Discount-offering and demand-rejection decisions for substitutable products with different profit levels

Previous Article
A global optimization approach to fractional optimal control
JIMO Home
This Issue
Next Article
Asymptotics for random-time ruin probability in a time-dependent renewal risk model with subexponential claims

January 2016, 12(1): 45-71. doi: 10.3934/jimo.2016.12.45

Discount-offering and demand-rejection decisions for substitutable products with different profit levels

Taofeng Ye ^1, and Shaohui Ma ^1,

1.	School of Economics and Management, Jiangsu University of Science and Technology, Zhenjiang, Jiangsu 212003, China, China

Received January 2013 Revised November 2014 Published April 2015

Abstract
Related Papers

This study focuses on discount-offering and demand-rejection decisions for a retailer selling substitutable products. Those products are assumed to be generated different unit net revenues. We first consider a basic model with only two substitutable products and formulate the retailer's objective function by means of dynamic programming model. We show that the retailer can employ simple offering- and rejection-decision rules that are derived in accordance with the stocking quantities of the products. Moreover, it is identified that the retailer's offering decision can also be made according to the number of remaining selling periods. We conduct some numerical examples to testify how those decision rules to vary with regard to different parameters. Further, we extend the basic model to the case with three partially substitutable products. It is shown that the simple offering-decision rules are existed only under some restrictive conditions, and especially, it is difficult to analytically develop any simple rejection-decision rules.

Keywords: dynamic programming, management decision making., demand-rejection, Substitutable products, discount-offering.

Mathematics Subject Classification: Primary: 90B50; Secondary: 49L6.

Citation: Taofeng Ye, Shaohui Ma. Discount-offering and demand-rejection decisions for substitutable products with different profit levels. Journal of Industrial and Management Optimization, 2016, 12 (1) : 45-71. doi: 10.3934/jimo.2016.12.45

References:

[1]	Y. Akcay, H. P. Natarajan and S. H. Xu, Joint dynamic pricing of multiple perishable products under consumer choice, Management Science, 56 (2010), 1345-1361. doi: 10.1287/mnsc.1100.1178.
[2]	G. R. Bitran, R. A. Caldentey and R. Vial, Pricing Policies for Perishable Products with Demand Substitution, working paper, New York University, New York, NY.
[3]	L. Dong, P. Kouvelis and Z. Tian, Dynamic pricing and inventory control of substitutable products, Manufacturing & Service Operations Management, 11 (2008), 317-339. doi: 10.1287/msom.1080.0221.
[4]	S.-W. Kim and P. C. Bell, Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution, Omega, 39 (2011), 528-538. doi: 10.1016/j.omega.2010.11.002.
[5]	A. G. Kök and Y. Xu, Optimal and competitive assortments with endogenous pricing under hierarchical consumer choice models, Management Science, 57 (2011), 1546-1563.
[6]	S. A. Lippman and K. F. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.
[7]	B. Maddah and E. K. Bish, Joint pricing, assortment, and inventory decisions for a retailer's product line, Naval Research Logistics, 54 (2007), 1-16. doi: 10.1002/nav.20209.
[8]	S. Mahajan and G. van Ryzin, Inventory competition under dynamic consumer choice, Operations Research, 49 (2001), 646-657. doi: 10.1287/opre.49.5.646.10603.
[9]	S. Netessine and N. Rudi, Centralized and competitive inventory models with demand substitution, Operations Research, 51 (2003), 329-335. doi: 10.1287/opre.51.2.329.12788.
[10]	S. Netessine, N. Rudi and Y. Wang, Inventory competition and incentives to back-order, IIE Transactions, 38 (2006), 883-902. doi: 10.1080/07408170600854750.
[11]	M. Parlar, Game theoretic analysis of the substitute product inventory problem with random demand, Naval Research Logistics, 35 (1988), 397-429. doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.
[12]	R. A. Shumsky and F. Zhang, Dynamic capacity management with substitution, Operations Research, 57 (2009), 671-684. doi: 10.1287/opre.1080.0610.
[13]	M. Suh and G. Aydin, Dynamic pricing of substitutable products with limited inventory under logit demand, IIE Transactions, 43 (2011), 323-331. doi: 10.1080/0740817X.2010.521803.
[14]	C. S. Tang and R. Yin, Joint ordering and pricing strategies for managing substitutable products, Production and Operations Management, 16 (2007), 138-153. doi: 10.1111/j.1937-5956.2007.tb00171.x.
[15]	Q. Wang and M. Parlar, A three-person game theory model arising in stochastic inventory control theory, European Journal of Operational Research, 76 (1994), 83-97. doi: 10.1016/0377-2217(94)90008-6.
[16]	H. Xu, D. D. Yao and S. Zheng, Optimal control of replenishment and substitution in an inventory system with nonstationary batch demand, Production and Operations Management, 20 (2011), 727-736. doi: 10.1111/j.1937-5956.2010.01191.x.
[17]	Z. Xue and J. Song, Demand Management and Inventory Control for Substitutable Products, working paper, Duke University, Durhan, NC.
[18]	P.-S You, Airline seat management with rejection-for-possible-upgrade decision, Transportation Research Part B, 35 (2001), 507-524. doi: 10.1016/S0191-2615(00)00007-2.
[19]	P.-S You, Dynamic rationing policies for product with incremental upgrading demands, European Journal of Operational Research, 144 (2003), 128-137. doi: 10.1016/S0377-2217(01)00397-6.
[20]	D. Zhang and W. L. Cooper, Pricing substitutable flights in airline revenue management, European Journal of Operational Research, 197 (2009), 848-861. doi: 10.1016/j.ejor.2006.10.067.
[21]	X. Zhao and D. R. Atkins, Newsvendors under simultaneous price and inventory competition, Manufacturing & Service Operations Management, 10 (2008), 539-546. doi: 10.1287/msom.1070.0186.

show all references

References:

[1]	Y. Akcay, H. P. Natarajan and S. H. Xu, Joint dynamic pricing of multiple perishable products under consumer choice, Management Science, 56 (2010), 1345-1361. doi: 10.1287/mnsc.1100.1178.
[2]	G. R. Bitran, R. A. Caldentey and R. Vial, Pricing Policies for Perishable Products with Demand Substitution, working paper, New York University, New York, NY.
[3]	L. Dong, P. Kouvelis and Z. Tian, Dynamic pricing and inventory control of substitutable products, Manufacturing & Service Operations Management, 11 (2008), 317-339. doi: 10.1287/msom.1080.0221.
[4]	S.-W. Kim and P. C. Bell, Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution, Omega, 39 (2011), 528-538. doi: 10.1016/j.omega.2010.11.002.
[5]	A. G. Kök and Y. Xu, Optimal and competitive assortments with endogenous pricing under hierarchical consumer choice models, Management Science, 57 (2011), 1546-1563.
[6]	S. A. Lippman and K. F. McCardle, The competitive newsboy, Operations Research, 45 (1997), 54-65. doi: 10.1287/opre.45.1.54.
[7]	B. Maddah and E. K. Bish, Joint pricing, assortment, and inventory decisions for a retailer's product line, Naval Research Logistics, 54 (2007), 1-16. doi: 10.1002/nav.20209.
[8]	S. Mahajan and G. van Ryzin, Inventory competition under dynamic consumer choice, Operations Research, 49 (2001), 646-657. doi: 10.1287/opre.49.5.646.10603.
[9]	S. Netessine and N. Rudi, Centralized and competitive inventory models with demand substitution, Operations Research, 51 (2003), 329-335. doi: 10.1287/opre.51.2.329.12788.
[10]	S. Netessine, N. Rudi and Y. Wang, Inventory competition and incentives to back-order, IIE Transactions, 38 (2006), 883-902. doi: 10.1080/07408170600854750.
[11]	M. Parlar, Game theoretic analysis of the substitute product inventory problem with random demand, Naval Research Logistics, 35 (1988), 397-429. doi: 10.1002/1520-6750(198806)35:3<397::AID-NAV3220350308>3.0.CO;2-Z.
[12]	R. A. Shumsky and F. Zhang, Dynamic capacity management with substitution, Operations Research, 57 (2009), 671-684. doi: 10.1287/opre.1080.0610.
[13]	M. Suh and G. Aydin, Dynamic pricing of substitutable products with limited inventory under logit demand, IIE Transactions, 43 (2011), 323-331. doi: 10.1080/0740817X.2010.521803.
[14]	C. S. Tang and R. Yin, Joint ordering and pricing strategies for managing substitutable products, Production and Operations Management, 16 (2007), 138-153. doi: 10.1111/j.1937-5956.2007.tb00171.x.
[15]	Q. Wang and M. Parlar, A three-person game theory model arising in stochastic inventory control theory, European Journal of Operational Research, 76 (1994), 83-97. doi: 10.1016/0377-2217(94)90008-6.
[16]	H. Xu, D. D. Yao and S. Zheng, Optimal control of replenishment and substitution in an inventory system with nonstationary batch demand, Production and Operations Management, 20 (2011), 727-736. doi: 10.1111/j.1937-5956.2010.01191.x.
[17]	Z. Xue and J. Song, Demand Management and Inventory Control for Substitutable Products, working paper, Duke University, Durhan, NC.
[18]	P.-S You, Airline seat management with rejection-for-possible-upgrade decision, Transportation Research Part B, 35 (2001), 507-524. doi: 10.1016/S0191-2615(00)00007-2.
[19]	P.-S You, Dynamic rationing policies for product with incremental upgrading demands, European Journal of Operational Research, 144 (2003), 128-137. doi: 10.1016/S0377-2217(01)00397-6.
[20]	D. Zhang and W. L. Cooper, Pricing substitutable flights in airline revenue management, European Journal of Operational Research, 197 (2009), 848-861. doi: 10.1016/j.ejor.2006.10.067.
[21]	X. Zhao and D. R. Atkins, Newsvendors under simultaneous price and inventory competition, Manufacturing & Service Operations Management, 10 (2008), 539-546. doi: 10.1287/msom.1070.0186.

[1]	Haiying Liu, Wenjie Bi, Kok Lay Teo, Naxing Liu. Dynamic optimal decision making for manufacturers with limited attention based on sparse dynamic programming. Journal of Industrial and Management Optimization, 2019, 15 (2) : 445-464. doi: 10.3934/jimo.2018050
[2]	Jing Zhao, Jie Wei, Yongjian Li. Pricing and remanufacturing decisions for two substitutable products with a common retailer. Journal of Industrial and Management Optimization, 2017, 13 (2) : 1125-1147. doi: 10.3934/jimo.2016065
[3]	Hamed Jafari, Soroush Safarzadeh. Producing two substitutable products under a supply chain including two manufacturers and one retailer: A game-theoretic approach. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022102
[4]	G.S. Liu, J.Z. Zhang. Decision making of transportation plan, a bilevel transportation problem approach. Journal of Industrial and Management Optimization, 2005, 1 (3) : 305-314. doi: 10.3934/jimo.2005.1.305
[5]	Naziya Parveen, Prakash N. Kamble. An extension of TOPSIS for group decision making in intuitionistic fuzzy environment. Mathematical Foundations of Computing, 2021, 4 (1) : 61-71. doi: 10.3934/mfc.2021002
[6]	Ana F. Carazo, Ignacio Contreras, Trinidad Gómez, Fátima Pérez. A project portfolio selection problem in a group decision-making context. Journal of Industrial and Management Optimization, 2012, 8 (1) : 243-261. doi: 10.3934/jimo.2012.8.243
[7]	Ruiyue Lin, Zhiping Chen, Zongxin Li. A new approach for allocating fixed costs among decision making units. Journal of Industrial and Management Optimization, 2016, 12 (1) : 211-228. doi: 10.3934/jimo.2016.12.211
[8]	Hamed Fazlollahtabar, Mohammad Saidi-Mehrabad. Optimizing multi-objective decision making having qualitative evaluation. Journal of Industrial and Management Optimization, 2015, 11 (3) : 747-762. doi: 10.3934/jimo.2015.11.747
[9]	Harald Held, Gabriela Martinez, Philipp Emanuel Stelzig. Stochastic programming approach for energy management in electric microgrids. Numerical Algebra, Control and Optimization, 2014, 4 (3) : 241-267. doi: 10.3934/naco.2014.4.241
[10]	Eungab Kim. On the admission control and demand management in a two-station tandem production system. Journal of Industrial and Management Optimization, 2011, 7 (1) : 1-18. doi: 10.3934/jimo.2011.7.1
[11]	Ximin Huang, Na Song, Wai-Ki Ching, Tak-Kuen Siu, Ka-Fai Cedric Yiu. A real option approach to optimal inventory management of retail products. Journal of Industrial and Management Optimization, 2012, 8 (2) : 379-389. doi: 10.3934/jimo.2012.8.379
[12]	Andrzej Nowakowski, Jan Sokolowski. On dual dynamic programming in shape control. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2473-2485. doi: 10.3934/cpaa.2012.11.2473
[13]	Jérôme Renault. General limit value in dynamic programming. Journal of Dynamics and Games, 2014, 1 (3) : 471-484. doi: 10.3934/jdg.2014.1.471
[14]	Harish Garg. Novel correlation coefficients under the intuitionistic multiplicative environment and their applications to decision-making process. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1501-1519. doi: 10.3934/jimo.2018018
[15]	Xue Yan, Heap-Yih Chong, Jing Zhou, Zhaohan Sheng, Feng Xu. Fairness preference based decision-making model for concession period in PPP projects. Journal of Industrial and Management Optimization, 2020, 16 (1) : 11-23. doi: 10.3934/jimo.2018137
[16]	Jian Jin, Weijian Mi. An AIMMS-based decision-making model for optimizing the intelligent stowage of export containers in a single bay. Discrete and Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1101-1115. doi: 10.3934/dcdss.2019076
[17]	Gholam Hassan Shirdel, Somayeh Ramezani-Tarkhorani. A new method for ranking decision making units using common set of weights: A developed criterion. Journal of Industrial and Management Optimization, 2020, 16 (2) : 633-651. doi: 10.3934/jimo.2018171
[18]	Saber Saati, Adel Hatami-Marbini, Per J. Agrell, Madjid Tavana. A common set of weight approach using an ideal decision making unit in data envelopment analysis. Journal of Industrial and Management Optimization, 2012, 8 (3) : 623-637. doi: 10.3934/jimo.2012.8.623
[19]	Weichao Yue, Weihua Gui, Xiaofang Chen, Zhaohui Zeng, Yongfang Xie. Evaluation strategy and mass balance for making decision about the amount of aluminum fluoride addition based on superheat degree. Journal of Industrial and Management Optimization, 2020, 16 (2) : 601-622. doi: 10.3934/jimo.2018169
[20]	Gleb Beliakov. Construction of aggregation operators for automated decision making via optimal interpolation and global optimization. Journal of Industrial and Management Optimization, 2007, 3 (2) : 193-208. doi: 10.3934/jimo.2007.3.193

2021 Impact Factor: 1.411

Tools

Metrics

Other articles
by authors

on AIMS
Taofeng Ye Shaohui Ma
on Google Scholar
Taofeng Ye Shaohui Ma

[Back to Top]