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

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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

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
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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 & 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. 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, ().
[3]	L. Dong, P. Kouvelis and Z. Tian, Dynamic pricing and inventory control of substitutable products,, Manufacturing & Service Operations Management, 11 (2008), 317. 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. 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.
[6]	S. A. Lippman and K. F. McCardle, The competitive newsboy,, Operations Research, 45 (1997), 54. 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. doi: 10.1002/nav.20209.
[8]	S. Mahajan and G. van Ryzin, Inventory competition under dynamic consumer choice,, Operations Research, 49 (2001), 646. 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. 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. 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. 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. 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. 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. 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. 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. 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, ().
[18]	P.-S You, Airline seat management with rejection-for-possible-upgrade decision,, Transportation Research Part B, 35 (2001), 507. 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. 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. 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. doi: 10.1287/msom.1070.0186.

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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. 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, ().
[3]	L. Dong, P. Kouvelis and Z. Tian, Dynamic pricing and inventory control of substitutable products,, Manufacturing & Service Operations Management, 11 (2008), 317. 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. 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.
[6]	S. A. Lippman and K. F. McCardle, The competitive newsboy,, Operations Research, 45 (1997), 54. 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. doi: 10.1002/nav.20209.
[8]	S. Mahajan and G. van Ryzin, Inventory competition under dynamic consumer choice,, Operations Research, 49 (2001), 646. 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. 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. 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. 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. 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. 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. 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. 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. 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, ().
[18]	P.-S You, Airline seat management with rejection-for-possible-upgrade decision,, Transportation Research Part B, 35 (2001), 507. 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. 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. 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. doi: 10.1287/msom.1070.0186.

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