Table 3. Extension of T.-M. Choi and...

Table 3.

Extension of T.-M. Choi and Choi (2008), T. M. Choi et al. (2019) and Shen et al. (2013)

	Member of supply chain
No coordination
Profit	Manufacturer	(w − C_m)q
	Retailer	(p − w − C_r)q − (p − S_r)(q − x)⁺
	Supply chain	(p − C_m − C_r)q − (p − S_r)(q − x)⁺
EP	Manufacturer	(w − C_m)q
	Retailer	(p − w − C_r)q − (p − S_r)(q – s(q))
	Supply chain	(p − C_m − C_r)q − (p − S_r)(q – S(q))
SDP	Manufacturer	0
	Retailer	$(p - S_{r}) \sqrt{Π (q)}$
	Supply chain	$(p - S_{r}) \sqrt{Π (q)}$
Wholesale price contract
Profit	Manufacturer	(w − C_m)q_sc
	Retailer	(p − w − C_r)q_sc − (p − S_r)(q_sc − x)⁺
	Supply chain	(p − C_m − C_r)q_sc − (p − S_r)(q_sc − x)⁺
EP	Manufacturer	(w − C_m)q_sc
	Retailer	(p − w − C_r)q_sc − (p − S_r) (q_sc – s(q_sc))
	Supply chain	(p − C_m − C_r)q_sc − (p − S_r) (q_sc – s(q_sc))
SDP	Manufacturer	0
	Retailer	$(p - S_{r}) \sqrt{Π (Q_{s c})}$
	Supply chain	$(p - S_{r}) \sqrt{Π (Q_{s c})}$
Buy-back contract
Profit	Manufacturer	(w – C_m)q_sc − (β – S_m)(q_sc − x)⁺
	Retailer	(p – C_r – w)q_sc − (p – β)(q_sc − x)⁺
	Supply chain	(p – C_m – C_r)q_sc − (p – S_m)(q_sc − x)⁺
EP	Manufacturer	(w – C_m)q_sc – (β – S_m)(q_sc – S(q_sc))
	Retailer	(p – C_r – w)q_sc – (p – β)(q_sc – S(q_sc))
	Supply chain	(p – C_m – C_r)q_sc – (p – S_m)(q_sc – S(q_sc))
SDP	Manufacturer	$(β - S_{m}) \sqrt{Π (Q_{s c})}$
	Retailer	$(p - β) \sqrt{Π (Q_{s c})}$
	Supply chain	$(p - S_{m}) \sqrt{Π (Q_{s c})}$
Revenue sharing contract
Profit	Manufacturer	(W – C_m + p(1 – φ))Q_sc – {(p(1 – φ) – S_r)(Q_sc – x)⁺}
	Retailer	(p – W – C_r)q_sc – (φp – S_r)(q_sc – x)⁺
	Supply chain	(p(2 – φ) – C_m – C_r)Q_sc – (p – 2S_r)(Q_sc – x)⁺
EP	Manufacturer	(W – C_m + p(1 – φ))Q_sc – {(p(1 – φ) – S_r)(Q_sc – S(Q_sc))}
	Retailer	(p – W – C_r)q_sc – (φ_p – S_r)(q_sc – S(q_sc))
	Supply chain	(p(2 – φ) – C_m – C_r)Q_sc – (p – 2S_r)(Q_sc – S(Q_sc))
SDP	Manufacturer	$(p (1 - φ) - S_{r}) \sqrt{Π (Q_{s c})}$
	Retailer	$(φ p - S_{r}) \sqrt{Π (Q_{s c})}$
	Supply chain	$(p - 2 S_{r}) \sqrt{Π (Q_{s c})}$
Markdown money policy
Profit	Manufacturer	(w – C_m)q_sc – B_m(q_sc – x)⁺
	Retailer	(p – w – C_r)q_sc – (p – B_m)(q_sc – x)⁺
	Supply chains	(p – C_m – C_r)q_sc – p(q_sc – x)⁺
EP	Manufacturer	(w – C_m)q_sc – B_m(q_sc – S(q_sc))
	Retailer	(p – w – C_r)q_sc – (p – B_m)(q_sc – s(q_sc))
	Supply chain	(p – C_m – C_r)q_sc – p(q_sc – S(q_sc))
SDP	Manufacturer	$B_{m} \sqrt{Π (Q_{s c})}$
	Retailer	$(p - B_{m}) \sqrt{Π (Q_{s c})}$
	Supply chain	$p \sqrt{Π (Q_{s c})}$
Sales rebate contract
Profit	Manufacturer	(w – C_m)q_sc – U_m(q_sc – T_m)⁺
	Retailer	(p – w – C_r)q_sc – (p – S_r)(q_sc – S(q_sc)) + U_m(q_sc – T_m)⁺
	Supply chain	(p – C_m – C_r)q_sc – (p – S_r)(q_sc – s(q_sc))
EP	Manufacturer	$(w - C_{m}) Q_{s c} - U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x$
	Retailer	$(p - w - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c})) + U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x$
	Supply chain	(p – C_m – C_r)q_sc – (p – S_r)(q_sc – s(q_sc))
SDP	Manufacturer	$(p - S_{r}) (Q_{s c} - s (Q_{s c})) + U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Retailer	$U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Supply chain	$(p - S_{r}) (Q_{s c} - s (Q_{s c})) + 2 U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$

	Member of supply chain
No coordination
Profit	Manufacturer	(w − C_m)q
	Retailer	(p − w − C_r)q − (p − S_r)(q − x)⁺
	Supply chain	(p − C_m − C_r)q − (p − S_r)(q − x)⁺
EP	Manufacturer	(w − C_m)q
	Retailer	(p − w − C_r)q − (p − S_r)(q – s(q))
	Supply chain	(p − C_m − C_r)q − (p − S_r)(q – S(q))
SDP	Manufacturer	0
	Retailer	$(p - S_{r}) \sqrt{Π (q)}$
	Supply chain	$(p - S_{r}) \sqrt{Π (q)}$
Wholesale price contract
Profit	Manufacturer	(w − C_m)q_sc
	Retailer	(p − w − C_r)q_sc − (p − S_r)(q_sc − x)⁺
	Supply chain	(p − C_m − C_r)q_sc − (p − S_r)(q_sc − x)⁺
EP	Manufacturer	(w − C_m)q_sc
	Retailer	(p − w − C_r)q_sc − (p − S_r) (q_sc – s(q_sc))
	Supply chain	(p − C_m − C_r)q_sc − (p − S_r) (q_sc – s(q_sc))
SDP	Manufacturer	0
	Retailer	$(p - S_{r}) \sqrt{Π (Q_{s c})}$
	Supply chain	$(p - S_{r}) \sqrt{Π (Q_{s c})}$
Buy-back contract
Profit	Manufacturer	(w – C_m)q_sc − (β – S_m)(q_sc − x)⁺
	Retailer	(p – C_r – w)q_sc − (p – β)(q_sc − x)⁺
	Supply chain	(p – C_m – C_r)q_sc − (p – S_m)(q_sc − x)⁺
EP	Manufacturer	(w – C_m)q_sc – (β – S_m)(q_sc – S(q_sc))
	Retailer	(p – C_r – w)q_sc – (p – β)(q_sc – S(q_sc))
	Supply chain	(p – C_m – C_r)q_sc – (p – S_m)(q_sc – S(q_sc))
SDP	Manufacturer	$(β - S_{m}) \sqrt{Π (Q_{s c})}$
	Retailer	$(p - β) \sqrt{Π (Q_{s c})}$
	Supply chain	$(p - S_{m}) \sqrt{Π (Q_{s c})}$
Revenue sharing contract
Profit	Manufacturer	(W – C_m + p(1 – φ))Q_sc – {(p(1 – φ) – S_r)(Q_sc – x)⁺}
	Retailer	(p – W – C_r)q_sc – (φp – S_r)(q_sc – x)⁺
	Supply chain	(p(2 – φ) – C_m – C_r)Q_sc – (p – 2S_r)(Q_sc – x)⁺
EP	Manufacturer	(W – C_m + p(1 – φ))Q_sc – {(p(1 – φ) – S_r)(Q_sc – S(Q_sc))}
	Retailer	(p – W – C_r)q_sc – (φ_p – S_r)(q_sc – S(q_sc))
	Supply chain	(p(2 – φ) – C_m – C_r)Q_sc – (p – 2S_r)(Q_sc – S(Q_sc))
SDP	Manufacturer	$(p (1 - φ) - S_{r}) \sqrt{Π (Q_{s c})}$
	Retailer	$(φ p - S_{r}) \sqrt{Π (Q_{s c})}$
	Supply chain	$(p - 2 S_{r}) \sqrt{Π (Q_{s c})}$
Markdown money policy
Profit	Manufacturer	(w – C_m)q_sc – B_m(q_sc – x)⁺
	Retailer	(p – w – C_r)q_sc – (p – B_m)(q_sc – x)⁺
	Supply chains	(p – C_m – C_r)q_sc – p(q_sc – x)⁺
EP	Manufacturer	(w – C_m)q_sc – B_m(q_sc – S(q_sc))
	Retailer	(p – w – C_r)q_sc – (p – B_m)(q_sc – s(q_sc))
	Supply chain	(p – C_m – C_r)q_sc – p(q_sc – S(q_sc))
SDP	Manufacturer	$B_{m} \sqrt{Π (Q_{s c})}$
	Retailer	$(p - B_{m}) \sqrt{Π (Q_{s c})}$
	Supply chain	$p \sqrt{Π (Q_{s c})}$
Sales rebate contract
Profit	Manufacturer	(w – C_m)q_sc – U_m(q_sc – T_m)⁺
	Retailer	(p – w – C_r)q_sc – (p – S_r)(q_sc – S(q_sc)) + U_m(q_sc – T_m)⁺
	Supply chain	(p – C_m – C_r)q_sc – (p – S_r)(q_sc – s(q_sc))
EP	Manufacturer	$(w - C_{m}) Q_{s c} - U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x$
	Retailer	$(p - w - C_{r}) Q_{s c} - (p - S_{r}) (Q_{s c} - S (Q_{s c})) + U_{m} \int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x$
	Supply chain	(p – C_m – C_r)q_sc – (p – S_r)(q_sc – s(q_sc))
SDP	Manufacturer	$(p - S_{r}) (Q_{s c} - s (Q_{s c})) + U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Retailer	$U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$
	Supply chain	$(p - S_{r}) (Q_{s c} - s (Q_{s c})) + 2 U_{m} \sqrt{\int_{T_{m}}^{Q_{s c}} \bar{F} (x) d x}$

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