Indices
j:	The index used to indicate number of products, j = 1, 2, ... N
a:	To indicate the parameters for first stage of manufacture
b:	Used with the vendor parameters
c:	To represent the final stage of manufacture
Decision variables
Tj:	Cycle time to manufacture the j-th product (units)
Lja:	Labors utilized at 1st stage to manufacture the j-th product (workers)
Ljc:	Labors utilized to manufacture the j-th product at 1st during final stage (workers)
Kja:	Number of machine units utilized at the 1st stage to manufacture the j-th product (workstations)
Kjc:	Number of machine units utilized to manufacture the j-th product during the finishing stage (workstations)
Pja:	Plant production rate of the j-th product in the 1st stage (units/year)
Pjc:	Plant production rate of the j-th product in the 2nd stage of manufacture (units/year)
Manufacturer Parameters
Crm	Raw material cost of the j-th product ($/unit)
TDmj	Manufacturer total tool-die cost of the j-th product ($/unit)
TDmaj	Tool-die cost of the j-th product in 1st stage of manufacture ($/unit)
TDmcj	Tool-die cost of the the j-th product in final stage ($/unit)
gj	Total indirect production cost of the j-th product ($/unit)
gmaj	Indirect cost of the j-th product in first stage of manufacture ($/unit)
gmcj	Indirect production cost of j-th product in the final stage of manufacture ($/unit)
Dj(Ω)	Variable demand depending emergency level due to pandemic ($/unit)
Qj	Production quantity (units)
lja	Average labor utilized per machine in first stage of manufacture (labor/machine)
ljc	Average labor utilized per machine in final stage of manufacture (labor/machine)
Wj	Average wedge of labor to manufacture the j-th product ($/labor)
Aj	Setup cost for j-th product ($/year)
hmj	Manufacturer’s holding cost of each product per cycle ($/unit/year)
Gj	Reworking cost of the j-th product ($/unit)
εja	Production rate of each machine unit to manufacture the j-th product in the 1st stage (units/machine)
εjc	Production rate of each machine unit at final stage to manufacture the j-th product (units/machine)
TCmj	Total cost of manufacture ($/cycle)
Vendor Parameters
TDbj	Vendor tool-die cost of the j-th product ($/unit)
Gbj	Indirect part production cost of the j-th product with the vendor ($/unit)
θj	Fixed inspection cost of the j-th product ($/year)
αj	Proportion of scrap produced in a defective j-th product (%)
βj	Defective rate for the j-th product (%)
ψj	Variable inspection cost of the j-th product ($/unit)
Rj	Reworking cost of the j-th product ($/unit)
γ1	Scrap disposal cost ($/unit)
ρ	Efficiency of the labor (%)
Pjb	Production rate of jth product manufactured by the vendor (units/year)
TCbj	Total cost of the vendor ($/cycle) MR marginal rate of the vendor ($/cycle)
Other Parameters
∆2	The maximum possible value of the parameters ($)
∆1	The minimum possible value of the parameters ($)
TCj	Total cost of supply chain management for the j-th product ($/cycle)
TI	Total inventory
A	Area