Figure 1.
Effect of the extant product's price on the new product's order quantity
-
Previous Article
An efficient algorithm for non-convex sparse optimization
- JIMO Home
- This Issue
-
Next Article
Homotopy method for solving generalized Nash equilibrium problem with equality and inequality constraints
doi: 10.3934/jimo.2018175
Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects
| 1. | Ingram School of Engineering, Texas State University, San Marcos, TX 78666, USA |
| 2. | School of Management and Engineering, Nanjing University, Nanjing, China 210093 |
| 3. | Amazon, Seattle, WA 98109, USA |
This paper studies a single-period inventory-pricing problem with two substitutable products, which is very important in the area of Operations Management but has received little attention. The proposed problem focuses on determining the optimal price of the existing product and the inventory level of the new product. Inspired by practice, the problem considers various pricing strategies for the existing product as well as the cross elasticity of demand between existing and new products. A mathematical model has been developed for different pricing strategies to maximize the expected profit. It has been proven that the objective function is concave and there exists the unique optimal solution. Different sets of computational examples are conducted to show that the optimal pricing and inventory strategy generated by the model can increase profits.
Mathematics Subject Classification:
Primary: 90B05; Secondary: 91B24, 91B26.
Citation:
Zhijie Sasha Dong, Wei Chen, Qing Zhao, Jingquan Li.
Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018175
![]()
References:
| [1] |
M. Akan, B. Ata and R. C. Savaskan-Ebert,
Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model, Annals of Operations Research, 211 (2013), 1-25.
doi: 10.1007/s10479-013-1409-1. |
| [2] |
G. Aydin and E. L. Porteus,
Joint inventory and pricing decisions for an assortment, Operations Research, 56 (2008), 1247-1255.
doi: 10.1287/opre.1080.0562. |
| [3] |
D. Honhon, V. Gaur and S. Seshadri,
Assortment planning and inventory decisions under stockout-based substitution, Operations Research, 58 (2010), 1364-1379.
doi: 10.1287/opre.1090.0805. |
| [4] |
C. C. Hsieh and C. H. Wu,
Coordinated decisions for substitutable products in a common retailer supply chain, European Journal of Operational Research, 196 (2009), 273-288.
doi: 10.1016/j.ejor.2008.02.019. |
| [5] |
M. Karakul,
Joint pricing and procurement of fashion products in the existence of clearance markets, International Journal of Production Economics, 114 (2008), 487-506.
doi: 10.1016/j.ijpe.2007.03.026. |
| [6] |
M. Karakul and L. M. A. Chan,
Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem, European Journal of Operational Research, 190 (2008), 179-204.
doi: 10.1016/j.ejor.2007.06.026. |
| [7] |
M. Karakul and L. M. A. Chan,
Joint pricing and procurement of substitutable products with random demands - A technical note, European Journal of Operational Research, 201 (2010), 324-328.
doi: 10.1016/j.ejor.2009.03.030. |
| [8] |
M. Khouja, A. Mehrez and G. Rabinowitz,
A two-item newsboy problem with substitutability, International Journal of Production Economics, 44 (1996), 267-275.
doi: 10.1016/0925-5273(96)80002-V. |
| [9] |
Y. Lan, Z. Liu and B. Niu, Pricing and design of after-sales service contract: The value of mining asymmetric sales cost information, Asia-Pacific Journal of Operational Research, 34 (2017), 1740002.
doi: 10.1142/S0217595917400024. |
| [10] |
Y. Lan, R. Zhao and W. Tang,
A fuzzy supply chain contract problem with pricing and warranty, Fuzzy Systems, 26 (2014), 1527-1538.
doi: 10.3233/IFS-130836. |
| [11] |
X. Li, G. Sun and Y. Li,
A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products, Annals of Operations Research, 242 (2016), 207-221.
doi: 10.1007/s10479-013-1498-x. |
| [12] |
S. Mou, D. J. Robb and N. DeHoratius,
Retail store operations: Literature review and research directions, European Journal of Operational Research, 265 (2018), 399-422.
doi: 10.1016/j.ejor.2017.07.003. |
| [13] |
M. Nagarajan and S. Rajagopalan,
Inventory models for substitutable products: Optimal policies and heuristics, Management Science, 54 (2008), 1453-1466.
doi: 10.1287/mnsc.1080.0871. |
| [14] |
X. A. Pan and D. Honhon,
Assortment planning for vertically differentiated products, Production and Operations Management, 21 (2012), 253-275.
doi: 10.1111/j.1937-5956.2011.01259.x. |
| [15] |
A. Sainathan,
Pricing and replenishment of competing perishable product variants under dynamic demand substitution, Production and Operations Management, 22 (2013), 1157-1181.
doi: 10.1111/poms.12004. |
| [16] |
Z. Sazvar, S. M. J. Mirzapour Al-e-hashem, K. Govindan and B. Bahli,
A novel mathematical model for a multi-period, multi-product optimal ordering problem considering expiry dates in a FEFO system, Transportation Research Part E: Logistics and Transportation Review, 93 (2016), 232-261.
doi: 10.1016/j.tre.2016.04.011. |
| [17] |
H. Shin, S. Park, E. Lee and W. C. Benton,
A classification of the literature on the planning of substitutable products, European Journal of Operational Research, 246 (2015), 686-699.
doi: 10.1016/j.ejor.2015.04.013. |
show all references
References:
| [1] |
M. Akan, B. Ata and R. C. Savaskan-Ebert,
Dynamic pricing of remanufacturable products under demand substitution: a product life cycle model, Annals of Operations Research, 211 (2013), 1-25.
doi: 10.1007/s10479-013-1409-1. |
| [2] |
G. Aydin and E. L. Porteus,
Joint inventory and pricing decisions for an assortment, Operations Research, 56 (2008), 1247-1255.
doi: 10.1287/opre.1080.0562. |
| [3] |
D. Honhon, V. Gaur and S. Seshadri,
Assortment planning and inventory decisions under stockout-based substitution, Operations Research, 58 (2010), 1364-1379.
doi: 10.1287/opre.1090.0805. |
| [4] |
C. C. Hsieh and C. H. Wu,
Coordinated decisions for substitutable products in a common retailer supply chain, European Journal of Operational Research, 196 (2009), 273-288.
doi: 10.1016/j.ejor.2008.02.019. |
| [5] |
M. Karakul,
Joint pricing and procurement of fashion products in the existence of clearance markets, International Journal of Production Economics, 114 (2008), 487-506.
doi: 10.1016/j.ijpe.2007.03.026. |
| [6] |
M. Karakul and L. M. A. Chan,
Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem, European Journal of Operational Research, 190 (2008), 179-204.
doi: 10.1016/j.ejor.2007.06.026. |
| [7] |
M. Karakul and L. M. A. Chan,
Joint pricing and procurement of substitutable products with random demands - A technical note, European Journal of Operational Research, 201 (2010), 324-328.
doi: 10.1016/j.ejor.2009.03.030. |
| [8] |
M. Khouja, A. Mehrez and G. Rabinowitz,
A two-item newsboy problem with substitutability, International Journal of Production Economics, 44 (1996), 267-275.
doi: 10.1016/0925-5273(96)80002-V. |
| [9] |
Y. Lan, Z. Liu and B. Niu, Pricing and design of after-sales service contract: The value of mining asymmetric sales cost information, Asia-Pacific Journal of Operational Research, 34 (2017), 1740002.
doi: 10.1142/S0217595917400024. |
| [10] |
Y. Lan, R. Zhao and W. Tang,
A fuzzy supply chain contract problem with pricing and warranty, Fuzzy Systems, 26 (2014), 1527-1538.
doi: 10.3233/IFS-130836. |
| [11] |
X. Li, G. Sun and Y. Li,
A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products, Annals of Operations Research, 242 (2016), 207-221.
doi: 10.1007/s10479-013-1498-x. |
| [12] |
S. Mou, D. J. Robb and N. DeHoratius,
Retail store operations: Literature review and research directions, European Journal of Operational Research, 265 (2018), 399-422.
doi: 10.1016/j.ejor.2017.07.003. |
| [13] |
M. Nagarajan and S. Rajagopalan,
Inventory models for substitutable products: Optimal policies and heuristics, Management Science, 54 (2008), 1453-1466.
doi: 10.1287/mnsc.1080.0871. |
| [14] |
X. A. Pan and D. Honhon,
Assortment planning for vertically differentiated products, Production and Operations Management, 21 (2012), 253-275.
doi: 10.1111/j.1937-5956.2011.01259.x. |
| [15] |
A. Sainathan,
Pricing and replenishment of competing perishable product variants under dynamic demand substitution, Production and Operations Management, 22 (2013), 1157-1181.
doi: 10.1111/poms.12004. |
| [16] |
Z. Sazvar, S. M. J. Mirzapour Al-e-hashem, K. Govindan and B. Bahli,
A novel mathematical model for a multi-period, multi-product optimal ordering problem considering expiry dates in a FEFO system, Transportation Research Part E: Logistics and Transportation Review, 93 (2016), 232-261.
doi: 10.1016/j.tre.2016.04.011. |
| [17] |
H. Shin, S. Park, E. Lee and W. C. Benton,
A classification of the literature on the planning of substitutable products, European Journal of Operational Research, 246 (2015), 686-699.
doi: 10.1016/j.ejor.2015.04.013. |
Figure 2.
Effect of the extant product's price on the expected profit
Table 1.
Effect of the inventory level of the existing product on the retailer's optimal policy and the expected profit
| Strategy | Variables | Values | |||||||||
| 160 | 170 | 180 | 190 | 200 | 210 | 220 | 230 | 240 | 250 | ||
| Unchanged | 840 | 830 | 820 | 810 | 800 | 800 | 800 | 800 | 800 | 800 | |
| 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | ||
| 5280 | 5360 | 5440 | 5520 | 5600 | 5600 | 5600 | 5600 | 5600 | 5600 | ||
| 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 101.0 | 102.0 | 103.0 | 104.0 | 105.0 | ||
| Decreased | 840 | 830 | 820 | 810 | 800 | 790 | 780 | 770 | 760 | 746.6 | |
| 12 | 12 | 12 | 12 | 12 | 11.7 | 11.4 | 11.1 | 10.8 | 10.5 | ||
| 5280 | 5360 | 5440 | 5520 | 5600 | 5617 | 5628 | 5633 | 5632 | 5611.4 | ||
| 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 99.7 | ||
| Strategy | Variables | Values | |||||||||
| 160 | 170 | 180 | 190 | 200 | 210 | 220 | 230 | 240 | 250 | ||
| Unchanged | 840 | 830 | 820 | 810 | 800 | 800 | 800 | 800 | 800 | 800 | |
| 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | ||
| 5280 | 5360 | 5440 | 5520 | 5600 | 5600 | 5600 | 5600 | 5600 | 5600 | ||
| 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 101.0 | 102.0 | 103.0 | 104.0 | 105.0 | ||
| Decreased | 840 | 830 | 820 | 810 | 800 | 790 | 780 | 770 | 760 | 746.6 | |
| 12 | 12 | 12 | 12 | 12 | 11.7 | 11.4 | 11.1 | 10.8 | 10.5 | ||
| 5280 | 5360 | 5440 | 5520 | 5600 | 5617 | 5628 | 5633 | 5632 | 5611.4 | ||
| 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 99.7 | ||
Table 2.
Effect of the salvage value of the existing product on the retailer's optimal policy and the expected profit
| Strategy | Variables | Values | |||||||||
| -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | ||
| Unchanged | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | |
| 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | ||
| 5350 | 5400 | 5450 | 5500 | 5550 | 5600 | 5650 | 5700 | 5750 | 5800 | ||
| 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | ||
| Decreased | 750 | 750 | 750 | 750 | 750 | 750 | 750 | 750 | 750 | 750 | |
| 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | ||
| 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | ||
| 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | ||
| Strategy | Variables | Values | |||||||||
| -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | ||
| Unchanged | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | 800 | |
| 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | ||
| 5350 | 5400 | 5450 | 5500 | 5550 | 5600 | 5650 | 5700 | 5750 | 5800 | ||
| 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | 105.0 | ||
| Decreased | 750 | 750 | 750 | 750 | 750 | 750 | 750 | 750 | 750 | 750 | |
| 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | 10.5 | ||
| 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | 5625 | ||
| 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | 100.0 | ||
| [1] |
Po-Chung Yang, Hui-Ming Wee, Shen-Lian Chung, Yong-Yan Huang. Pricing and replenishment strategy for a multi-market deteriorating product with time-varying and price-sensitive demand. Journal of Industrial & Management Optimization, 2013, 9 (4) : 769-787. doi: 10.3934/jimo.2013.9.769 |
| [2] |
Yanyi Xu, Arnab Bisi, Maqbool Dada. New structural properties of inventory models with Polya frequency distributed demand and fixed setup cost. Journal of Industrial & Management Optimization, 2017, 13 (2) : 931-945. doi: 10.3934/jimo.2016054 |
| [3] |
Yujing Wang, Changjun Yu, Kok Lay Teo. A new computational strategy for optimal control problem with a cost on changing control. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 339-364. doi: 10.3934/naco.2016016 |
| [4] |
Xiaoming Yan, Ping Cao, Minghui Zhang, Ke Liu. The optimal production and sales policy for a new product with negative word-of-mouth. Journal of Industrial & Management Optimization, 2011, 7 (1) : 117-137. doi: 10.3934/jimo.2011.7.117 |
| [5] |
Bing-Bing Cao, Zhi-Ping Fan, Tian-Hui You. The optimal pricing and ordering policy for temperature sensitive products considering the effects of temperature on demand. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1153-1184. doi: 10.3934/jimo.2018090 |
| [6] |
Ruopeng Wang, Jinting Wang, Chang Sun. Optimal pricing and inventory management for a loss averse firm when facing strategic customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1521-1544. doi: 10.3934/jimo.2018019 |
| [7] |
Wai-Ki Ching, Tang Li, Sin-Man Choi, Issic K. C. Leung. A tandem queueing system with applications to pricing strategy. Journal of Industrial & Management Optimization, 2009, 5 (1) : 103-114. doi: 10.3934/jimo.2009.5.103 |
| [8] |
Ka Wo Lau, Yue Kuen Kwok. Optimal execution strategy of liquidation. Journal of Industrial & Management Optimization, 2006, 2 (2) : 135-144. doi: 10.3934/jimo.2006.2.135 |
| [9] |
Jia Shu, Zhengyi Li, Weijun Zhong. A market selection and inventory ordering problem under demand uncertainty. Journal of Industrial & Management Optimization, 2011, 7 (2) : 425-434. doi: 10.3934/jimo.2011.7.425 |
| [10] |
Fengjun Wang, Qingling Zhang, Bin Li, Wanquan Liu. Optimal investment strategy on advertisement in duopoly. Journal of Industrial & Management Optimization, 2016, 12 (2) : 625-636. doi: 10.3934/jimo.2016.12.625 |
| [11] |
Xiangyu Gao, Yong Sun. A new heuristic algorithm for laser antimissile strategy optimization. Journal of Industrial & Management Optimization, 2012, 8 (2) : 457-468. doi: 10.3934/jimo.2012.8.457 |
| [12] |
Mitali Sarkar, Young Hae Lee. Optimum pricing strategy for complementary products with reservation price in a supply chain model. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1553-1586. doi: 10.3934/jimo.2017007 |
| [13] |
Guibin Lu, Qiying Hu, Youying Zhou, Wuyi Yue. Optimal execution strategy with an endogenously determined sales period. Journal of Industrial & Management Optimization, 2005, 1 (3) : 289-304. doi: 10.3934/jimo.2005.1.289 |
| [14] |
Jianbin Li, Ruina Yang, Niu Yu. Optimal capacity reservation policy on innovative product. Journal of Industrial & Management Optimization, 2013, 9 (4) : 799-825. doi: 10.3934/jimo.2013.9.799 |
| [15] |
Konstantina Skouri, Ioannis Konstantaras. Two-warehouse inventory models for deteriorating products with ramp type demand rate. Journal of Industrial & Management Optimization, 2013, 9 (4) : 855-883. doi: 10.3934/jimo.2013.9.855 |
| [16] |
Wei Liu, Shiji Song, Cheng Wu. Single-period inventory model with discrete stochastic demand based on prospect theory. Journal of Industrial & Management Optimization, 2012, 8 (3) : 577-590. doi: 10.3934/jimo.2012.8.577 |
| [17] |
Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. A two-echelon inventory model with stock-dependent demand and variable holding cost for deteriorating items. Numerical Algebra, Control & Optimization, 2017, 7 (1) : 21-50. doi: 10.3934/naco.2017002 |
| [18] |
Lizhao Yan, Fei Xu, Yongzeng Lai, Mingyong Lai. Stability strategies of manufacturing-inventory systems with unknown time-varying demand. Journal of Industrial & Management Optimization, 2017, 13 (4) : 2033-2047. doi: 10.3934/jimo.2017030 |
| [19] |
Katherinne Salas Navarro, Jaime Acevedo Chedid, Whady F. Florez, Holman Ospina Mateus, Leopoldo Eduardo Cárdenas-Barrón, Shib Sankar Sana. A collaborative EPQ inventory model for a three-echelon supply chain with multiple products considering the effect of marketing effort on demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-14. doi: 10.3934/jimo.2019020 |
| [20] |
Magfura Pervin, Sankar Kumar Roy, Gerhard Wilhelm Weber. Deteriorating inventory with preservation technology under price- and stock-sensitive demand. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-28. doi: 10.3934/jimo.2019019 |
2017 Impact Factor: 0.994
Tools
Metrics
Other articles
by authors
[Back to Top]