“…Indexes i process stream j process sink k stage in the superstructure p property p a second property to be treated r fresh source Sets NCOLD set for cold process streams NFRESH set for fresh sources NHOT set for hot process streams NPROP set for properties NSINK set for process sinks NSOURCE set for process sources upper limit for temperature difference T min minimum temperature approach (p) min minimum property operator for property p (p) max maximum property operator for property p Positive variables f i,w segregated flowrate for process stream to the waste f i,j segregated flowrate for process stream to heat transfer f i,j,0 segregated flowrate for process stream directed to process sink f i,j,p segregated flowrate for process stream to the property treatment f i,j,p,p segregated flowrate for process stream to second property interceptor F r total flowrate for fresh source f r,j segregated flowrate for fresh source to the sinks F w total flowrate for waste q i,j,i ,j ,k heat transferred between process streams in stage k T temperature T k i,j,k temperature for border k TAC total annual cost w waste stream (p) property operator for property p Binary variable y i,j,i ,j ,k binary variable for existence of heat exchangers well as for applications for dealing with reverse problem forumulations (Eljack et al, 2005) and the simultaneous consideration of process and product design Eljack et al, 2007;Kazantzi et al, 2007). After the development of pinch concepts that gave rise to the mass, energy and property integration tasks, the use of mathematical programming techniques that took advantage of more powerful computing resources and deeper theory on the subject was reported.…”