Table 4. Description of numerical...

Table 4.

Description of numerical example for assessment of six cases

Contract	Member	Coefficient of variation
Case 0 – No coordination	Manufacturer	0
	Retailer	$\frac{(p - S_{r}) \sqrt{Π (q)}}{(p - C_{m} - C_{r}) q - (p - S_{r}) (q - S (q))}$
	Supply chain	$\frac{(p - S_{r}) \sqrt{Π (q)}}{(p - C_{m} - C_{r}) q - (p - S_{r}) (q - S (q))}$

Case 1 – Wholesale price contract	Manufacturer	0
	Retailer	$\frac{(p - S_{r}) \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c}))}$
	Supply chain	$\frac{(p - S_{r}) \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c}))}$

Case 2 – Buyback contract	Manufacturer	$\frac{(β - S_{m}) \sqrt{Π (Q_{s c})}}{(w - C_{m}) Q_{s c} - (β - S_{m}) (Q_{s c} - S (Q_{s c}))}$
	Retailer	$\frac{(p - β) \sqrt{Π (Q_{s c})}}{(p - C_{r} - w) Q_{s c} - (p - β) (Q_{s c} - S (Q_{s c}))}$
	Supply chain	$\frac{(p - S_{m}) \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{m}) (Q_{s c} - S (Q_{s c}))}$

Case 3 – Revenue sharing contract	Manufacturer	$\frac{(p (1 - φ) - S_{r}) \sqrt{Π (Q_{s c})}}{(W - C_{m} + p (1 - φ)) Q_{s c} - {(p (1 - φ) - S_{r}) (Q_{s c} - S (Q_{s c}))}}$
	Retailer	$\frac{(φ p - S_{r}) \sqrt{Π (Q_{s c})}}{(p - W - C_{r}) Q_{s c} - (φ p - S_{r}) (Q_{s c} - S (Q_{s c}))}$
	Supply chain	$\frac{(p - 2 S_{r}) \sqrt{Π (Q_{s c})}}{(p (2 - φ) - C_{m} - C_{r}) Q_{s c} - (p - 2 S_{r}) (Q_{s c} - S (Q_{s c}))}$

Case 4 – Markdown money Policy	Manufacturer	$\frac{B_{m} \sqrt{Π (Q_{s c})}}{(w - C_{m}) Q_{s c} - B_{m} (Q_{s c} - S (Q_{s c}))}$
	Retailer	$\frac{(p - B_{m}) \sqrt{Π (Q_{s c})}}{(p - w - C_{r}) Q_{s c} - (p - B_{m}) (Q_{s c} - s (Q_{s c}))}$
	Supply chain	$\frac{p \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - p (Q_{s c} - S (Q_{s c}))}$

Case 5 – Sales rebate contract	Manufacturer	$\frac{(p - S_{r}) (Q_{s c} - s (Q_{s c})) + U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}}{(w - C_{m}) Q_{s c} - U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Retailer	$\frac{U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}}{(p - w - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c})) + U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Supply chain	$\frac{(p - S_{r}) (Q_{s c} - s (Q_{s c})) + 2 U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - s (Q_{s c}))}$

Contract	Member	Coefficient of variation
Case 0 – No coordination	Manufacturer	0
	Retailer	$\frac{(p - S_{r}) \sqrt{Π (q)}}{(p - C_{m} - C_{r}) q - (p - S_{r}) (q - S (q))}$
	Supply chain	$\frac{(p - S_{r}) \sqrt{Π (q)}}{(p - C_{m} - C_{r}) q - (p - S_{r}) (q - S (q))}$

Case 1 – Wholesale price contract	Manufacturer	0
	Retailer	$\frac{(p - S_{r}) \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c}))}$
	Supply chain	$\frac{(p - S_{r}) \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c}))}$

Case 2 – Buyback contract	Manufacturer	$\frac{(β - S_{m}) \sqrt{Π (Q_{s c})}}{(w - C_{m}) Q_{s c} - (β - S_{m}) (Q_{s c} - S (Q_{s c}))}$
	Retailer	$\frac{(p - β) \sqrt{Π (Q_{s c})}}{(p - C_{r} - w) Q_{s c} - (p - β) (Q_{s c} - S (Q_{s c}))}$
	Supply chain	$\frac{(p - S_{m}) \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{m}) (Q_{s c} - S (Q_{s c}))}$

Case 3 – Revenue sharing contract	Manufacturer	$\frac{(p (1 - φ) - S_{r}) \sqrt{Π (Q_{s c})}}{(W - C_{m} + p (1 - φ)) Q_{s c} - {(p (1 - φ) - S_{r}) (Q_{s c} - S (Q_{s c}))}}$
	Retailer	$\frac{(φ p - S_{r}) \sqrt{Π (Q_{s c})}}{(p - W - C_{r}) Q_{s c} - (φ p - S_{r}) (Q_{s c} - S (Q_{s c}))}$
	Supply chain	$\frac{(p - 2 S_{r}) \sqrt{Π (Q_{s c})}}{(p (2 - φ) - C_{m} - C_{r}) Q_{s c} - (p - 2 S_{r}) (Q_{s c} - S (Q_{s c}))}$

Case 4 – Markdown money Policy	Manufacturer	$\frac{B_{m} \sqrt{Π (Q_{s c})}}{(w - C_{m}) Q_{s c} - B_{m} (Q_{s c} - S (Q_{s c}))}$
	Retailer	$\frac{(p - B_{m}) \sqrt{Π (Q_{s c})}}{(p - w - C_{r}) Q_{s c} - (p - B_{m}) (Q_{s c} - s (Q_{s c}))}$
	Supply chain	$\frac{p \sqrt{Π (Q_{s c})}}{(p - C_{m} - C_{r}) Q_{s c} - p (Q_{s c} - S (Q_{s c}))}$

Case 5 – Sales rebate contract	Manufacturer	$\frac{(p - S_{r}) (Q_{s c} - s (Q_{s c})) + U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}}{(w - C_{m}) Q_{s c} - U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Retailer	$\frac{U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}}{(p - w - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c})) + U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Supply chain	$\frac{(p - S_{r}) (Q_{s c} - s (Q_{s c})) + 2 U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}}{(p - C_{m} - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - s (Q_{s c}))}$

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