Applying Fuzzy Multiobjective Integrated Logistics Model to Green Supply Chain Problems

Table 7

Notations for our proposed model.

Manufacturing chain cost
MC	Total cost
MIC	Total inventory cost
MMC	Total manufacturing cost
MPC	Total raw material procurement cost
MTC	Total transportation cost
MRC	Total recycling fees paid from the manufacturing layer of a given manufacturing chain to the corresponding EPA
MLC	Labor cost
Manufacturing chain revenue
MTR	Total revenue
Reverse chain cost
RC	Total cost
RTCC	Total collection cost of corresponding used products
RFC	Total final disposal cost of corresponding used products
RIC	Total inventory cost
RTC	Total transportation cost
RTTC	Total transitional treatment cost of the corresponding used products
RLC	Labor cost
Reverse chain revenue
RTR	Total revenue
RR	Total revenue oriented specifically from general vendor-buyer business operations
RS	Total subsidies
Revenue
𝑅𝑚𝑖/𝑚𝑖+1	The generalized revenues from layer 𝑖 of the given manufacturing chain to layer 𝑖+1 of the given manufacturing chain (𝑖=2,3,4)
𝑅𝑚5/𝑟𝑗	The generalized revenues from end customers in layer 5 of the given manufacturing chain to layer 𝑗 of the given reverse chain (𝑗=1,2,3)
𝑅𝑟1/𝑟𝑗	The generalized revenues from the collecting points in layer 1 of the given reverse chain to layer 𝑗 of the given reverse chain (𝑗=2,3)
𝑅𝑟𝑗/𝑟𝑗+1	The generalized revenues from layer 𝑗 of the given reverse chain to layer 𝑗+1 of the given reverse chain (𝑗=2,3)
𝑅𝑟4/𝑚2	The generalized revenues from the second material market in layer 4 of the given reverse chain to the manufactures in layer 2 of the given manufacturing chain
EPO	The unit subsidy of environmental protection offered by EPA
Cost
𝐶^𝐶	Collecting cost of used product returned from end customer
𝐶^𝐼	Inventory cost for storing products
𝐶^IR	Inventory cost for storing raw materials
C^IT	Inventory cost for storing used product that has been treated by a reverse logistics chain member
𝐶^IT	Inventory cost for storing used product that has not been treated by a reverse logistics chain member
𝐶^𝑀	Manufacturing cost of used product
𝐶^𝑃	Procurement cost of physical flow 𝑖
𝐶^𝑇	Transportation cost
𝐶^TT	Transitional treatment cost
𝐹	Recycling fees charged by the corresponding EPA for manufacturing products
𝐶^𝐹	Unit cost of final disposal
𝐶^𝐿	Hourly labor cost
𝐶^𝑅	Raw material cost
Quantity
𝑄^𝐼	Quantity of inventory—decision variable
𝑄^IR	Quantity of raw materials inventory—decision variable
𝑄^IT	Quantity of inventory of used product that has been treated
𝑄^IT	Quantity of inventory of used product that has not been treated invent
𝑄^𝐹	Quantity of final disposal—decision variable
𝑄^𝑀	Manufacturing quantity—decision variable
𝑄^𝑅	Raw materials quantity—decision variable
𝑄^TT	Transitional treatment quantity—decision variable
𝑄^RE	Quantity of used product that has been returned by end customers
𝑄^𝐿	Quantity of labors—decision variable
𝑄𝑚𝑖,𝑚5	The generalized form of a decision variable referring to the physical flow quantity transported from layer 𝑖 given in the manufacturing chain to end customers in layer 5 given in the manufacturing chain (𝑖=2,3,4)
𝑄𝑚𝑖,𝑚𝑖+1	The generalized form of a decision variable referring to the physical flow quantity transported from layer 𝑖 given in the manufacturing chain to layer 𝑖+1 given in the manufacturing chain (𝑖=1,2,3,4)
𝑄𝑚5,𝑟𝑗	The generalized form of a decision variable referring to the physical flow quantity transported from end customers in layer 5 given in the manufacturing chain to layer 𝑗 given in the reverse chain (𝑗=1,2,3)
𝑄𝑟1,𝑟2	The generalized form of a decision variable referring to the physical flow quantity transported from collecting points in layer 1 of the given reverse chain to recycling plants in layer 2 given in the reverse chain
𝑄𝑟1,𝑟3	The generalized form of a decision variable referring to the physical flow quantity transported from collecting points in layer 1 of the given reverse chain to disassembly plants in layer 3 given in the reverse chain
𝑄𝑟2,𝑟3	The generalized form of a decision variable referring to the physical flow quantity transported from recycling plants in layer 2 given in the reverse chain to disassembly plants in layer 3 of the given reverse chain
𝑄𝑟3,𝑟4	The generalized form of a decision variable referring to the physical flow quantity transported from disassembly plants in layer 3 of the given reverse chain to final disposal in layer 4 given in the reverse chain
𝑄𝑟3,𝑟5	The generalized form of a decision variable referring to the physical flow quantity transported from disassembly plants in layer 3 given in the reverse chain to final disposal in layer 5 of the given reverse chain
𝑄𝑟5,𝑚2	The generalized form of a decision variable referring to the physical flow quantity transported from final disposal in layer 5 of the given reverse chain to manufactures in layer 2 given in the manufacturing chain
Facility capacity
𝑆	Safety stock
𝑆^𝐼	Facility capacity for inventory
𝑆^IR	Facility capacity for raw material inventory
𝑆^IT	Facility capacity for inventory that has already been treated
𝑆^IT	Facility capacity for inventory that has not been treated
Others
𝛽	Predetermined used-product return ratio
𝛾	A coefficient referring to the transformation
𝐷	Demand of manufacturing chain end customer