2012, 2(4): 669-693. doi: 10.3934/naco.2012.2.669

The integrated size and price optimization problem

1. 

Universität Bayreuth, 95440 Bayreuth, Germany

2. 

Universität Bayreuth, 95440 Bayreuth, Germany, Germany

Received  December 2011 Revised  October 2012 Published  November 2012

We present the Integrated Size and Price Optimization Problem (ISPO) for a fashion discounter with many branches. Based on a two-stage stochastic programming model with recourse, we develop an exact algorithm and a production-compliant heuristic that produces small optimality gaps. In a field study we show that a distribution of supply over branches and sizes based on ISPO solutions is significantly better than a one-stage optimization of the distribution ignoring the possibility of optimal pricing.
Citation: Miriam Kiessling, Sascha Kurz, Jörg Rambau. The integrated size and price optimization problem. Numerical Algebra, Control and Optimization, 2012, 2 (4) : 669-693. doi: 10.3934/naco.2012.2.669
References:
[1]

Elodie Adida and Georgia Perakis, A robust optimization approach to dynamic pricing and inventory control with no backorders, Math. Program., 107 (2006), 97-129. doi: 10.1007/s10107-005-0681-5.

[2]

Elodie Adida and Georgia Perakis, Dynamic pricing and inventory control: Uncertainty and competition, Oper. Res., 58 (2010), 289-302. doi: 10.1287/opre.1090.0718.

[3]

Dimitris Bertsimas and Sanne de Boer, Dynamic pricing and inventory control for multiple products, JRPM, 3 (2005), 303-319. doi: 10.1057/palgrave.rpm.5170117.

[4]

John R. Birge and Francois Louveaux, "Introduction To Stochastic Programming," 2nd ed, Springer Series in Operations Research and Financial Engineering, New York, 2011. doi: 10.1007/978-1-4614-0237-4.

[5]

Gabriel Bitran and Reneé Caldentey, An overview of pricing models for revenue management, MSOM, 5 (2003), 203-229. doi: 10.1287/msom.5.3.203.16031.

[6]

Lap M. A. Chan, Zuo-Jun M. Shen, David Simchi-Levi and Julie Swann, Coordination of pricing and inventory decisions: A survey and classification, Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era, (2004), 335-392.

[7]

Andreas Christmann and Ingo Steinwart, "Support Vector Machines," Information Science and Statistics, Springer, 2008.

[8]

Antonio J. Conejo, Enrique Castillo, Roberto Minguez and Raquel Garcia-Bertrand, "Decomposition Techniques in Mathematical Programming: Engineering and Science Applications," Springer, 2010.

[9]

Awi Federgruen and Aliza Heching, Combined pricing and inventory control under uncertainty, Oper. Res., 47 (1999), 454-475. doi: 10.1287/opre.47.3.454.

[10]

David Freedman, Robert Pisani and Roger Purves, "Statistics," 4th Edition, W. W. Norton & Company, 2007.

[11]

Constantin Gaul, Sascha Kurz and Jörg Rambau, On the lot-type design problem, Optim. Methods Softw., 25 (2010), 217-227. doi: 10.1080/10556780902965163.

[12]

Guillermo Gallego and Garrett van Ryzin, Optimal dynamic pricing of inventories with stochastic demand over finite horizons, Manage. Sci., 40 (1994), 999-1020. doi: 10.1287/mnsc.40.8.999.

[13]

Guillermo Gallego and Garrett van Ryzin, A multiproduct dynamic pricing problem and its applications to network yield management, Oper. Res., 45 (1997), 24-41. doi: 10.1287/opre.45.1.24.

[14]

Lars Grüne and Jürgen Pannek, "Nonlinear Model Predictive Control," Communications and Control Engineering, Springer, 2011. doi: 10.1007/978-0-85729-501-9.

[15]

Miriam Kießling, Sascha Kurz and Jörg Rambau, An exact column-generation approach for the lot-type design problem, Preprint, Universität Bayreuth, 2012.

[16]

Kaisa M. Miettinen, "Evolutionary Algorithms In Engineering & Computer Science," John Wiley & Sons LTD, 1999.

[17]

Alan L. Montgomery, The implementation challenge of pricing decision support systems for retail managers, Appl. Stoch. Models Bus. Ind., 21 (2005), 367-378. doi: 10.1002/asmb.572.

[18]

Serguei Netessine, Dynamic pricing of inventory/capacity with infrequent price changes, Eur. J. Oper. Res., 174 (2006), 553-580. doi: 10.1016/j.ejor.2004.12.015.

[19]

Frank Wilcoxon, Individual comparisons by ranking methods, Biometrics Bulletin, 1 (1945), 80-83. doi: 10.2307/3001968.

[20]

Rui Yin, Yossi Aviv, Amat Pazgal and Christopher S. Tang, Optimal markdown pricing: implications of inventory display formats in the presence of strategic customers, Manage. Sci., 55 (2009), 1391-1408. doi: 10.1287/mnsc.1090.1029.

[21]

Wen Zhao and Yu-Sheng Zheng, Optimal dynamic pricing for perishable assets with nonhomogeneous demand, Manage. Sci., 46 (2000), 375-388. doi: 10.1287/mnsc.46.3.375.12063.

show all references

References:
[1]

Elodie Adida and Georgia Perakis, A robust optimization approach to dynamic pricing and inventory control with no backorders, Math. Program., 107 (2006), 97-129. doi: 10.1007/s10107-005-0681-5.

[2]

Elodie Adida and Georgia Perakis, Dynamic pricing and inventory control: Uncertainty and competition, Oper. Res., 58 (2010), 289-302. doi: 10.1287/opre.1090.0718.

[3]

Dimitris Bertsimas and Sanne de Boer, Dynamic pricing and inventory control for multiple products, JRPM, 3 (2005), 303-319. doi: 10.1057/palgrave.rpm.5170117.

[4]

John R. Birge and Francois Louveaux, "Introduction To Stochastic Programming," 2nd ed, Springer Series in Operations Research and Financial Engineering, New York, 2011. doi: 10.1007/978-1-4614-0237-4.

[5]

Gabriel Bitran and Reneé Caldentey, An overview of pricing models for revenue management, MSOM, 5 (2003), 203-229. doi: 10.1287/msom.5.3.203.16031.

[6]

Lap M. A. Chan, Zuo-Jun M. Shen, David Simchi-Levi and Julie Swann, Coordination of pricing and inventory decisions: A survey and classification, Handbook of Quantitative Supply Chain Analysis: Modeling in the E-Business Era, (2004), 335-392.

[7]

Andreas Christmann and Ingo Steinwart, "Support Vector Machines," Information Science and Statistics, Springer, 2008.

[8]

Antonio J. Conejo, Enrique Castillo, Roberto Minguez and Raquel Garcia-Bertrand, "Decomposition Techniques in Mathematical Programming: Engineering and Science Applications," Springer, 2010.

[9]

Awi Federgruen and Aliza Heching, Combined pricing and inventory control under uncertainty, Oper. Res., 47 (1999), 454-475. doi: 10.1287/opre.47.3.454.

[10]

David Freedman, Robert Pisani and Roger Purves, "Statistics," 4th Edition, W. W. Norton & Company, 2007.

[11]

Constantin Gaul, Sascha Kurz and Jörg Rambau, On the lot-type design problem, Optim. Methods Softw., 25 (2010), 217-227. doi: 10.1080/10556780902965163.

[12]

Guillermo Gallego and Garrett van Ryzin, Optimal dynamic pricing of inventories with stochastic demand over finite horizons, Manage. Sci., 40 (1994), 999-1020. doi: 10.1287/mnsc.40.8.999.

[13]

Guillermo Gallego and Garrett van Ryzin, A multiproduct dynamic pricing problem and its applications to network yield management, Oper. Res., 45 (1997), 24-41. doi: 10.1287/opre.45.1.24.

[14]

Lars Grüne and Jürgen Pannek, "Nonlinear Model Predictive Control," Communications and Control Engineering, Springer, 2011. doi: 10.1007/978-0-85729-501-9.

[15]

Miriam Kießling, Sascha Kurz and Jörg Rambau, An exact column-generation approach for the lot-type design problem, Preprint, Universität Bayreuth, 2012.

[16]

Kaisa M. Miettinen, "Evolutionary Algorithms In Engineering & Computer Science," John Wiley & Sons LTD, 1999.

[17]

Alan L. Montgomery, The implementation challenge of pricing decision support systems for retail managers, Appl. Stoch. Models Bus. Ind., 21 (2005), 367-378. doi: 10.1002/asmb.572.

[18]

Serguei Netessine, Dynamic pricing of inventory/capacity with infrequent price changes, Eur. J. Oper. Res., 174 (2006), 553-580. doi: 10.1016/j.ejor.2004.12.015.

[19]

Frank Wilcoxon, Individual comparisons by ranking methods, Biometrics Bulletin, 1 (1945), 80-83. doi: 10.2307/3001968.

[20]

Rui Yin, Yossi Aviv, Amat Pazgal and Christopher S. Tang, Optimal markdown pricing: implications of inventory display formats in the presence of strategic customers, Manage. Sci., 55 (2009), 1391-1408. doi: 10.1287/mnsc.1090.1029.

[21]

Wen Zhao and Yu-Sheng Zheng, Optimal dynamic pricing for perishable assets with nonhomogeneous demand, Manage. Sci., 46 (2000), 375-388. doi: 10.1287/mnsc.46.3.375.12063.

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