Optimizing Product Configuration Problems with Multisourcing Supplier Selections under Both Carbon Cap and Carbon Tax Regulations

Table 1

Notations.

Index and sets
I	Index of product,
	Index of module,
l	Index of instance, l. k index of supplier,
SEL	Set of selection pair (jl, j′l′) representing that selection of instance l of module j requires instance l′ of module j′ in the same configuration
INC	Set of incompatible pair (jl, j′l′) representing that instance l of module j and instance l′ of module j′ cannot exist together in the same configuration
REQI	Set of pair (i, j, l) representing that a customer needs instance l of module j in product i
REQN	Set of pair (i, j, l) representing that a customer does not need instance l of module j in product i
Parameters
	Annual demand of product i
	Configuration cost of instance l of module j in product i
	Number of instances l of module j contained in product i (from bill of material)
	Per unit purchased cost of instance l of module j from supplier k
	Maximum carbon emission cap
	Carbon emissions of instance l of module j during the assembly process
	Carbon emissions of instance l of module j during manufacturing process
	Carbon tax rate
	Supply capacity of instance l of module j from supplier k
Decision variables
	Binary decision variable,  = 1 indicating where instance l of module j exists in a configuration of product i; otherwise  = 0
	Purchase amount of instance l of module j from supplier k