Quantity Discount Supply Chain Models with Fashion Products and Uncertain Yields

Table 1

Instruction for variables.

Variable	Definition
ℎ0	Inventory cost for raw material per unit
ℎ1	Inventory cost for finished products per unit
𝑟0	Shortage cost for raw material per unit
𝑟1	Shortage cost for finished product per unit
𝑐0	Cost of production of raw material per unit
𝑐1	Cost of production of finished product per unit
𝑝0	Price of the raw material per unit
𝑝1	Price of finished product per unit
𝜋0	Total profit of the supply chain
𝜋1	Profit for the supplier
𝜋2	Profit for the manufacturer
𝑞0	Planned output of the supplier
𝑞1	Ordering quantity by the manufacturer
X	Random variables by the supplier
Y	Random variable by the manufacturer
Z	Random variables of market demand
D	Expectation of the market demand
𝑓1(𝑥)	Probability density function of X
𝑓2(𝑦)	Probability density function of Y
𝑔(𝑧)	Probability density function of Z
𝑞^∗	Qualification point of quantity discount
𝛼	Discount rate of the price
U	Independent and non-coordinated decision
C	Centralized decision
QD	Quantity discount decision