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. Author manuscript; available in PMC: 2012 Sep 21.
Published in final edited form as: Ind Eng Chem Res. 2011 Sep 21;50(18):10567–10603. doi: 10.1021/ie200150p
i I tasks
Is tasks which produce or consume state (s)
Ij tasks which can be performed in unit (j)
jJ units
Ji units which are suitable for performing task (i)
nN event points representing the beginning of a task
sS states
Sp states belong to products
Sr states belong to raw materials
prices price of state (s)
STIs initial amount of state (s)
STFs final amount of state (s)
ds,n amount of state (s) delivered to the market at event point (n)
wvi,j,n binary, whether or not task (i) in unit (j) start at event point (n)
sts,n continuous, amount of state (s) at event point (n)
ρs,iP, ρs,iC proportion of state (s) produced, consumed by task(i), respectively
bi,j,n amount of material undertaking task (i) in unit (j) at event point (n)
stmaxs available maximum storage capacity for state (s)
νi,jmin, νi,jmax minimum amount, maximum capacity of unit (j) when processing task (i)
rs market demand for state (s) at the end of the time horizon
Tfi,j,n time at which task (i) finishes in unit (j) while it starts at event point (n)
Tsi,j,n time at which task (i) starts in unit (j) at event point (n)
αi,j, βi,j variable term of processing time of task (i) in unit (j)
H time horizon