Article Contents
Article Contents

# Pricing and ordering strategies of supply chain with selling gift cards

• * Corresponding author: Jingming Pan

Mathematics Subject Classification: Primary: 90B05, 90B60; Secondary: 91B42.

 Citation:

• Figure 1.  Decision behaviors in supply chain without gift cards

Figure 2.  Decision behaviors in supply chain with gift cards

Figure 3.  $w^*$, $q^*$ and $\pi^*$ vs. $CV$ (Note: $c=5, \theta=0.15, \alpha=0.8, \beta=0.5$ and $m=0.3$)

Figure 4.  $w^*$, $q^*$ and $\pi^*$ vs. $c/p$ (Note: $\sigma=40, \theta=0.15, \alpha=0.8, \beta=0.5$ and $m=0.3$)

Figure 5.  $w^*$, $q^*$ and $\pi^*$ vs. $\alpha$ (Note: $\sigma=40, c=5, \theta=0.15, \beta=0.5$ and $m=0.3$)

Figure 6.  $w^*$, $q^*$ and $\pi^*$ vs. $\beta$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.5$ and $m=0.3$)

Figure 7.  $w^*$, $q^*$ and $\pi^*$ vs. $\beta$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.8$ and $m=0.3$)

Figure 8.  $w^*$, $q^*$ and $\pi^*$ vs. $m$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.8$ and $\beta=0.5$)

Table 1.  Notation

Table 2.  Optimal solutions for uniformly distributed demand

 Optimal wholesale price Optimal order quantity Conditions $w_{NG}^* = \frac{1}{2}\left[ {c + \left( {1 - \theta } \right)p + \theta v} \right]$ $q_{NG}^* = \frac{{b\left[ {\left( {1 - \theta } \right)p + \theta v - c} \right]}}{{2\left( {1 - \theta } \right)\left( {p - v} \right)}}$ -- $w_{RG}^* = \frac{1}{2}\left[ {c + \left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p} \right]$ $q_{RG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - c} \right]}}{{2\left( {1 -\beta- m\alpha \beta + \alpha \beta } \right)p - v}}$ $\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - v \ge 0$ $w_{SG}^* = \frac{1}{2}\left[ {c + \left( {1 - m\alpha \beta } \right)p} \right]$ $q_{SG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - m\alpha \beta } \right)p - c} \right]}}{{2\left( {1 - m\alpha \beta } \right)p - v}}$ $\left( {1 - m\alpha \beta } \right)p - v \ge 0$

Figures(8)

Tables(2)