Optimal Operational Decision Making of Manufacturers and Authorized Remanufacturers with Patent Licensing under Carbon Cap-and-Trade Regulations

Table 1

Notation.

Notation	Description
Model parameter
cm	Manufacturing cost per unit of new product
cr	Remanufacturing cost per unit of remanufactured product (generally, cr < cm)
em	Carbon emissions for producing a new product
er	Carbon emissions for producing a remanufactured product (generally, em > er)
ɛ1	Selling price for one unit of carbon emission permit
ɛ2	Buying price for one unit of carbon emission permit. For simplicity, we set ɛ1 < ɛ2
Mm	Carbon emissions cap the government allocates to the OEM
Mr	Carbon emissions cap the government allocates to the TPR
A	Market capacity
Θ	Consumer’s willingness to pay
Γ	Yield rate, γ ϵ (0, 1)
Α	Quantity that the consumers return voluntarily at zero price
Β	Sensitivity of consumers to acquisition price
G	Acquired quantity of used product
G	Government subsidy per unit of acquired used product
Decision variables for TPR
p2r	Sales price per unit of remanufactured product in scenario 2
q2r	Remanufacturing quantity/demand for remanufactured products in scenario 2
u	Acquisition price the TPR collects per unit of used product
Decision variables for OEM
qim	Manufacturing quantity/demand for new products in scenario i, i = 1, 2
pim	Sales price per unit of new product in scenario i
f	Royalty rate that the OEM charges the TPR per unit of remanufactured product
Objective function
Пim	Total profit of OEM in scenario i, i = 1, 2
П2r	Total profit of TPR in scenario 2
Пs	Total profit of the entire supply chain with centralized decision making