Sets
|
j
| Possible locations for cultivating Jatropha |
n
| Possible locations for cultivating Norouzak |
w
| Possible locations for WCO supply sites |
e
| Possible locations for oil extraction sites |
r
| Possible locations for refineries |
k
| Possible locations for distribution sites |
u
| Biodiesel consumer centers |
l
| Transport modes |
o
| Capacity options for refineries |
t
| Time period |
s
| Scenarios |
Technical parameters
|
\({\text{DB}}_{uts}\)
| Demand for biodiesel at consumer center u at period t under scenario s |
\({\text{WS}}_{wts}\)
| Quantity of WCO supplied by supply site w at period t under scenario s |
\(L_{j}^{1}\)
| Minimum Jatropha cultivation area in location j |
\(U_{j}^{1}\)
| Maximum Jatropha cultivation area in location j |
\(L_{n}^{2}\)
| Minimum Norouzak cultivation area in location n |
\(U_{n}^{2}\)
| Maximum Norouzak cultivation area in location n |
\(L_{e}^{3}\)
| Minimum capacity of oil extraction site e |
\(U_{e}^{3}\)
| Maximum capacity of oil extraction site e |
\(L_{r}^{4}\)
| Minimum capacity of refinery r |
\(U_{r}^{4}\)
| Maximum capacity of refinery r |
\(L_{k}^{5}\)
| Minimum capacity of distribution site k |
\(U_{k}^{5}\)
| Maximum capacity of distribution site k |
\({\text{MN}}^{1}\)
| Minimum number of locations that must be considered for cultivating Jatropha |
\({\text{MN}}^{2}\)
| Minimum number of locations that must be considered for cultivating Norouzak |
\({\text{MX}}^{1}\)
| Maximum number of locations that can be considered for opening oil extraction centers |
\({\text{MX}}^{2}\)
| Maximum number of locations that can be considered for opening refineries |
\({\text{MX}}^{3}\)
| Maximum number of locations that can be considered for opening distribution centers |
\(\alpha_{jt}^{1}\)
| Quantity of Jatropha yields per hectare in site j at period t |
\(\alpha^{2}\)
| Quantity of Norouzak yields per hectare |
\(\beta^{1}\)
| Conversion rate of Jatropha to Jatropha oil |
\(\beta^{2}\)
| Conversion rate of Norouzak to Norouzak oil |
\(\beta^{3}\)
| Conversion rate of WCO to pretreated WCO |
\(\varphi^{1}\)
| Conversion rate of Jatropha oil to biodiesel |
\(\varphi^{2}\)
| Conversion rate of Norouzak oil to biodiesel |
\(\varphi^{3}\)
| Conversion rate of pretreated WCO to biodiesel |
\({\text{FW}}_{rt}\)
| Initial capacity of refinery r at period t |
\({\text{CW}}_{ort}\)
| Capacity of option o for refinery r at period t |
\({\text{PR}}_{s}\)
| Probability of scenario s |
Cost parameters
|
\({\text{FC}}_{js}^{1}\)
| Fixed cost of cultivating Jatropha in site j under scenario s |
\({\text{FC}}_{ns}^{2}\)
| Fixed cost of cultivating Norouzak in site n under scenario s |
\({\text{FC}}_{es}^{3}\)
| Fixed cost of establishing oil extraction site e at period t under scenario s |
\({\text{FC}}_{rs}^{4}\)
| Fixed cost of establishing refinery r under scenario s |
\({\text{FC}}_{ks}^{5}\)
| Fixed cost of establishing distribution site k under scenario s |
\({\text{FO}}_{orts}\)
| Fixed cost of adding capacity option o to refinery r at period t under scenario s |
\({\text{VC}}_{js}^{1}\)
| Variable unit cost of cultivating Jatropha in site j under scenario s |
\({\text{VC}}_{ns}^{2}\)
| Variable unit cost of cultivating Norouzak in site n under scenario s |
\({\text{VC}}_{ets}^{3}\)
| Variable unit cost of oil extraction site e at period t under scenario s |
\({\text{VC}}_{rts}^{4}\)
| Variable unit cost of refinery r at period t under scenario s |
\({\text{VC}}_{kts}^{5}\)
| Variable unit cost of establishing distribution site k at period t under scenario s |
\({\text{PC}}_{jts}^{1}\)
| Production cost per unit of Jatropha in Jatropha cultivation site j at period t under scenario s |
\({\text{PC}}_{nts}^{2}\)
| Production cost per unit of Norouzak in Norouzak cultivation site n at period t under scenario s |
\({\text{PC}}_{wts}^{3}\)
| Collection cost per unit of WCO in supply site w at period t under scenario s |
\({\text{PC}}_{ets}^{4}\)
| Production cost per unit of Jatropha oil in oil extraction site e at period t under scenario s |
\({\text{PC}}_{ets}^{5}\)
| Production cost per unit of Norouzak oil in oil extraction site e at period t under scenario s |
\({\text{PC}}_{rts}^{6}\)
| Production cost per unit of pretreated WCO in refinery r at period t under scenario s |
\({\text{PC}}_{rts}^{7}\)
| Production cost per unit of biodiesel in refinery r at period t under scenario s |
\({\text{IC}}_{ets}^{1}\)
| Inventory holding unit cost of Jatropha in oil extraction site e at period t under scenario s |
\({\text{IC}}_{ets}^{2}\)
| Inventory holding unit cost of Norouzak in oil extraction site e at period t under scenario s |
\({\text{IC}}_{rts}^{3}\)
| Inventory holding unit cost of biodiesel in refinery r at period t under scenario s |
\({\text{IC}}_{kts}^{4}\)
| Inventory holding unit cost of biodiesel in distribution site k at period t under scenario s |
\({\text{TC}}_{jlets}^{1}\)
| Per unit transportation cost of Jatropha from Jatropha cultivation site j to oil extraction site e using mode l at period t under scenario s |
\({\text{TC}}_{nlets}^{2}\)
| Per unit transportation cost of Norouzak from Norouzak cultivation site n to oil extraction site e using mode l at period t under scenario s |
\({\text{TC}}_{wlrts}^{3}\)
| Per unit transportation cost of WCO from supply site w to refinery r using mode l at period t under scenario s |
\({\text{TC}}_{elrts}^{4}\)
| Per unit transportation cost of Jatropha oil from oil extraction site e to refinery r using mode l at period t under scenario s |
\({\text{TC}}_{elrts}^{5}\)
| Per unit transportation cost of Norouzak oil from oil extraction site e to refinery r using mode l at period t under scenario s |
\({\text{TC}}_{rlkts}^{6}\)
| Per unit transportation cost of biodiesel from refinery r to distribution site k using mode l at period t under scenario s |
\({\text{TC}}_{kluts}^{7}\)
| Per unit transportation cost of biodiesel from distribution site k to consumer center u using mode l at period t under scenario s |
Environmental impact parameters
|
MGW | Maximum permitted global warming potential by the supply chain |
\({\text{EC}}_{s}^{1}\)
| Environmental effect of harvesting per unit of Jatropha under scenario s |
\({\text{EC}}_{s}^{2}\)
| Environmental effect of harvesting per unit of Norouzak under scenario s |
\({\text{EC}}_{s}^{3}\)
| Environmental effect of establishing per unit capacity of oil extraction sites under scenario s |
\({\text{EC}}_{s}^{4}\)
| Environmental effect of establishing per unit capacity of refineries under scenario s |
\({\text{EC}}_{s}^{5}\)
| Environmental effect of establishing per unit capacity of distribution sites under scenario s |
\({\text{EP}}_{s}^{1}\)
| Environmental effect of producing per unit of Jatropha oil in oil extraction sites under scenario s |
\({\text{EP}}_{s}^{2}\)
| Environmental effect of producing per unit of Norouzak oil in oil extraction sites under scenario s |
\({\text{EP}}_{s}^{3}\)
| Environmental effect of producing per unit of biodiesel in refineries under scenario s |
\({\text{ET}}_{jles}^{1}\)
| Environmental effect of transporting per unit of Jatropha from Jatropha cultivation site j to oil extraction site e using mode l under scenario s |
\({\text{ET}}_{nles}^{2}\)
| Environmental effect of transporting per unit of Norouzak from Norouzak cultivation site n to oil extraction site e using mode l under scenario s |
\({\text{ET}}_{wlrs}^{3}\)
| Environmental effect of transporting per unit of WCO from supply site w to refinery r using mode l under scenario s |
\({\text{ET}}_{elrs}^{4}\)
| Environmental effect of transporting per unit of Jatropha oil from oil extraction site e to refinery r using mode l under scenario s |
\({\text{ET}}_{elrs}^{5}\)
| Environmental effect of transporting per unit of Norouzak oil from oil extraction site e to refinery r using mode l under scenario s |
\({\text{ET}}_{rlks}^{6}\)
| Environmental effect of transporting per unit of biodiesel from refinery r to distribution site k using mode l under scenario s |
\({\text{ET}}_{klus}^{7}\)
| Environmental effect of transporting per unit of biodiesel from distribution site k to consumer center u using mode l under scenario s |
\({\text{EI}}_{s}^{1}\)
| Environmental effect of inventory holding per unit of Jatropha in oil extraction sites under scenario s |
\({\text{EI}}_{s}^{2}\)
| Environmental effect of inventory holding per unit of Norouzak in oil extraction sites under scenario s |
\({\text{EI}}_{s}^{3}\)
| Environmental effect of inventory holding per unit of biodiesel in refineries under scenario s |
\({\text{EI}}_{s}^{4}\)
| Environmental effect of inventory holding per unit of biodiesel in distribution sites under scenario s |
\(D_{jle}^{1}\)
| Distance between Jatropha cultivation site j and oil extraction site e using mode l |
\(D_{nle}^{2}\)
| Distance between Norouzak cultivation site n and oil extraction site e using mode l |
\(D_{wlr}^{3}\)
| Distance between supply site w and refinery r using mode l |
\(D_{elr}^{4}\)
| Distance between oil extraction site e and refinery r using mode l |
\(D_{rlk}^{5}\)
| Distance between refinery r and distribution site k using mode l |
\(D_{klu}^{6}\)
| Distance between distribution site k and consumer center u using mode l |
Binary decision variables
|
\(v_{j}^{1}\)
| 1 if a Jatropha cultivation center is selected in location j; 0 otherwise |
\(v_{n}^{2}\)
| 1 if a Norouzak cultivation center is selected in location n; 0 otherwise |
\(v_{e}^{3}\)
| 1 if an oil extraction center is established in location e; 0 otherwise |
\(v_{rt}^{4}\)
| 1 if a refinery is established in location r at period t; 0 otherwise |
\(v_{k}^{5}\)
| 1 if a distribution center is established in location k; 0 otherwise |
\(z_{ort}\)
| 1 if capacity option o is added to refinery r at period t; 0 otherwise |
Continuous decision variables
|
\(h_{ets}^{1}\)
| Inventory amount of Jatropha in oil extraction site e at period t under scenario s |
\(h_{ets}^{2}\)
| Inventory amount of Norouzak in oil extraction site e at period t under scenario s |
\(h_{rts}^{3}\)
| Inventory amount of biodiesel in refinery r at period t under scenario s |
\(h_{kts}^{4}\)
| Inventory amount of biodiesel in distribution site k at period t under scenario s |
\(p_{jts}^{1}\)
| Amount of Jatropha produced in Jatropha cultivation site j at period t under scenario s |
\(p_{nts}^{2}\)
| Amount of Norouzak produced in Norouzak cultivation site n at period t under scenario s |
\(p_{ets}^{4}\)
| Amount of Jatropha oil produced in oil extraction site e at period t under scenario s |
\(p_{ets}^{5}\)
| Amount of Norouzak oil produced in oil extraction site e at period t under scenario s |
\(p_{rts}^{6}\)
| Amount of pretreated WCO produced at refinery r at period t under scenario s |
\(p_{rts}^{7}\)
| Amount of biodiesel produced in refinery r at period t under scenario s |
\(f_{jlets}^{1}\)
| Amount of Jatropha transported from Jatropha cultivation site j to oil extraction site e using mode l at period t under scenario s |
\(f_{nlets}^{2}\)
| Amount of Norouzak transported from Norouzak cultivation site n to oil extraction site e using mode l at period t under scenario s |
\(f_{wlrts}^{3}\)
| Amount of WCO transported from supply site w to refinery r using mode l at period t under scenario s |
\(f_{elrts}^{4}\)
| Amount of Jatropha oil transported from oil extraction site e to refinery r using mode l at period t under scenario s |
\(f_{elrts}^{5}\)
| Amount of Norouzak oil transported from oil extraction site e to refinery r using mode l at period t under scenario s |
\(f_{rlkts}^{6}\)
| Amount of biodiesel transported from refinery r to distribution site k using mode l at period t under scenario s |
\(f_{kluts}^{7}\)
| Amount of biodiesel transported from distribution site k to consumer center u using mode l at period t under scenario s |
\(q_{j}^{1}\)
| Quantity of cultivated area of Jatropha in site j |
\(q_{n}^{2}\)
| Quantity of cultivated area of Norouzak in site n |
\(q_{et}^{3}\)
| Capacity of oil extraction site e at period t |
\(q_{rt}^{4}\)
| Capacity of refinery r at period t |
\(q_{kt}^{5}\)
| Capacity of distribution site k at period t |
\(qe_{et}^{1}\)
| Quantity of capacity expansion in oil extraction site e at period t |
\(qe_{kt}^{2}\)
| Quantity of capacity expansion in distribution site k at period t |