American Institute of Mathematical Sciences

Advanced
  • Previous Article
    Inventory replenishment policies for two successive generations price-sensitive technology products
  • JIMO Home
  • This Issue
  • Next Article
    Sharp bounds on the minimum $M$-eigenvalue and strong ellipticity condition of elasticity $Z$-tensors-tensors
doi: 10.3934/jimo.2021180
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

A new data-driven robust optimization approach to multi-item newsboy problems

Ying Kou and  Zhong Wan ,

School of Mathematics and Statistics, Central South University, Changsha 410083, China

* Corresponding authors: Zhong Wan

Received  May 2021 Revised  August 2021 Early access October 2021

Fund Project: This research is supported by the National Social Science Foundation of China (Grant No. 21BGL122)

A newsboy problem is a typical stochastic inventory management problem and has extensive applications in the fields of operational research, management sciences and marketing sciences. One of the challenges underlying such problems is to handle the uncertainty of demands. In the existing results, it is often to assume that the demand distribution is given to facilitate solution of the problems. In this paper, a novel data-driven robust optimization model for solving multi-item newsboy problems is proposed by combining the absolute robust optimization with a data-driven uncertainty set, and the latter is leveraged to address the uncertainty of demands. For the single-item situation, a closed-form solution is obtained and influences of parameters on the optimal solutions are analyzed. Owing to complexity of the multi-item situation, a uniform smoothing function is leveraged to smooth the proposed model. Then, an algorithm, called a modified Frank-Wolfe feasible direction algorithm, is developed to solve a series of smooth subproblems. Numerical simulation demonstrates that the proposed model in this paper can reduce over-conservation of robust optimization methods and is more robust than other similar well-established methods in the literature. By numerical simulation and sensitivity analysis, it is concluded that: (1) The proposed method can provide more stable optimal order policy and profits than the existing ones; (2) For a product with a higher unit purchase price, the optimal order quantities are more sensitive to its change; (3) In view of profitability, the newsboy should not to be too risk-averse.

Keywords: Data-driven, newsboy problem, uncertainty set, robustness, uniform smooth approximation.
Mathematics Subject Classification: Primary: 90B06, 62K05; Secondary: 68T37.
Citation: Ying Kou, Zhong Wan. A new data-driven robust optimization approach to multi-item newsboy problems. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021180
References:
[1]

M. A. Abdel-Aal and S. Z. Selim, Robust optimization for selective newsvendor problem with uncertain demand, Computers & Industrial Engineering, 135 (2019), 838-854.  doi: 10.1016/j.cie.2019.06.047.  Google Scholar

[2]

L. L. Abdel-Malek and N. Areeratchakul, A quadratic programming approach to the multi-product newsboy problem with side constraints, European J. Oper. Res., 176 (2007), 1607-1619.  doi: 10.1016/j.ejor.2005.11.002.  Google Scholar

[3]

K. J. Arrow, T. Harris and J. Marschak, Optimal inventory policy, Econometrica, 19 (1951), 250-272.  doi: 10.2307/1906813.  Google Scholar

[4]

A. Ben-Tal and A. Nemirovski, Robust optimization-methodology and applications, Math. Program., 92 (2002), 453-480.  doi: 10.1007/s101070100286.  Google Scholar

[5]

A. Ben-Tal and A. Nemirovski, Robust solutions of uncertain linear programs, Oper. Res. Lett., 25 (1999), 1-13.  doi: 10.1016/S0167-6377(99)00016-4.  Google Scholar

[6]

Y. Cao and Z. J. M. Shen, Quantile forecasting and data-driven inventory management under nonstationary demand, Oper. Res. Lett., 47 (2019), 465-472.  doi: 10.1016/j.orl.2019.08.008.  Google Scholar

[7]

E. Carrizosa, A. V. Olivares-Nadal and P. Ram$\acute{i}$rez-Cobo, Robust newsvendor problem with autoregressive demand, Comput. Oper. Res., 68 (2016), 123-133.  doi: 10.1016/j.cor.2015.11.002.  Google Scholar

[8]

L. H. Chen and Y. C. Chen, A multiple-item budget-constraint newsboy problem with a reservation policy, Omega, 38 (2010), 431-439.  doi: 10.1016/j.omega.2009.10.007.  Google Scholar

[9]

Z. Chen, S. Peng and J. Liu, Data-driven robust chance constrained problems: A mixture model approach, J. Optim. Theory Appli., 179 (2018), 1065-1085.  doi: 10.1007/s10957-018-1376-4.  Google Scholar

[10]

X. Chen, Smoothing methods for nonsmooth, nonconvex minimization, Math. Program., 134 (2012), 71-99.  doi: 10.1007/s10107-012-0569-0.  Google Scholar

[11]

S. Deng, Z. Wan and Y. Zhou, Optimization model and solution method for dynamically correlated two-product newsboy problems based on Copula, Discrete Contin. Dyn. Syst. Ser. S, 13 (2018), 1637-1652.  doi: 10.3934/dcdss.2020096.  Google Scholar

[12]

K. W. Ding, N. J. Huang and Y. B. Xiao, Distributionally robust chance constrained problems under general moments information, J. Ind. Manag. Optim., 16 (2020), 2923-2942.  doi: 10.3934/jimo.2019087.  Google Scholar

[13]

F. Fang, T. D. Nguyen and C. S. Currie, Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty, European J. Oper. Res., 293 (2021), 594-602.  doi: 10.1016/j.ejor.2020.08.002.  Google Scholar

[14]

A. Fuduli, M. Gaudioso and G. Giallombardo, Minimizing nonconvex nonsmooth functions via cutting planes and proximity control, SIAM J. Optim., 14 (2003), 743-756.  doi: 10.1137/S1052623402411459.  Google Scholar

[15]

R. Huang, S. Qu, X. Yang and Z. Liu, Multi-stage distributionally robust optimization with risk aversion, J. Ind. Manag. Optim., 17 (2021), 233-259.  doi: 10.3934/jimo.2019109.  Google Scholar

[16]

J. Huber, S. M$\ddot{u}$ller, M. Fleischmann and H. Stuckenschmidt, A data-driven newsvendor problem: From data to decision, European J. Oper. Res., 278 (2019), 904-915.  doi: 10.1016/j.ejor.2019.04.043.  Google Scholar

[17]

O. Jadidi, M. Y. Jaber, S. Zolfaghri, R. Pinto and F. Firouzi, Dynamic pricing and lot sizing for a newsvendor problem with supplier selection, quantity discounts, and limited supply capacity, Computers & Industrial Engineering, 154 (2021), 107113.  doi: 10.1016/j.cie.2021.107113.  Google Scholar

[18]

A. Jalilvand-Nejad, R. Shafaei and H. Shahriari, Robust optimization under correlated polyhedral uncertainty set, Computers & Industrial Engineering, 92 (2016), 82-94.  doi: 10.1016/j.cie.2015.12.006.  Google Scholar

[19]

G. J. Kyparisis and C. Koulamas, The price-setting newsvendor problem with nonnegative linear additive demand, European J. Oper. Res., 269 (2018), 695-698.  doi: 10.1016/j.ejor.2018.02.019.  Google Scholar

[20]

R. Levi, G. Perakis and J. Uichanco, The data-driven newsvendor problem: New bounds and insights, Oper. Res., 63 (2015), 1294-1306.  doi: 10.1287/opre.2015.1422.  Google Scholar

[21]

C. Ning and F. You, Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods, Computers & Chemical Engineering, 112 (2018), 190-210.  doi: 10.1016/j.compchemeng.2018.02.007.  Google Scholar

[22]

D. Noll, Cutting plane oracles to minimize non-smooth non-convex functions, Set-Valued Var. Anal., 18 (2010), 531-568.  doi: 10.1007/s11228-010-0159-3.  Google Scholar

[23]

S. Punia, S. P. Singh and J. K. Madaan, From predictive to prescriptive analytics: A data-driven multi-item newsvendor model, Decision Support Systems, 136 (2020), 113340.  doi: 10.1016/j.dss.2020.113340.  Google Scholar

[24]

Y. Qin, R. Wang, A. J. Vakharia, Y. Chen and M. M. Seref, The newsvendor problem: Review and directions for future research, European J. Oper. Res., 213 (2011), 361-374.  doi: 10.1016/j.ejor.2010.11.024.  Google Scholar

[25]

R. Qiu, Y. Sun and M. Sun, A distributionally robust optimization approach for multi-product inventory decisions with budget constraint and demand and yield uncertainties, Comput. Oper. Res., 126 (2021), 105081.  doi: 10.1016/j.cor.2020.105081.  Google Scholar

[26]

R. Qiu, Y. Sun, Z. P. Fan and M. Sun, Robust multi-product inventory optimization under support vector clustering-based data-driven demand uncertainty set, Soft Computing, 24 (2019), 6259-6275.  doi: 10.1007/s00500-019-03927-2.  Google Scholar

[27]

A. L. Sachs and S. Minner, The data-driven newsvendor with censored demand observations, International Journal of Production Economics, 149 (2014), 28-36.   Google Scholar

[28]

H. E. Scarf, A Min-Max Solution of an Inventory Problem, Rand Corp Santa Monica Calif, 1957. Google Scholar

[29]

N. Turken, Y. Tan, A. J. Vakharia, L. Wang, R. Wang and A. Yenipazarli, The multi-product newsvendor problem: Review, extensions, and directions for future research, Handbook of Newsboy Problems, 176 (2012), 3-39.  doi: 10.1007/978-1-4614-3600-3_1.  Google Scholar

[30]

G. L. Vairaktarakis, Robust multi-item newsboy models with a budget constraint, International Journal of Production Economics, 66 (2000), 213-226.  doi: 10.1016/S0925-5273(99)00129-2.  Google Scholar

[31]

Z. Wan, S. Zhu and Z. Wan, An integrated stochastic model and algorithm for multi-product newsvendor problems, International Journal of Modeling, Simulation, and Scientific Computing, 11 (2020), 2050027.  doi: 10.1142/S1793962320500270.  Google Scholar

[32]

Z. Wan, J. Liu and J. Zhang, Nonlinear optimization to management problems of end-of-life vehicles with environmental protection awareness and damaged/aging degrees, J. Ind. Manag. Optim., 16 (2020), 2117-2139.  doi: 10.3934/jimo.2019046.  Google Scholar

[33]

Z. Wang, F. Liu, C. Zhao, Z. Ma and W. Wei, Distributed optimal load frequency control considering nonsmooth cost functions, Systems Control Lett., 136 (2020), 104607.  doi: 10.1016/j.sysconle.2019.104607.  Google Scholar

[34]

X. Xu, H. Wang, C. Dang and P. Ji, The loss-averse newsvendor model with backordering, International Journal of Production Economics, 188 (2017), 1-10.  doi: 10.1016/j.ijpe.2017.03.005.  Google Scholar

[35]

L. Xu, Y. Zheng and L. Jiang, A robust data-driven approach for the newsvendor problem with nonparametric information, Manufacturing & Service Operations Management, 2021. doi: 10.1287/msom.2020.0961.  Google Scholar

[36]

Y. Yang, M. Pesavento, Z. Q. Luo and B. Ottersten, Inexact block coordinate descent algorithms for nonsmooth nonconvex optimization, IEEE Trans. Signal Process., 68 (2019), 947-961.  doi: 10.1109/TSP.2019.2959240.  Google Scholar

[37]

L. Yong, Some uniform smooth approximating functions and their properties, Journal of Shaanxi University of Technology (Natural Science Edition), 43 (2018), 74–79. (in Chinese) Google Scholar

[38]

H. Yu and J. Sun, Robust stochastic optimization with convex risk measures: A discretized subgradient scheme, J. Ind. Manag. Optim., 17 (2021), 81-99.  doi: 10.3934/jimo.2019100.  Google Scholar

[39]

L. Zhang, G. Zhang and Z. Yao, Analysis of two substitute products newsvendor problem with a budget constraint, Computers & Industrial Engineering, 140 (2020), 106235.  doi: 10.1016/j.cie.2019.106235.  Google Scholar

[40]

G. Zhang, The multi-product newsboy problem with supplier quantity discounts and a budget constraint, European J. Oper. Res, 206 (2010), 350-360.  doi: 10.1016/j.ejor.2010.02.038.  Google Scholar

[41]

J. Zhang, W. Xie and S. C. Sarin, Robust multi-product newsvendor model with uncertain demand and substitution, European J. Oper. Res., 293 (2021), 190-202.  doi: 10.1016/j.ejor.2020.12.023.  Google Scholar

[42]

X. Zhang, S. Huang and Z. Wan, Optimal pricing and ordering in global supply chain management with constraints under random demand, Appl. Math. Model., 40 (2016), 10105-10130.  doi: 10.1016/j.apm.2016.06.054.  Google Scholar

show all references

References:
[1]

M. A. Abdel-Aal and S. Z. Selim, Robust optimization for selective newsvendor problem with uncertain demand, Computers & Industrial Engineering, 135 (2019), 838-854.  doi: 10.1016/j.cie.2019.06.047.  Google Scholar

[2]

L. L. Abdel-Malek and N. Areeratchakul, A quadratic programming approach to the multi-product newsboy problem with side constraints, European J. Oper. Res., 176 (2007), 1607-1619.  doi: 10.1016/j.ejor.2005.11.002.  Google Scholar

[3]

K. J. Arrow, T. Harris and J. Marschak, Optimal inventory policy, Econometrica, 19 (1951), 250-272.  doi: 10.2307/1906813.  Google Scholar

[4]

A. Ben-Tal and A. Nemirovski, Robust optimization-methodology and applications, Math. Program., 92 (2002), 453-480.  doi: 10.1007/s101070100286.  Google Scholar

[5]

A. Ben-Tal and A. Nemirovski, Robust solutions of uncertain linear programs, Oper. Res. Lett., 25 (1999), 1-13.  doi: 10.1016/S0167-6377(99)00016-4.  Google Scholar

[6]

Y. Cao and Z. J. M. Shen, Quantile forecasting and data-driven inventory management under nonstationary demand, Oper. Res. Lett., 47 (2019), 465-472.  doi: 10.1016/j.orl.2019.08.008.  Google Scholar

[7]

E. Carrizosa, A. V. Olivares-Nadal and P. Ram$\acute{i}$rez-Cobo, Robust newsvendor problem with autoregressive demand, Comput. Oper. Res., 68 (2016), 123-133.  doi: 10.1016/j.cor.2015.11.002.  Google Scholar

[8]

L. H. Chen and Y. C. Chen, A multiple-item budget-constraint newsboy problem with a reservation policy, Omega, 38 (2010), 431-439.  doi: 10.1016/j.omega.2009.10.007.  Google Scholar

[9]

Z. Chen, S. Peng and J. Liu, Data-driven robust chance constrained problems: A mixture model approach, J. Optim. Theory Appli., 179 (2018), 1065-1085.  doi: 10.1007/s10957-018-1376-4.  Google Scholar

[10]

X. Chen, Smoothing methods for nonsmooth, nonconvex minimization, Math. Program., 134 (2012), 71-99.  doi: 10.1007/s10107-012-0569-0.  Google Scholar

[11]

S. Deng, Z. Wan and Y. Zhou, Optimization model and solution method for dynamically correlated two-product newsboy problems based on Copula, Discrete Contin. Dyn. Syst. Ser. S, 13 (2018), 1637-1652.  doi: 10.3934/dcdss.2020096.  Google Scholar

[12]

K. W. Ding, N. J. Huang and Y. B. Xiao, Distributionally robust chance constrained problems under general moments information, J. Ind. Manag. Optim., 16 (2020), 2923-2942.  doi: 10.3934/jimo.2019087.  Google Scholar

[13]

F. Fang, T. D. Nguyen and C. S. Currie, Joint pricing and inventory decisions for substitutable and perishable products under demand uncertainty, European J. Oper. Res., 293 (2021), 594-602.  doi: 10.1016/j.ejor.2020.08.002.  Google Scholar

[14]

A. Fuduli, M. Gaudioso and G. Giallombardo, Minimizing nonconvex nonsmooth functions via cutting planes and proximity control, SIAM J. Optim., 14 (2003), 743-756.  doi: 10.1137/S1052623402411459.  Google Scholar

[15]

R. Huang, S. Qu, X. Yang and Z. Liu, Multi-stage distributionally robust optimization with risk aversion, J. Ind. Manag. Optim., 17 (2021), 233-259.  doi: 10.3934/jimo.2019109.  Google Scholar

[16]

J. Huber, S. M$\ddot{u}$ller, M. Fleischmann and H. Stuckenschmidt, A data-driven newsvendor problem: From data to decision, European J. Oper. Res., 278 (2019), 904-915.  doi: 10.1016/j.ejor.2019.04.043.  Google Scholar

[17]

O. Jadidi, M. Y. Jaber, S. Zolfaghri, R. Pinto and F. Firouzi, Dynamic pricing and lot sizing for a newsvendor problem with supplier selection, quantity discounts, and limited supply capacity, Computers & Industrial Engineering, 154 (2021), 107113.  doi: 10.1016/j.cie.2021.107113.  Google Scholar

[18]

A. Jalilvand-Nejad, R. Shafaei and H. Shahriari, Robust optimization under correlated polyhedral uncertainty set, Computers & Industrial Engineering, 92 (2016), 82-94.  doi: 10.1016/j.cie.2015.12.006.  Google Scholar

[19]

G. J. Kyparisis and C. Koulamas, The price-setting newsvendor problem with nonnegative linear additive demand, European J. Oper. Res., 269 (2018), 695-698.  doi: 10.1016/j.ejor.2018.02.019.  Google Scholar

[20]

R. Levi, G. Perakis and J. Uichanco, The data-driven newsvendor problem: New bounds and insights, Oper. Res., 63 (2015), 1294-1306.  doi: 10.1287/opre.2015.1422.  Google Scholar

[21]

C. Ning and F. You, Data-driven decision making under uncertainty integrating robust optimization with principal component analysis and kernel smoothing methods, Computers & Chemical Engineering, 112 (2018), 190-210.  doi: 10.1016/j.compchemeng.2018.02.007.  Google Scholar

[22]

D. Noll, Cutting plane oracles to minimize non-smooth non-convex functions, Set-Valued Var. Anal., 18 (2010), 531-568.  doi: 10.1007/s11228-010-0159-3.  Google Scholar

[23]

S. Punia, S. P. Singh and J. K. Madaan, From predictive to prescriptive analytics: A data-driven multi-item newsvendor model, Decision Support Systems, 136 (2020), 113340.  doi: 10.1016/j.dss.2020.113340.  Google Scholar

[24]

Y. Qin, R. Wang, A. J. Vakharia, Y. Chen and M. M. Seref, The newsvendor problem: Review and directions for future research, European J. Oper. Res., 213 (2011), 361-374.  doi: 10.1016/j.ejor.2010.11.024.  Google Scholar

[25]

R. Qiu, Y. Sun and M. Sun, A distributionally robust optimization approach for multi-product inventory decisions with budget constraint and demand and yield uncertainties, Comput. Oper. Res., 126 (2021), 105081.  doi: 10.1016/j.cor.2020.105081.  Google Scholar

[26]

R. Qiu, Y. Sun, Z. P. Fan and M. Sun, Robust multi-product inventory optimization under support vector clustering-based data-driven demand uncertainty set, Soft Computing, 24 (2019), 6259-6275.  doi: 10.1007/s00500-019-03927-2.  Google Scholar

[27]

A. L. Sachs and S. Minner, The data-driven newsvendor with censored demand observations, International Journal of Production Economics, 149 (2014), 28-36.   Google Scholar

[28]

H. E. Scarf, A Min-Max Solution of an Inventory Problem, Rand Corp Santa Monica Calif, 1957. Google Scholar

[29]

N. Turken, Y. Tan, A. J. Vakharia, L. Wang, R. Wang and A. Yenipazarli, The multi-product newsvendor problem: Review, extensions, and directions for future research, Handbook of Newsboy Problems, 176 (2012), 3-39.  doi: 10.1007/978-1-4614-3600-3_1.  Google Scholar

[30]

G. L. Vairaktarakis, Robust multi-item newsboy models with a budget constraint, International Journal of Production Economics, 66 (2000), 213-226.  doi: 10.1016/S0925-5273(99)00129-2.  Google Scholar

[31]

Z. Wan, S. Zhu and Z. Wan, An integrated stochastic model and algorithm for multi-product newsvendor problems, International Journal of Modeling, Simulation, and Scientific Computing, 11 (2020), 2050027.  doi: 10.1142/S1793962320500270.  Google Scholar

[32]

Z. Wan, J. Liu and J. Zhang, Nonlinear optimization to management problems of end-of-life vehicles with environmental protection awareness and damaged/aging degrees, J. Ind. Manag. Optim., 16 (2020), 2117-2139.  doi: 10.3934/jimo.2019046.  Google Scholar

[33]

Z. Wang, F. Liu, C. Zhao, Z. Ma and W. Wei, Distributed optimal load frequency control considering nonsmooth cost functions, Systems Control Lett., 136 (2020), 104607.  doi: 10.1016/j.sysconle.2019.104607.  Google Scholar

[34]

X. Xu, H. Wang, C. Dang and P. Ji, The loss-averse newsvendor model with backordering, International Journal of Production Economics, 188 (2017), 1-10.  doi: 10.1016/j.ijpe.2017.03.005.  Google Scholar

[35]

L. Xu, Y. Zheng and L. Jiang, A robust data-driven approach for the newsvendor problem with nonparametric information, Manufacturing & Service Operations Management, 2021. doi: 10.1287/msom.2020.0961.  Google Scholar

[36]

Y. Yang, M. Pesavento, Z. Q. Luo and B. Ottersten, Inexact block coordinate descent algorithms for nonsmooth nonconvex optimization, IEEE Trans. Signal Process., 68 (2019), 947-961.  doi: 10.1109/TSP.2019.2959240.  Google Scholar

[37]

L. Yong, Some uniform smooth approximating functions and their properties, Journal of Shaanxi University of Technology (Natural Science Edition), 43 (2018), 74–79. (in Chinese) Google Scholar

[38]

H. Yu and J. Sun, Robust stochastic optimization with convex risk measures: A discretized subgradient scheme, J. Ind. Manag. Optim., 17 (2021), 81-99.  doi: 10.3934/jimo.2019100.  Google Scholar

[39]

L. Zhang, G. Zhang and Z. Yao, Analysis of two substitute products newsvendor problem with a budget constraint, Computers & Industrial Engineering, 140 (2020), 106235.  doi: 10.1016/j.cie.2019.106235.  Google Scholar

[40]

G. Zhang, The multi-product newsboy problem with supplier quantity discounts and a budget constraint, European J. Oper. Res, 206 (2010), 350-360.  doi: 10.1016/j.ejor.2010.02.038.  Google Scholar

[41]

J. Zhang, W. Xie and S. C. Sarin, Robust multi-product newsvendor model with uncertain demand and substitution, European J. Oper. Res., 293 (2021), 190-202.  doi: 10.1016/j.ejor.2020.12.023.  Google Scholar

[42]

X. Zhang, S. Huang and Z. Wan, Optimal pricing and ordering in global supply chain management with constraints under random demand, Appl. Math. Model., 40 (2016), 10105-10130.  doi: 10.1016/j.apm.2016.06.054.  Google Scholar

Figure 1.  Impacts of confidence level on order quantities and profits
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 2.  Impacts of demands on optimal order quantities
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 3.  Impacts of uniform approximation levels
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 4.  Impacts of confidence level and deviation on order quantities
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 5.  Impacts of confidence levels and data volatility on profits
Figure Options

Download full-size image

Download as PowerPoint slide

Figure 6.  Impacts of unit purchase prices on optimal order quantities
Figure Options

Download full-size image

Download as PowerPoint slide

Table 1.  Values of model parameters
Item $ s $ (Yuan RMB) $ v $ (Yuan RMB) $ p $ (Yuan RMB) $ c $ (Yuan RMB)
A 80 3 6 12
B 97 10 16 32
Table Options

Download as excel

Item $ s $ (Yuan RMB) $ v $ (Yuan RMB) $ p $ (Yuan RMB) $ c $ (Yuan RMB)
A 80 3 6 12
B 97 10 16 32
Table 2.  Profits of different robust methods with changing demands
($ \mu_1 $, $ \sigma_1 $) ($ \mu_2 $, $ \sigma _2 $) $ R_U $ $ R_A $ $ R_D $ $ R_R $
(239.55, 5.80) (82.34, 3.87) 20824.79 20523.29 20205.75 20214.74
(+10.82, 0) (0, 0) +767.31 +737.58 +738.20 +738.10
(-8.85, 0) (0, 0) -625.43 -601.57 -601.61 -601.57
(0, 0) (+10.20, 0) +691.21 +663.47 +663.91 +662.99
(0, 0) (-5.13, 0) -350.61 -331.46 -330.69 -330.23
(0, +9.61) (0, 0) -702.95 -1096.27 -1329.40 -1320.59
(0, -1.42) (0, 0) +101.46 +161.14 +195.23 +194.66
(0, 0) (0, +5.55) -608.36 -656.60 -910.03 -869.37
(0, 0) (0, -0.48) +42.60 +57.51 +79.44 +77.63
Table Options

Download as excel

($ \mu_1 $, $ \sigma_1 $) ($ \mu_2 $, $ \sigma _2 $) $ R_U $ $ R_A $ $ R_D $ $ R_R $
(239.55, 5.80) (82.34, 3.87) 20824.79 20523.29 20205.75 20214.74
(+10.82, 0) (0, 0) +767.31 +737.58 +738.20 +738.10
(-8.85, 0) (0, 0) -625.43 -601.57 -601.61 -601.57
(0, 0) (+10.20, 0) +691.21 +663.47 +663.91 +662.99
(0, 0) (-5.13, 0) -350.61 -331.46 -330.69 -330.23
(0, +9.61) (0, 0) -702.95 -1096.27 -1329.40 -1320.59
(0, -1.42) (0, 0) +101.46 +161.14 +195.23 +194.66
(0, 0) (0, +5.55) -608.36 -656.60 -910.03 -869.37
(0, 0) (0, -0.48) +42.60 +57.51 +79.44 +77.63
[1]

Stefano Almi, Massimo Fornasier, Richard Huber. Data-driven evolutions of critical points. Foundations of Data Science, 2020, 2 (3) : 207-255. doi: 10.3934/fods.2020011
[2]

Michael Herty, Adrian Fazekas, Giuseppe Visconti. A two-dimensional data-driven model for traffic flow on highways. Networks & Heterogeneous Media, 2018, 13 (2) : 217-240. doi: 10.3934/nhm.2018010
[3]

Matthew O. Williams, Clarence W. Rowley, Ioannis G. Kevrekidis. A kernel-based method for data-driven koopman spectral analysis. Journal of Computational Dynamics, 2015, 2 (2) : 247-265. doi: 10.3934/jcd.2015005
[4]

Tieliang Gong, Chen Xu, Hong Chen. Modal additive models with data-driven structure identification. Mathematical Foundations of Computing, 2020, 3 (3) : 165-183. doi: 10.3934/mfc.2020016
[5]

Hailiang Liu, Xuping Tian. Data-driven optimal control of a seir model for COVID-19. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021093
[6]

Sarah Jane Hamilton, Andreas Hauptmann, Samuli Siltanen. A data-driven edge-preserving D-bar method for electrical impedance tomography. Inverse Problems & Imaging, 2014, 8 (4) : 1053-1072. doi: 10.3934/ipi.2014.8.1053
[7]

Meixin Xiong, Liuhong Chen, Ju Ming, Jaemin Shin. Accelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decomposition. Electronic Research Archive, 2021, 29 (5) : 3383-3403. doi: 10.3934/era.2021044
[8]

Vladimir Djordjevic, Vladimir Stojanovic, Hongfeng Tao, Xiaona Song, Shuping He, Weinan Gao. Data-driven control of hydraulic servo actuator based on adaptive dynamic programming. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021145
[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]

Yong Zhang, Xingyu Yang, Baixun Li. Distribution-free solutions to the extended multi-period newsboy problem. Journal of Industrial & Management Optimization, 2017, 13 (2) : 633-647. doi: 10.3934/jimo.2016037
[11]

Sylvain Ervedoza, Enrique Zuazua. A systematic method for building smooth controls for smooth data. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1375-1401. doi: 10.3934/dcdsb.2010.14.1375
[12]

Mieczysław Cichoń, Bianca Satco. On the properties of solutions set for measure driven differential inclusions. Conference Publications, 2015, 2015 (special) : 287-296. doi: 10.3934/proc.2015.0287
[13]

María Ángeles García-Ferrero, Angkana Rüland, Wiktoria Zatoń. Runge approximation and stability improvement for a partial data Calderón problem for the acoustic Helmholtz equation. Inverse Problems & Imaging, 2022, 16 (1) : 251-281. doi: 10.3934/ipi.2021049
[14]

Ting Chen, Fusheng Lv, Wenchang Sun. Uniform approximation property of frames with applications to erasure recovery. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2022011
[15]

Stephen Thompson, Thomas I. Seidman. Approximation of a semigroup model of anomalous diffusion in a bounded set. Evolution Equations & Control Theory, 2013, 2 (1) : 173-192. doi: 10.3934/eect.2013.2.173
[16]

Yangrong Li, Lianbing She, Jinyan Yin. Longtime robustness and semi-uniform compactness of a pullback attractor via nonautonomous PDE. Discrete & Continuous Dynamical Systems - B, 2018, 23 (4) : 1535-1557. doi: 10.3934/dcdsb.2018058
[17]

Vinicius Albani, Uri M. Ascher, Xu Yang, Jorge P. Zubelli. Data driven recovery of local volatility surfaces. Inverse Problems & Imaging, 2017, 11 (5) : 799-823. doi: 10.3934/ipi.2017038
[18]

Xiao-Bing Li, Qi-Lin Wang, Zhi Lin. Optimality conditions and duality for minimax fractional programming problems with data uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1133-1151. doi: 10.3934/jimo.2018089
[19]

Clark Robinson. Uniform subharmonic orbits for Sitnikov problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (4) : 647-652. doi: 10.3934/dcdss.2008.1.647
[20]

Peter Giesl, Boumediene Hamzi, Martin Rasmussen, Kevin Webster. Approximation of Lyapunov functions from noisy data. Journal of Computational Dynamics, 2020, 7 (1) : 57-81. doi: 10.3934/jcd.2020003

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (143)
  • HTML views (131)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy