American Institute of Mathematical Sciences

January  2018, 14(1): 349-369. doi: 10.3934/jimo.2017050

Pricing and ordering strategies of supply chain with selling gift cards

 School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 611731, China

* Corresponding author: Jingming Pan

Received  April 2016 Revised  May 2016 Published  June 2017

Citation: Jingming Pan, Wenqing Shi, Xiaowo Tang. Pricing and ordering strategies of supply chain with selling gift cards. Journal of Industrial & Management Optimization, 2018, 14 (1) : 349-369. doi: 10.3934/jimo.2017050
References:

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References:
Decision behaviors in supply chain without gift cards
Decision behaviors in supply chain with gift cards
$w^*$, $q^*$ and $\pi^*$ vs. $CV$ (Note: $c=5, \theta=0.15, \alpha=0.8, \beta=0.5$ and $m=0.3$)
$w^*$, $q^*$ and $\pi^*$ vs. $c/p$ (Note: $\sigma=40, \theta=0.15, \alpha=0.8, \beta=0.5$ and $m=0.3$)
$w^*$, $q^*$ and $\pi^*$ vs. $\alpha$ (Note: $\sigma=40, c=5, \theta=0.15, \beta=0.5$ and $m=0.3$)
$w^*$, $q^*$ and $\pi^*$ vs. $\beta$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.5$ and $m=0.3$)
$w^*$, $q^*$ and $\pi^*$ vs. $\beta$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.8$ and $m=0.3$)
$w^*$, $q^*$ and $\pi^*$ vs. $m$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.8$ and $\beta=0.5$)
Notation
Optimal solutions for uniformly distributed demand
 Optimal wholesale price Optimal order quantity Conditions $w_{NG}^* = \frac{1}{2}\left[ {c + \left( {1 - \theta } \right)p + \theta v} \right]$ $q_{NG}^* = \frac{{b\left[ {\left( {1 - \theta } \right)p + \theta v - c} \right]}}{{2\left( {1 - \theta } \right)\left( {p - v} \right)}}$ -- $w_{RG}^* = \frac{1}{2}\left[ {c + \left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p} \right]$ $q_{RG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - c} \right]}}{{2\left( {1 -\beta- m\alpha \beta + \alpha \beta } \right)p - v}}$ $\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - v \ge 0$ $w_{SG}^* = \frac{1}{2}\left[ {c + \left( {1 - m\alpha \beta } \right)p} \right]$ $q_{SG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - m\alpha \beta } \right)p - c} \right]}}{{2\left( {1 - m\alpha \beta } \right)p - v}}$ $\left( {1 - m\alpha \beta } \right)p - v \ge 0$
 Optimal wholesale price Optimal order quantity Conditions $w_{NG}^* = \frac{1}{2}\left[ {c + \left( {1 - \theta } \right)p + \theta v} \right]$ $q_{NG}^* = \frac{{b\left[ {\left( {1 - \theta } \right)p + \theta v - c} \right]}}{{2\left( {1 - \theta } \right)\left( {p - v} \right)}}$ -- $w_{RG}^* = \frac{1}{2}\left[ {c + \left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p} \right]$ $q_{RG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - c} \right]}}{{2\left( {1 -\beta- m\alpha \beta + \alpha \beta } \right)p - v}}$ $\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - v \ge 0$ $w_{SG}^* = \frac{1}{2}\left[ {c + \left( {1 - m\alpha \beta } \right)p} \right]$ $q_{SG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - m\alpha \beta } \right)p - c} \right]}}{{2\left( {1 - m\alpha \beta } \right)p - v}}$ $\left( {1 - m\alpha \beta } \right)p - v \ge 0$
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