The basic products are processed by one or multiple technologies T to be converted to intermediate products I. Each final/output product k ∈ P has a demand amount d k ∈ R + , and minimum demand requirement d k ∈ R + (demand to be met). The demand amount denotes the amount of final product produced in the system. Each technology t ∈ T has a processing amount ξ t ∈ R + , a set of yield parameters γ t,m ∈ R, processing cost α c t ∈ R + , and carbon cost (associated with footprints that result from operations, such as energy use) α CO 2 t ∈ R. The processing amount is defined as the amount of the reference product generated in the technology. Yield parameters indicate the amount of material consumed or generated per unit of the reference product generated in the technology. The yield parameter is positive if the material is generated by the technology and is negative if the material is consumed in the technology. The processing cost is the production cost of generating a unit of reference product. The cost associated with GHG emissions can be considered as the social cost of carbon or carbon price imposed for GHG emissions per unit of reference product produced in the technology. entering the node n ∈ N is defined as