# American Institute of Mathematical Sciences

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

* Corresponding author: Jingquan Li

Received  July 2017 Revised  August 2018 Published  December 2018

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.

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
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##### References:
Effect of the extant product's price on the new product's order quantity
Effect of the extant product's price on the expected profit
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
 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
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
 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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