
G. Gallego and I. Moon,
The distribution free newsboy problem: review and extensions, Journal of the Operational Research Society, 44 (1993), 825-834.
doi: 10.2307/2583894. |
[8] |
W. T. Huh, R. Levi, P. Rusmevichientong and J. B. Orlin,
Adaptive data-driven inventory control with censored demand based on Kaplan-Meier estimator, Operations Research, 59 (2011), 929-941.
doi: 10.1287/opre.1100.0906. |
[9] |
W. T. Huh and P. Rusmevichientong,
A non-parametric asymptotic analysis of inventory planning with censored demand, Mathematics of Operations Research, 34 (2009), 103-123.
doi: 10.1287/moor.1080.0355. |
[10] |
Y. Kalnishkan and M. V. Vyugin,
The weak aggregating algorithm and weak mixability, Journal of Computer and System Sciences, 74 (2008), 1228-1244.
doi: 10.1016/j.jcss.2007.08.003. |
[11] |
M. Keisuke,
The multi-period newsboy problem, European Journal of Operational Research, 171 (2006), 170-188.
doi: 10.1016/j.ejor.2004.08.030. |
[12] |
S. Kunnumkal and H. Topaloglu,
Using stochastic approximation methods to compute optimal base-stock levels in inventory inventory control problems, Operations Research, 56 (2008), 646-664.
doi: 10.1287/opre.1070.0477. |
[13] |
S. Kunnumkal and H. Topaloglu,
A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions, Mathematical Methods of Operations Research, 70 (2009), 477-504.
doi: 10.1007/s00186-008-0278-x. |
[14] |
T. Levina, Y. Levin, J. McGill, M. Nediak and V. Vovk,
Weak aggregating algorithm for the distribution-free perishable inventory problem, Operations Research Letters, 38 (2010), 516-521.
doi: 10.1016/j.orl.2010.09.006. |
[15] |
X. Lu, J. Song and K. Zhu,
Analysis of perishable-inventory systems with censored demand data, Operations Research, 56 (2008), 1034-1038.
doi: 10.1287/opre.1080.0553. |
[16] |
I. Moon and S. Choi, Distribution free newsboy problem with balking, Journal of the Operational Research Society, 46 (1995), 537-542. Google Scholar |
[17] |
I. Moon and S. Choi,
Distribution free procedures for make-to-order (MTO), make-in-advance (MIA), and composite policies, International Journal of Production Economics, 48 (1997), 21-28.
doi: 10.1016/S0925-5273(96)00026-6. |
[18] |
I. Moon and E. A. Silver, The multi-item newsvendor problem with a budget constraint and fixed ordering costs, Journal of the Operational Research Society, 51 (2000), 602-608. Google Scholar |
[19] |
G. R. Murray and E. A. Silver,
A Bayesian analysis of the style goods inventory problem, Management Science, 12 (1996), 785-797.
doi: 10.1287/mnsc.12.11.785. |
[20] |
H. Scarf, A min-max solution of an inventory problem, in: K. Arrow, S. Karlin, H. Scarf (Eds.), Studies in The Mathematical Theory of Inventory and Production, Stanford University Press, California, (1958), 201–209. Google Scholar |
[21] |
H. Scarf,
Bayes solution of the statistical inventory problem, Annals of Mathematical Statistics, 30 (1959), 490-508.
doi: 10.1214/aoms/1177706264. |
[22] |
G. L. Vairaktarakis, Robust multi-item newsboy models with abudget constraint, International Journal of Production Economics, 66 (2000), 213-226. Google Scholar |
[23] |
Y. Zhang, V. Vovk and W. G Zhang,
Probability-free solutions to the non-stationary newsvendor problem, Annals of Operation Research, 223 (2014), 433-449.
doi: 10.1007/s10479-014-1620-8. |
show all references
References:
[1] |
S. Al-Binali,
A risk-reward framework for the competitive analysis of financial games, Algorithmica, 25 (1999), 99-115.
doi: 10.1007/PL00009285. |
[2] |
H. K. Alfares and H. H. Elmorra,
The distribution-free newsboy problem: extension to the shortage penalty case, International Journal of Production Economics, 93-94 (2005), 465-477.
doi: 10.1016/j.ijpe.2004.06.043. |
[3] |
O. Besbes and A. Muharremoglu, On implications of demand censoring in the newsvendor problem, Management Science, 59 (2013), 1407-1424. Google Scholar |
[4] |
A. Burnetas and C. Smith,
Adaptive ordering and pricing for perishable products, Operations Research, 48 (2000), 436-443.
doi: 10.1287/opre.48.3.436.12437. |
[5] |
N. Cesa-Bianchi and G. Lugosi,
Prediction, Learning, and Games, Cambridge University Press, Cambridge, 2006.
doi: 10.1017/CBO9780511546921. |
[6] |
L. L. Ding, X. M. Liu and Y. F. Xu,
Competitive risk management for online Bahncard problem, Journal of Industrial and Management Optimization, 6 (2010), 1-14.
doi: 10.3934/jimo.2010.6.1. |
[7] |
G. Gallego and I. Moon,
The distribution free newsboy problem: review and extensions, Journal of the Operational Research Society, 44 (1993), 825-834.
doi: 10.2307/2583894. |
[8] |
W. T. Huh, R. Levi, P. Rusmevichientong and J. B. Orlin,
Adaptive data-driven inventory control with censored demand based on Kaplan-Meier estimator, Operations Research, 59 (2011), 929-941.
doi: 10.1287/opre.1100.0906. |
[9] |
W. T. Huh and P. Rusmevichientong,
A non-parametric asymptotic analysis of inventory planning with censored demand, Mathematics of Operations Research, 34 (2009), 103-123.
doi: 10.1287/moor.1080.0355. |
[10] |
Y. Kalnishkan and M. V. Vyugin,
The weak aggregating algorithm and weak mixability, Journal of Computer and System Sciences, 74 (2008), 1228-1244.
doi: 10.1016/j.jcss.2007.08.003. |
[11] |
M. Keisuke,
The multi-period newsboy problem, European Journal of Operational Research, 171 (2006), 170-188.
doi: 10.1016/j.ejor.2004.08.030. |
[12] |
S. Kunnumkal and H. Topaloglu,
Using stochastic approximation methods to compute optimal base-stock levels in inventory inventory control problems, Operations Research, 56 (2008), 646-664.
doi: 10.1287/opre.1070.0477. |
[13] |
S. Kunnumkal and H. Topaloglu,
A stochastic approximation method for the single-leg revenue management problem with discrete demand distributions, Mathematical Methods of Operations Research, 70 (2009), 477-504.
doi: 10.1007/s00186-008-0278-x. |
[14] |
T. Levina, Y. Levin, J. McGill, M. Nediak and V. Vovk,
Weak aggregating algorithm for the distribution-free perishable inventory problem, Operations Research Letters, 38 (2010), 516-521.
doi: 10.1016/j.orl.2010.09.006. |
[15] |
X. Lu, J. Song and K. Zhu,
Analysis of perishable-inventory systems with censored demand data, Operations Research, 56 (2008), 1034-1038.
doi: 10.1287/opre.1080.0553. |
[16] |
I. Moon and S. Choi, Distribution free newsboy problem with balking, Journal of the Operational Research Society, 46 (1995), 537-542. Google Scholar |
[17] |
I. Moon and S. Choi,
Distribution free procedures for make-to-order (MTO), make-in-advance (MIA), and composite policies, International Journal of Production Economics, 48 (1997), 21-28.
doi: 10.1016/S0925-5273(96)00026-6. |
[18] |
I. Moon and E. A. Silver, The multi-item newsvendor problem with a budget constraint and fixed ordering costs, Journal of the Operational Research Society, 51 (2000), 602-608. Google Scholar |
[19] |
G. R. Murray and E. A. Silver,
A Bayesian analysis of the style goods inventory problem, Management Science, 12 (1996), 785-797.
doi: 10.1287/mnsc.12.11.785. |
[20] |
H. Scarf, A min-max solution of an inventory problem, in: K. Arrow, S. Karlin, H. Scarf (Eds.), Studies in The Mathematical Theory of Inventory and Production, Stanford University Press, California, (1958), 201–209. Google Scholar |
[21] |
H. Scarf,
Bayes solution of the statistical inventory problem, Annals of Mathematical Statistics, 30 (1959), 490-508.
doi: 10.1214/aoms/1177706264. |
[22] |
G. L. Vairaktarakis, Robust multi-item newsboy models with abudget constraint, International Journal of Production Economics, 66 (2000), 213-226. Google Scholar |
[23] |
Y. Zhang, V. Vovk and W. G Zhang,
Probability-free solutions to the non-stationary newsvendor problem, Annals of Operation Research, 223 (2014), 433-449.
doi: 10.1007/s10479-014-1620-8. |





100 | 200 | 300 | 400 | |
DAS | 3864/3721 | 6843/6211 | 9978/8928 | 12672/11339 |
1520/-1966 | 3040/-3218 | 4560/-4568 | 6080/-5582 | |
2635/325 | 5093/1089 | 7678/1952 | 10187/3033 | |
3497/2223 | 6489/4375 | 9531/6507 | 12396/8700 | |
3955/3493 | 6923/6167 | 10068/9018 | 12733/11459 | |
3780/3780 | 6269/6269 | 8936/8936 | 10995/10995 | |
Ratios | 0.977/0.984 | 0.988/0.986 | 0.991/0.990 | 0.995/0.989 |
100 | 200 | 300 | 400 | |
DAS | 3864/3721 | 6843/6211 | 9978/8928 | 12672/11339 |
1520/-1966 | 3040/-3218 | 4560/-4568 | 6080/-5582 | |
2635/325 | 5093/1089 | 7678/1952 | 10187/3033 | |
3497/2223 | 6489/4375 | 9531/6507 | 12396/8700 | |
3955/3493 | 6923/6167 | 10068/9018 | 12733/11459 | |
3780/3780 | 6269/6269 | 8936/8936 | 10995/10995 | |
Ratios | 0.977/0.984 | 0.988/0.986 | 0.991/0.990 | 0.995/0.989 |
TN | 10 | 20 | 30 | 40 |
AVE | 0.9861/0.9917 | 0.9821/0.9904 | 0.9802/0.9905 | 0.9800/0.9910 |
STD | 0.0152/0.0041 | 0.0135/0.0035 | 0.0147/0.0037 | 0.0148/0.0034 |
TN | 10 | 20 | 30 | 40 |
AVE | 0.9861/0.9917 | 0.9821/0.9904 | 0.9802/0.9905 | 0.9800/0.9910 |
STD | 0.0152/0.0041 | 0.0135/0.0035 | 0.0147/0.0037 | 0.0148/0.0034 |
trial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
DAS | 235 | 110 | 164 | 185 | 153 | 227 | 158 | 188 | 196 | 150 |
ANS | 241 | 106 | 159 | 180 | 151 | 211 | 153 | 183 | 192 | 147 |
trial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
DAS | 235 | 110 | 164 | 185 | 153 | 227 | 158 | 188 | 196 | 150 |
ANS | 241 | 106 | 159 | 180 | 151 | 211 | 153 | 183 | 192 | 147 |
[1] |
Hong Seng Sim, Wah June Leong, Chuei Yee Chen, Siti Nur Iqmal Ibrahim. Multi-step spectral gradient methods with modified weak secant relation for large scale unconstrained optimization. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 377-387. doi: 10.3934/naco.2018024 |
[2] |
Kaifang Liu, Lunji Song, Shan Zhao. A new over-penalized weak galerkin method. Part Ⅰ: Second-order elliptic problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2411-2428. doi: 10.3934/dcdsb.2020184 |
[3] |
Namsu Ahn, Soochan Kim. Optimal and heuristic algorithms for the multi-objective vehicle routing problem with drones for military surveillance operations. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021037 |
[4] |
J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control & Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008 |
[5] |
Jian Yang, Bendong Lou. Traveling wave solutions of competitive models with free boundaries. Discrete & Continuous Dynamical Systems - B, 2014, 19 (3) : 817-826. doi: 10.3934/dcdsb.2014.19.817 |
[6] |
Demetres D. Kouvatsos, Jumma S. Alanazi, Kevin Smith. A unified ME algorithm for arbitrary open QNMs with mixed blocking mechanisms. Numerical Algebra, Control & Optimization, 2011, 1 (4) : 781-816. doi: 10.3934/naco.2011.1.781 |
[7] |
Dmitry Treschev. A locally integrable multi-dimensional billiard system. Discrete & Continuous Dynamical Systems - A, 2017, 37 (10) : 5271-5284. doi: 10.3934/dcds.2017228 |
[8] |
Ritu Agarwal, Kritika, Sunil Dutt Purohit, Devendra Kumar. Mathematical modelling of cytosolic calcium concentration distribution using non-local fractional operator. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021017 |
[9] |
Mingxin Wang, Qianying Zhang. Dynamics for the diffusive Leslie-Gower model with double free boundaries. Discrete & Continuous Dynamical Systems - A, 2018, 38 (5) : 2591-2607. doi: 10.3934/dcds.2018109 |
[10] |
Yizhuo Wang, Shangjiang Guo. A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1627-1652. doi: 10.3934/dcdsb.2018223 |
[11] |
Joel Fotso Tachago, Giuliano Gargiulo, Hubert Nnang, Elvira Zappale. Multiscale homogenization of integral convex functionals in Orlicz Sobolev setting. Evolution Equations & Control Theory, 2021, 10 (2) : 297-320. doi: 10.3934/eect.2020067 |
[12] |
Caifang Wang, Tie Zhou. The order of convergence for Landweber Scheme with $\alpha,\beta$-rule. Inverse Problems & Imaging, 2012, 6 (1) : 133-146. doi: 10.3934/ipi.2012.6.133 |
[13] |
Alexandre B. Simas, Fábio J. Valentim. $W$-Sobolev spaces: Higher order and regularity. Communications on Pure & Applied Analysis, 2015, 14 (2) : 597-607. doi: 10.3934/cpaa.2015.14.597 |
[14] |
Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022 |
[15] |
Alexandr Mikhaylov, Victor Mikhaylov. Dynamic inverse problem for Jacobi matrices. Inverse Problems & Imaging, 2019, 13 (3) : 431-447. doi: 10.3934/ipi.2019021 |
[16] |
Armin Lechleiter, Tobias Rienmüller. Factorization method for the inverse Stokes problem. Inverse Problems & Imaging, 2013, 7 (4) : 1271-1293. doi: 10.3934/ipi.2013.7.1271 |
[17] |
Carlos Fresneda-Portillo, Sergey E. Mikhailov. Analysis of Boundary-Domain Integral Equations to the mixed BVP for a compressible stokes system with variable viscosity. Communications on Pure & Applied Analysis, 2019, 18 (6) : 3059-3088. doi: 10.3934/cpaa.2019137 |
[18] |
Saima Rashid, Fahd Jarad, Zakia Hammouch. Some new bounds analogous to generalized proportional fractional integral operator with respect to another function. Discrete & Continuous Dynamical Systems - S, 2021 doi: 10.3934/dcdss.2021020 |
[19] |
Qian Liu. The lower bounds on the second-order nonlinearity of three classes of Boolean functions. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2020136 |
[20] |
Zaihong Wang, Jin Li, Tiantian Ma. An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1995-1997. doi: 10.3934/dcdsb.2013.18.1995 |
2019 Impact Factor: 1.366
Tools
Metrics
Other articles
by authors
[Back to Top]