Optimal pricing and inventory strategies for introducing a new product based on demand substitution effects

Zhijie Sasha Dong; Wei Chen; Qing Zhao; Jingquan Li

doi:10.3934/jimo.2018175

Article Contents

2020, Volume 16, Issue 2: 725-739. Doi: 10.3934/jimo.2018175

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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

* Corresponding author: Jingquan Li
* Corresponding author: Jingquan Li

Received: June 30, 2017

Revised: July 31, 2018

Early access: December 2018

Published: February 2020

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B05; Secondary: 91B24, 91B26.

Citation:

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Figure 1. Effect of the extant product's price on the new product's order quantity

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Figure 2. Effect of the extant product's price on the expected profit

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Table 1. Effect of the inventory level of the existing product on the retailer's optimal policy and the expected profit

Strategy	Variables	Values
	$ Q_1 $	160	170	180	190	200	210	220	230	240	250
Unchanged	$ Q_2 $	840	830	820	810	800	800	800	800	800	800
	$ s_1 (\$)$	12	12	12	12	12	12	12	12	12	12
	$ EP (\$)$	5280	5360	5440	5520	5600	5600	5600	5600	5600	5600
	$ RP (\$)$	100.0	100.0	100.0	100.0	100.0	101.0	102.0	103.0	104.0	105.0
Decreased	$ Q_2 $	840	830	820	810	800	790	780	770	760	746.6
	$ s_1 (\$)$	12	12	12	12	12	11.7	11.4	11.1	10.8	10.5
	$ EP (\$)$	5280	5360	5440	5520	5600	5617	5628	5633	5632	5611.4
	$ RP (\$)$	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	99.7

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Table 2. Effect of the salvage value of the existing product on the retailer's optimal policy and the expected profit

Strategy	Variables	Values
	$ h_1 $	-5	-4	-3	-2	-1	0	1	2	3	4
Unchanged	$ Q_2 $	800	800	800	800	800	800	800	800	800	800
	$ s_1 (\$)$	12	12	12	12	12	12	12	12	12	12
	$ EP (\$)$	5350	5400	5450	5500	5550	5600	5650	5700	5750	5800
	$ RP (\$)$	105.0	105.0	105.0	105.0	105.0	105.0	105.0	105.0	105.0	105.0
Decreased	$ Q_2 $	750	750	750	750	750	750	750	750	750	750
	$ s_1 (\$)$	10.5	10.5	10.5	10.5	10.5	10.5	10.5	10.5	10.5	10.5
	$ EP (\$)$	5625	5625	5625	5625	5625	5625	5625	5625	5625	5625
	$ RP (\$)$	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0	100.0

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