Table A.1
The indices, parameters, and variables of the proposed model.
| Indices |
|
| of | Index of locations for oil fields |
| so | Index of locations for crude oil storage |
| du | Index of locations for crude oil distillation centers |
| pu | Index of locations for refinery production units |
| uu | Index of locations for upgrading units in the gas-oil supply chain |
| s | Index of locations for fuel storage centers |
| ex | Index of locations for export centers |
| cu | Index of locations for customers |
| in | Index of locations for industries |
| dc | Index of locations for distribution centers |
| h | Index of locations for Jatropha harvesting centers |
| c | Index of locations for Jatropha collection centers |
| p | Index of locations for pre-processing units |
| u | Index of locations for upgrading units in the biodiesel supply chain |
| br | Index of locations for bio-refineries |
| t | Index of time periods |
| Parameters |
|
 |
Cost of construction upgrading unit uu in gas-oil supply chain in period t ($/period) |
 |
Cost of expanding a unit capacity of refinery production unit pu in the gas-oil supply chain in the period t ($/period) |
 |
Cost of purchasing a unit of the capacity of the Jatropha harvesting center h in period t ($/period) |
 |
Cost of constructing the Jatropha collection center c in period t ($/period) |
 |
Cost of constructing pre-processing unit p in period t ($/period) |
 |
Cost of construction distribution center dc in period t ($/period) |
 |
Cost of constructing upgrading unit u in biodiesel supply chain in period t ($/period) |
 |
Cost of construction bio-refinery br in period t ($/period) |
 |
Demand of customer cu of fuel in period t (barrel/period). |
 |
Demand of industry in of fuel in period t (barrel/period). |
 |
Demand of export terminal ex of fuel in period t (barrel/period). |
 |
Demand of export terminal ex of crude oil in period t (barrel/period). |
| ca of | Maximum capacity of oil field processing of (barrel) |
| ca so | Maximum capacity of crude oil storage so (barrel) |
| ca du | Maximum capacity of distillation unit du (barrel) |
| ca uu | Maximum capacity of upgrading unit uu in gas-oil supply chain (barrel) |
| ca s | Maximum capacity of fuel storage s (barrel) |
| ca ex | Maximum capacity of export terminal ex (barrel) |
| ca dc | Maximum capacity of distribution center dc (barrel) |
| ca h | Maximum capacity of harvesting site h (ton) |
| ca c | Maximum capacity of Jatropha collection center c (ton) |
| ca p | Maximum Jatropha input capacity to pre-processing unit p (ton) |
| ca u | Maximum capacity of upgrading unit u in biodiesel supply chain (barrel) |
| ca br | Maximum capacity of bio-refinery br (barrel) |
| oex t | Selling price of crude oil to export terminals in the period t ($/period). |
| prcu t | Selling price of fuel to customers in the period t ($/period) |
| prex t | Selling price of fuel to export terminals in the period t ($/period) |
| prin t | Selling price of fuel to industries in the period t ($/period) |
| d of,so | Distance between the oil field of and the crude oil storage so (km) |
| d so,ex | Distance between the crude oil storage so and the export terminal ex (km) |
| d so,du | Distance between the crude oil storage so and the distillation unit du (km). |
| d du,pu | Distance between the distillation unit du and the refinery production unit pu (km). |
| d pu,s | Distance between the refinery production unit pu and the fuel storage center s (km) |
| d uu,s | Distance between the upgrading units in the gas-oil supply chain uu and the fuel storage center s (km) |
| d dc,ex | Distance between the distribution center dc and the export terminal ex (km) |
| d dc,in | Distance between the distribution center dc and the industry in (km) |
| d h,c | Distance between the harvesting center h and the collection center c (km) |
| d c,p | Distance between the collection center c and the pre-processing unit p (km) |
| d p,so | Distance between the pre-processing unit p and the crude oil storage so (km) |
| d c,br | Distance between the collection center c and the bio-refinery br (km) |
| d p,u | Distance between the pre-processing unit p and the upgrading unit u in the biodiesel supply chain (km) |
| d p,uu | Distance between the pre-processing unit p and the upgrading unit uu in the gas-oil supply chain (km) |
| d s,dc | Distance between the fuel storage center s and the distribution center dc (km) |
| d dc,cu | Distance between the distribution center dc and the customer cu (km). |
| d u,s | Distance between the upgrading unit u in the biodiesel supply chain and the fuel storage center s (km) |
| d u,dc | Distance between the upgrading unit u in the biodiesel supply chain and the distribution center dc (km) |
| d br,s | Distance between the bio-refinery br and the fuel storage center s (km) |
| d br,dc | Distance between the bio-refinery br and the distribution center dc (km) |
| cprpu t | Processing cost of refinery production units in period t ($/period) |
| cprdu t | Processing cost of distillation units in period t ($/period) |
| cpruu t | Processing cost of upgrading units in the gas-oil supply chain in period t ($/period) |
| cprru t | Processing cost of upgrading units in the biodiesel supply chain in period t ($/period) |
| cprbr t | Processing cost of bio-refineries in period t ($/period) |
| cprp t | Processing cost of pre-processing units in period t ($/period) |
 |
Cost of holding an inventory unit at the crude oil storage so in period t ($/period) |
 |
Cost of holding an inventory unit at the fuel storage center s in period t ($/period) |
 |
Cost of holding an inventory unit at the collection center c in period t ($/period) |
| ctr of,so | Cost of transporting between the oil field of and the crude oil storage so ($) |
| ctr so,ex | Cost of transporting between the crude oil storage so and the export terminal ex ($) |
| ctr so,du | Cost of transporting between the crude oil storage so and the distillation unit du ($) |
| ctr du,pu | Cost of transporting between the distillation unit du and the refinery production unit pu ($) |
| ctr pu,s | Cost of transporting between the refinery production unit pu and the fuel storage center s ($) |
| ctr uu,s | Cost of transporting between the upgrading unit uu in the gas-oil supply chain and the fuel storage center s ($) |
| ctr dc,ex | Cost of transporting between the distribution center dc and the export terminal ex ($) |
| ctr dc,cu | Cost of transporting between the distribution center dc and the customer cu ($) |
| ctr dc,in | Cost of transporting between the distribution center dc and the industry in ($) |
| ctr h,c | Cost of transporting between the harvesting center h and the collection center c ($) |
| ctr c,p | Cost of transporting between the collection center c and the pre-processing unit p ($) |
| ctr c,br | Cost of transporting between the collection center c and the bio-refinery br ($) |
| ctr p,u | Cost of transporting between the pre-processing unit p and the upgrading unit u in the biodiesel supply chain ($) |
| ctr p,uu | Cost of transporting between the pre-processing unit p and the upgrading unit uu in the gas-oil supply chain ($) |
| ctr p,so | Cost of transporting between the pre-processing unit p and the crude oil storage so ($) |
| ctr br,s | Cost of transporting between the bio-refinery br and the fuel storage center s ($) |
| ctr br,dc | Cost of transporting between the bio-refinery br and the distribution center dc ($) |
| ctr s,dc | Cost of transporting between the fuel storage center s and the distribution center dc ($) |
| ctr u,s | Cost of transporting between the upgrading unit u in the biodiesel supply chain and the fuel storage center s ($) |
| ctr u,dc | Cost of transporting between the upgrading unit u in the biodiesel supply chain and the distribution center dc ($) |
| dr | Interest rate |
| chan | Conversion factor of millions of barrels to the number of fuel tankers |
| entr | Amount of carbon dioxide emissions per unit distance due to transportation in the supply chain (ton) |
| echan | Reduction coefficient of carbon dioxide emissions due to biodiesel consumption instead of gas-oil |
| enchan | Conversion factor number of barrels to the number of tankers carrying fuel |
| alpha1 | Percentage of waste in upgrading units in the gas-oil supply chain |
| alpha2 | Percentage of waste in refinery production units |
| alpha3 | Percentage of waste in pre-processing units |
| alpha4 | Percentage of waste in bio-refineries |
| alpha5 | Percentage of waste in upgrading units in the biodiesel supply chain |
| ca-peak | Maximum allowable increase in refinery capacity (barrel) |
| Binary variables |
|
 |
1 if location uu in period t is selected for constructing an upgrading unit in the gas-oil supply chain; 0 otherwise |
 |
1 if location h in period t is selected for harvesting Jatropha; 0 otherwise |
 |
1 if location c in period t is selected for constructing a collection center Jatropha; 0 otherwise |
 |
1 if location p in period t is selected for constructing a pre-processing unit; 0 otherwise |
 |
1 if location uu in period t is selected for constructing an upgrading unit in the biodiesel supply chain; 0 otherwise |
 |
1 if location dc in period t is selected for constructing a distribution center; 0 otherwise |
 |
1 if location br in period t is selected for constructing a bio-refinery; 0 otherwise |
 |
1 if location uu is active as the upgrading unit in the gas-oil supply chain in period t; 0 otherwise |
 |
1 if location h is active as the harvesting center in period t; 0 otherwise |
 |
1 if location h is active as the collection center in period t; 0 otherwise |
 |
1 if location p is active as the pre-processing unit in period t; 0 otherwise |
 |
1 if location uu is active as the upgrading unit in the biodiesel supply chain in period t; 0 otherwise |
 |
1 if location br is active as the bio-refinery in period t; 0 otherwise |
 |
1 if location dc is active as the distribution center in period t; 0 otherwise |
| Continous variables |
|
 |
Quantity of crude oil transferred from the oil field of to the crude oil storage so in period t (barrel/period) |
 |
Quantity of crude oil transferred from the crude oil storage so to the export terminal ex in period t (barrel/period) |
 |
Quantity of crude oil transferred from the crude oil storage so to the distillation unit du in period t (barrel/period) |
 |
Quantity of intermediate product transferred from the distillation unit du to the refinery production unit pu in period t (barrel/period) |
 |
Quantity of gas-oil transferred from the production unit pu to the fuel storage center s in period t (barrel/period) |
 |
Quantity of biodiesel transferred from the upgrading unit uu in the gas-oil supply chain to the fuel storage center s in period t (barrel/period) |
 |
Quantity of fuel transferred from the fuel storage center s to the distribution center dc in period t (barrel/period) |
 |
Quantity of fuel transferred from the distribution center dc to the export terminal ex in period t (barrel/period) |
 |
Quantity of fuel transferred from the distribution center dc to the customer cu in period t (barrel/period) |
 |
Quantity of fuel transferred from the distribution center dc to the industry in in period t (barrel/period) |
 |
Quantity of Jatropha transferred from the harvesting center h to the collection center c in period t (ton/period) |
 |
Quantity of Jatropha transferred from the collection center c to the pre-processing unit p in period t (ton/period) |
 |
Quantity of Jatropha transferred from the collection center c to the bio-refinery br in period t (ton/period) |
 |
Quantity of intermediate product transferred from the pre-processing unit p to the upgrading unit u in the biodiesel supply chain in period t (barrel/period) |
 |
Quantity of bio-slurry transferred from the pre-processing unit p to the crude oil storage so in period t (barrel/period) |
 |
Quantity of bio-oil transferred from the pre-processing unit p to the upgrading unit uu in the gas-oil supply chain in period t (barrel/period) |
 |
Quantity of biodiesel transferred from the bio-refinery br to the fuel storage s in period t (barrel/period) |
 |
Quantity of biodiesel transferred from the upgrading unit u in the biodiesel supply chain to the distribution center dc in period t (barrel/period) |
 |
Quantity of biodiesel transferred from the bio-refinery br to the distribution center dc in period t (barrel/period) |
 |
Quantity of biodiesel transferred from the upgrading unit u in the biodiesel supply chain to the fuel storage s in period t (barrel/period) |
 |
Amount of increase in the capacity of the refinery production unit pu in period t (barrel/period) |
 |
Capacity of refinery production unit pu in period t (barrel/period) |
 |
The difference between inputs and outputs to the crude oil storage so in period t (barrel/period) |
 |
The difference between inputs and outputs to the fuel storage s in period t (barrel/period) |
 |
The difference between inputs and outputs to the collection center c in period t (barrel/period) |
 |
Inventory of crude oil storage so in period t (barrel/period) |
 |
Inventory of fuel storage s in period t (barrel/period) |
 |
Inventory of collection center c in period t (barrel/period) |
| ctr t | Transportation costs in the period t ($/period) |
| cop t | Operational costs in the period t ($/period) |
| cinv t | Investment costs in the period t ($/period) |
| ch t | Holding costs in the period t ($/period) |
| inc t | Income in the period t ($/period) |
| profit | Amount of economic objective function. The present value of the supply chain profit on the planning horizon ($) |
| income | The present value of supply chain revenue on the planning horizon ($) |
| cost | The present value of supply chain costs on the planning horizon ($) |
| envi t | Amount of reduction due to the emission of carbon dioxide due to the consumption of biodiesel (instead of fossil fuels) in the period t (ton/period) |
| envt t | Amount of carbon dioxide emissions due to total supply chain transportation in the period t (ton/period) |
| enviro | Amount of environmental objective function (ton) |