Oil refinery production optimization (ampl-only version)#
Description: In this document, we present an enhanced approach to oil refining optimization for improved decision-making.
This notebook showcases how to model a complex model with AMPL, solving it with the open-source solver Highs.
Tags: Oil production, Production optimization, Profitability, Refinery, mip, ampl-only, highs, industry
Notebook author: Mikhail Riabtsev <mail@solverytic.com>
1. Introduction#
Context and Significance#
The petroleum refining industry is one of the most crucial and intricate sectors in the global economy. It plays a pivotal role in converting crude oil into an array of valuable products such as gasoline, diesel, jet fuel, lubricants, and petrochemicals, which are indispensable to modern life and industrial processes. The industry’s complexity arises from the need to manage and optimize a series of interconnected processes, each with its own set of constraints and requirements. Furthermore, the industry operates in a highly volatile environment, influenced by fluctuating crude oil prices, stringent environmental regulations, technological advancements, and dynamic market demands.
Effective decision-making in this context is paramount. Refinery managers must balance multiple objectives: maximizing output and profitability, minimizing costs, ensuring compliance with environmental standards, and maintaining operational efficiency. These challenges underscore the necessity for sophisticated optimization models that can integrate various facets of refinery operations and provide strategic insights.
Problem Statement#
The primary goal of this project is to develop a comprehensive optimization model for a petroleum refinery. This model aims to maximize the refinery’s total profit over a specified planning horizon. To achieve this, the model will encompass various stages of the refining process, including distillation, reforming, cracking, and lubricating. Additionally, it will incorporate elements such as production planning, blending operations, inventory management, financial planning, pollutant emission controls, and maintenance scheduling.
The proposed model will serve as a decision-support tool, guiding refinery managers in:
Production Planning: Optimizing the production levels of intermediate and final products to align with market demand and operational capacities.
Blending Operations: Determining optimal blending ratios to meet product quality specifications while maximizing efficiency.
Inventory Management: Efficiently managing the storage and movement of crude oil and intermediate products to minimize holding costs and avoid shortages or surpluses.
Market and Demand Management: Adjusting production and blending strategies in response to market demand and price fluctuations.
Financial Planning: Ensuring effective management of cash flows, loans, and financial balances to support ongoing operations and investments.
Regulatory Compliance: Adhering to environmental regulations by managing pollutant emissions and other environmental impacts.
Maintenance Scheduling: Planning for equipment maintenance and plant shutdowns to minimize downtime and associated costs.
Scope and Objectives#
The scope of this optimization model is to provide a holistic framework that integrates all aspects of refinery operations. The specific objectives include:
Decision Variables: Identifying key variables such as production levels, blending ratios, inventory levels, cash flows, loan amounts, and binary variables for plant and equipment status.
Constraints: Incorporating constraints related to operational capacities, storage limits, delivery schedules, pollutant emission limits, financial balances, loan limits, market demand, product quality standards, and maintenance requirements.
Objective Function: Developing a total profit maximization function that accounts for revenues from product sales, costs of production and blending, inventory holding costs, costs of disposal of production waste, costs of planned plant shutdown,loan interest expenses, and maintenance costs. By achieving these objectives, the model will provide actionable insights and recommendations for optimizing refinery operations, thereby enhancing profitability and sustainability.
In this example, we’ll demonstrate how to use mathematical optimization to optimize the output of a refinery. You’ll learn how to generate an optimal production plan that maximizes total profit, while taking into account production capacity and other restrictions.
Expected Outcomes#
The successful implementation of this optimization model is anticipated to deliver several key benefits:
Enhanced Profitability: Optimizing production, blending, and financial decisions will maximize profit margins and overall financial performance.
Operational Efficiency: Improved planning and scheduling will enhance the efficiency of production processes and maintenance activities.
Market Responsiveness: The model’s ability to incorporate demand elasticity will allow the refinery to adapt swiftly to changes in market conditions.
Regulatory Compliance: Ensuring adherence to environmental standards will help avoid legal penalties and enhance the refinery’s reputation.
Strategic Financial Management: Effective management of cash flows and loans will ensure financial stability and reduce the cost of capital.
Conclusion#
In conclusion, the development and implementation of this optimization model will provide a powerful tool for refinery management. It will facilitate informed decision-making, driving long-term success in a competitive and ever-changing industry. By addressing the multifaceted challenges of refinery operations, this model will help achieve a balance between profitability, efficiency, and sustainability, ensuring the refinery’s resilience and growth in the face of future challenges.
The operating pattern of an oil refinery depends on its specialization (type of equipment installed) and the type(s) of oil processed. In this example, we will use the part of the general scheme of oil refining.
2. Problem Description#
Stage 1: Distillation#
An oil refinery purchases two types of crude oil (Crude1 and Crude2). The cost of purchased oil changes over time periods, $/barrel:
Oil type |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|
80 |
80 |
82 |
83 |
84 |
85 |
86 |
87 |
88 |
89 |
90 |
91 |
|
85 |
86 |
87 |
88 |
89 |
90 |
90 |
90 |
90 |
91 |
91 |
91 |
The terms of the concluded contracts include restrictions on the maximum volume of oil supplied in each period, barrels:
Oil type |
Max |
|---|---|
|
40000 |
|
25000 |
Purchased crude oil is distilled into several fractions:
Light Naphta(with an octane number of 90)Medium Naphta(with an octane number of 80)Heavy Naphta(with an octane number of 70)Light Oil(with an vapor pressur of 1)Heavy Oil(with an vapor pressur of 0.6)Residuum(with an vapor pressur of 0.05)
One barrel of crude separates into the following fractions:
Operating mode |
Oil type |
|
|
|
|
|
|
|---|---|---|---|---|---|---|---|
|
|
0.1 |
0.2 |
0.2 |
0.12 |
0.2 |
0.13 |
|
|
0.15 |
0.25 |
0.18 |
0.08 |
0.19 |
0.12 |
|
|
0.12 |
0.19 |
0.19 |
0.13 |
0.19 |
0.13 |
|
|
0.14 |
0.24 |
0.19 |
0.09 |
0.18 |
0.13 |
The distillation process operates under different modes (e.g., D1, D2), each with its own capacity, cost, setup characteristics, pollution level and the cost of waste disposal:
Operating mode |
Maximum productivity, barrels/period |
Duration of the equipment setup period |
Equipment reconfiguring cost, $ |
|---|---|---|---|
|
45 000 |
50 000 |
0.5 |
|
47 000 |
70 000 |
0.5 |
*The costs of reconfiguring equipment are taken into account only if reconfiguration is needed.
The cost of distilling 1 barrel of crude oil and the cost of disposal of process residues are:
Operating mode |
Oil type |
Cost of Distillation, per barrel |
Residue disposal cost, per barrel |
|---|---|---|---|
|
|
18 |
2 |
|
|
15 |
3 |
|
|
17 |
1.5 |
|
|
16 |
2.2 |
The process of recycling the residues of the distillation process is accompanied by the release of the following amount of harmful substances:
Operating mode |
Oil type |
|
|
|---|---|---|---|
|
|
100 |
120 |
|
|
105 |
116 |
|
|
99 |
115 |
|
|
108 |
111 |
The refinery then uses some amount of the distillation products as inputs for further processing in Reforming, Cracking, and Lubricating processes.
Stage 2:#
2.1. Reforning#
This process converts specific distillation products (Light Naphta,Medium Naphta, Heavy Naphta ) into reforming products such as Reformed gasoline (with an octane number of 115).
From 1 barrel of distillation products, the following amounts of reformed gasoline can be obtained:
Operating mode |
Distillation product |
|
|---|---|---|
|
|
0.6 |
|
|
0.52 |
|
|
0.45 |
|
|
0.6 |
|
|
0.52 |
|
|
0.48 |
The reforming installation can operate in different modes (e.g., R1, R2), each with its own capacity and cost.
Operating mode |
Maximum productivity, barrels/period |
Duration of the equipment setup period |
Equipment reconfiguring cost, $ |
|---|---|---|---|
|
10 000 |
0.5 |
80 000 |
|
12 000 |
0.6 |
90 000 |
*The costs of reconfiguring equipment are taken into account only if reconfiguration is needed.
The cost of reforming 1 barrel of distilling products and the cost of disposal of process residues are:
Operating mode |
Distillation product |
Cost of Reforming, per barrel |
Residue disposal cost, per barrel |
|---|---|---|---|
|
|
20 |
2 |
|
|
26 |
1.8 |
|
|
28 |
2.2 |
|
|
22 |
2 |
|
|
24 |
3 |
|
|
26 |
1.3 |
The process of recycling the residues of the reforming process is accompanied by the release of the following amount of harmful substances:
Operating mode |
Distillation product |
|
|
|---|---|---|---|
|
|
60 |
180 |
|
|
70 |
140 |
|
|
72 |
115 |
|
|
65 |
180 |
|
|
40 |
150 |
|
|
70 |
118 |
2.2. Cracking#
This process converts specific distillation products (Light Oil,Heavy Oil) into cracking products such as Cracked oil (with an vapor pressur of 1.5) and Cracked gasoline (with an octane number of 105).
From 1 barrel of distillation products the following amounts of cracked products can be obtained:
Operating mode |
Distillation product |
|
|
|---|---|---|---|
|
|
0.68 |
0.28 |
|
|
0.75 |
0.2 |
|
|
0.6 |
0.34 |
|
|
0.52 |
0.25 |
The cracking installation can operate in different modes (e.g., CR1, CR2), each with its own capacity and cost.
Operating mode |
Maximum productivity, barrels/period |
Duration of the equipment setup period |
Equipment reconfiguring cost, $ |
|---|---|---|---|
|
8 000 |
0.3 |
25 000 |
|
9 000 |
0.2 |
36 300 |
*The costs of reconfiguring equipment are taken into account only if reconfiguration is needed.
The cost of cracking 1 barrel of distilling products and the cost of disposal of process residues are:
Operating mode |
Distillation product |
Cost of Cracking, per barrel |
Residue disposal cost, per barrel |
|---|---|---|---|
|
|
20 |
1 |
|
|
22 |
1.2 |
|
|
21 |
1.36 |
|
|
18 |
1.05 |
The process of recycling the residues of the cracking process is accompanied by the release of the following amount of harmful substances:
Operating mode |
Distillation product |
|
|
|---|---|---|---|
|
|
100 |
200 |
|
|
150 |
250 |
|
|
120 |
180 |
|
|
150 |
240 |
2.3. Lubricating#
This process converts specific distillation products (Residuum) into Lube Oil.
From 1 barrel of distillation products the following amounts of lubrication products can be obtained:
Operating mode |
Distillation product |
|
|---|---|---|
|
|
0.5 |
|
|
0.6 |
The lubricating installation can operate in different modes (e.g., L1, L2), each with its own capacity and cost.
Operating mode |
Maximum productivity, barrels/period |
Duration of the equipment setup period |
Equipment reconfiguring cost, per barrel |
|---|---|---|---|
|
500 |
0.2 |
5 000 |
|
1 000 |
0.1 |
8 000 |
*The costs of reconfiguring equipment are taken into account only if reconfiguration is needed.
The cost of lubricating 1 barrel of distilling products and the cost of disposal of process residues are:
Operating mode |
Distillation product |
Cost of Lubricating, per barrel |
Residue disposal cost, per barrel |
|---|---|---|---|
|
|
21 |
1.2 |
|
|
22 |
1.4 |
The process of recycling the residues of the lubricating process is accompanied by the release of the following amount of harmful substances:
Operating mode |
Distillation product |
|
|
|---|---|---|---|
|
|
60 |
180 |
|
|
70 |
140 |
It is advisable to produce Lube Oil in a volume of no more than 1000.
Stage 3: Blending#
All intermediate components obtained at the stages Distillation, Reforming, Cracking, Lubricating can be mixed to obtain the final petroleum products:
3.1. Regular and premium gasoline
Can be made by blending Light Naphta, Medium Naphta, Heavy Naphta, Reformed gasoline and Cracked gasoline. The only requirement is that Regular gasoline must have an octane of at least 84 and Premium gasoline must have an octane number of at least 94. It is assumed that octane numbers blend linearly by volume.
Premium gasoline production must be at least 40% of Regular gasoline production.
3.2. Jet Fuel
Can be made by blending Light Oil, Heavy Oil, Residuum, and Cracked Oil. Jet fuel must have a vapor pressure that does not exceed 1.0. It is assumed that vapor pressures blend linearly by volume.
3.3. Fuel Oil
To produce Fuel Oil, it is necessary to mix Light Oil, Cracked Oil, Heavy Oil and Residuum in the ratio of 10:4:3:1.
3.4. Lube Oil
Was produced at the Stage 2.3. Lubricating.
The cost of the process of blending various petroleum products has the following cost:
Product |
Cost of blending, $/barrel |
|---|---|
|
2 |
|
1.9 |
|
2.2 |
|
2 |
|
2.4 |
Stage 4: Storage#
Finished petroleum products are delivered to fuel storage facilities. Storage capacity, storage cost, loss percentage during storage are presented below:
Product |
Storage Capacity, barrels |
Storage Cost, $/barrel |
Storage Waste, % |
|---|---|---|---|
|
50 000 |
3 |
0.3 |
|
50 000 |
5 |
0.2 |
|
30 000 |
7 |
0.1 |
|
10 000 |
2 |
0.05 |
|
4 500 |
4 |
0.05 |
The cost of delivery petroleum products to gas stations is:
Product |
|
|---|---|
|
2 |
|
2 |
|
3 |
|
2 |
|
4 |
Factory restrictions#
Operating an oil refinery involves fixed costs of 300,000 each period. In addition, during the periods under review, a planned technical shutdown of the plant lasting 1 period is required. During the planned shutdown, the plant can only release finished petroleum products to customers but not produce new ones. The cost of various technical works during the suspension is 100,000. During the technological shutdown, all fixed costs of the plant continue to apply. At the beginning of the period under review, the plant’s current account contains 2 million.
Demand#
Historical data on demand for petroleum products demonstrates seasonal variations in demand:
Product |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
‘Premium Gasoline’ |
4 500 |
4 500 |
4 500 |
4 500 |
5 000 |
7 000 |
7 500 |
7 000 |
6 000 |
5 000 |
4 500 |
5 000 |
‘Regular Gasoline’ |
8 500 |
8 500 |
8 500 |
8 800 |
9 200 |
13 500 |
14 000 |
13 500 |
12 000 |
10 000 |
9 000 |
10 000 |
‘Jet Fuel’ |
7 000 |
7 000 |
7 000 |
9 000 |
12 000 |
10 000 |
9 000 |
8 000 |
8 000 |
9 000 |
7 000 |
7 000 |
‘Fuel Oil’ |
4 000 |
3 800 |
3 800 |
3 800 |
2 900 |
2 500 |
2 500 |
2 800 |
3 300 |
3 400 |
3 500 |
3 600 |
‘Lube Oil’ |
500 |
500 |
700 |
700 |
700 |
500 |
400 |
500 |
600 |
700 |
700 |
700 |
During the periods under review, the following changes in the average market price are expected:
Average market price: |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
‘Premium Gasoline’ |
162 |
165 |
165 |
165 |
165 |
165 |
165 |
167 |
168 |
168 |
167 |
165 |
‘Regular Gasoline’ |
126 |
126 |
127 |
127 |
128 |
128 |
129 |
129 |
129 |
129 |
130 |
130 |
‘Jet Fuel’ |
115 |
115 |
115 |
115 |
115 |
116 |
116 |
116 |
117 |
117 |
118 |
118 |
‘Fuel Oil’ |
154 |
154 |
154 |
155 |
155 |
155 |
155 |
156 |
156 |
156 |
155 |
155 |
‘Lube Oil’ |
176 |
176 |
177 |
177 |
177 |
178 |
178 |
178 |
178 |
178 |
177 |
178 |
The following price elasticities apply for all petroleum products:
Relative price change* |
Relative change in demand |
|---|---|
+6% |
-20% |
+4% |
-12% |
+2% |
-5% |
-2% |
+2% |
-4% |
+5% |
-6% |
+9% |
This means that when the price of petroleum products increases by 6% relative to the market average, demand decreases by 20% relative to average historical data.
Finance#
To financially evaluate all transactions, use a discount rate of 5%. The purchase of raw materials and the sale of finished petroleum products assumes the availability of the full amount of necessary payments. In case of a shortage of working capital, the oil refinery has the opportunity to obtain bank loans every period on the following conditions:
Name |
Term |
Interest rate |
Maximum amount, $ |
|---|---|---|---|
I |
1 |
6.5 |
10 000 000 |
The loan received in the previous period and the interest accrued on it must be paid in the current period.
Objective#
How should the operations of the refinery be planned in order to maximize total profit?
Let’s start by downloading the necessary extensions and libraries
# Install dependencies
%pip install -q amplpy pandas
import pandas as pd
import numpy as np
# Google Colab & Kaggle integration
from amplpy import AMPL, ampl_notebook
ampl = ampl_notebook(
modules=["highs"], # modules to install
license_uuid="default", # license to use
) # instantiate AMPL object and register magics
3. Formulation of the model#
%%writefile oil_refining.mod
reset ;
### SETS
set CRUD ; # Types of crude oil (Crude1, Crude2)
set DIST ; # Distillation products
set REF ; # Reforming products
set CRACK ; # Cracking products
set LUBR ; # Lubricating products
set PROD ; # Final products
set STAT ; # Delivery stations
set D_MODE ; # Operating modes of the equipment of the Distillation installation
set R_MODE ; # Operating modes of the equipment of the Reforming installation
set CR_MODE ; # Operating modes of the equipment of the Cracking installation
set L_MODE ; # Operating modes of the equipment of the Lubrication process
set POLLUT ; # Types of pollutants
set DISTILLATION within {D_MODE, CRUD, DIST} ; # Pairs of the Distillation process
set REFORMING within {R_MODE, DIST, REF} ; # Pairs of the Reforming process
set DIST_R := setof{(m,d,r) in REFORMING}(d) ; # List of included components
set CRACKING within {CR_MODE, DIST, CRACK} ; # Pairs of the Cracking process
set DIST_CR := setof{(m,d,cr) in CRACKING}(d) ; # List of included components
set LUBRICATING within {L_MODE, DIST, LUBR} ; # Pairs of the Lubricating process
set DIST_L := setof{(m,d,l) in LUBRICATING}(d) ; # List of included components
set BLENDING within # Pairs of Intermediate and final products involved in blending
{DIST union REF union CRACK union LUBR, PROD} ;
set INTERMED:= setof{(i,j) in BLENDING}i ; # Set of Intermediate products before blending
### PARAMETERS
param nPeriod >= 0 ; # Number of weeks in the planning period
param nPeriodByYear >= 0 ; # Number of nPeriods in the Year
## Crude oil
param crude_Min{CRUD} >= 0 ; # Minimum supply limits for each crude oil type
param crude_Max{c in CRUD} >= crude_Min[c] ; # Maximum supply limits for each crude oil type
param crude_Cost{CRUD, 1..nPeriod} >= 0 ; # Cost of crude oil per week
## Distillation
param distill_Yield{DISTILLATION} >= 0 ; # Yield of products
param distill_Pollute{D_MODE, CRUD, POLLUT} ; # Pollutant emissions
param distill_Cost{D_MODE, CRUD} >= 0 ; # Cost of process
param distill_Waste_Cost{D_MODE, CRUD} >= 0 ; # Residue disposal cost
param distill_Equipment_Setup_Period{D_MODE} >= 0 ; # Equipment setup period
param distill_Equipment_Setup_Cost{D_MODE} >= 0 ; # Equipment setup cost
param distill_Cap_Max{D_MODE} >= 0 ; # Maximum capacity
## Reforming
param reform_Yield{REFORMING} >= 0 ; # Yield of products
param reform_Pollute{R_MODE, DIST_R, POLLUT} ; # Pollutant emissions
param reform_Cost{R_MODE, DIST_R} >= 0 ; # Cost of process
param reform_Waste_Cost{R_MODE, DIST_R} >= 0 ; # Residue disposal cost
param reform_Cap_Max{R_MODE} >= 0 ; # Maximum capacity
param reform_Equipment_Setup_Period{R_MODE} >= 0 ; # Equipment setup period
param reform_Equipment_Setup_Cost{R_MODE} >= 0 ;# Equipment setup cost
## Cracking
param crack_Yield{CRACKING} >= 0 ; # Yield of products
param crack_Pollute{CR_MODE, DIST, POLLUT} ; # Pollutant emissions
param crack_Cost{CR_MODE, DIST} >= 0 ; # Cost of process
param crack_Waste_Cost{CR_MODE, DIST_CR} >= 0 ; # Residue disposal cost
param crack_Cap_Max{CR_MODE} >= 0 ; # Maximum capacity
param crack_Equipment_Setup_Period{CR_MODE} >= 0 ; # Equipment setup period
param crack_Equipment_Setup_Cost{CR_MODE} >=0 ; # Equipment setup cost
## Lubrication
param lube_Yield{LUBRICATING} >= 0 ; # Yield of products
param lube_Pollute{L_MODE, DIST_L, POLLUT} ; # Pollutant emissions
param lube_Waste_Cost{L_MODE, DIST_L} >= 0 ; # Residue disposal cost
param lube_Cost{L_MODE, DIST_L} >= 0 ; # Cost of process
param lube_Cap_Max{L_MODE} >= 0 ; # Maximum production of lube oil
param lube_Equipment_Setup_Period{L_MODE} >= 0 ;# Equipment setup period
param lube_Equipment_Setup_Cost{L_MODE} >= 0 ; # Equipment setup cost
param lube_limit_Min >= 0 ; # Minimum production of lube oil
param lube_limit_Max >= lube_limit_Min ; # Maximum production of lube oil
## Intermediate components
param Intermed_Octane{INTERMED} >= 0 ; # Octane number
param Intermed_VaporPressure{INTERMED} >= 0 ; # Vapor pressure
## Blending
param blending_Cost{PROD} >= 0 ; # Cost of blending
## Products
param prod_Octane_Min{PROD} >= 0 ; # Minimum octane number for final products
param prod_VaporPressure_Max{PROD} >= 0 ; # Maximum vapor pressure for final products
param prod_Premium_Regular_Gas_Min >= 0 ; # Minimum production of premium gas
param prod_FuelOil_Ratio{INTERMED} >= 0 ; # Ratios for fuel oil production components
## Storage
param storage_Capacity{PROD} >=0 ; # Storage capacity for each product
param storage_Cost{PROD} >= 0 ; # Storage cost per product
param storage_Waste{PROD} >= 0 ; # Waste during storage
## Product delivery
param delivery_Cost{PROD, STAT} >= 0 ; # Delivery cost per product to each station
## Plant
param plant_Shutdown_Period >= 0 ; # Equipment setup period
param plant_Shutdown_Cost >= 0 ; # Equipment setup cost
param plant_Const_Cost >= 0 ; # Plant fixed costs
## Market
param seasonal_Base_Demand{PROD, 1..nPeriod} >= 0 ; # Base demand for products per week.
param seasonal_Base_Price {PROD, 1..nPeriod} >= 0 ; # Base price for products per week.
# Price elasticity
param nStep integer > 0 ; # Number of steps for price elasticity
param price_nStep_Value{1..nStep+1} >= 0 ; # Step values for price elasticity
param demand_nStep_Value{1..nStep+1} >= 0 ; # Step values for price elasticity
## Finance
param discount_Rate >= 0 ; # Discount rate for future cash flows
param initial_Cash >= 0 ; # Initial cash available
## Loans
set LOANS; # Set of loan periods
set LOAN_param; # Parameters of loans (term, interest, Max_Money)
param loan{LOANS, LOAN_param} >= 0 ; # Conditions for obtaining credit
### VARIABLES
## Plant working
var Plant_Working{t in 1..nPeriod} binary; # 1 if the plant is running. 0 if the plant is shutdown
## Distillation
var Crude_Supply{D_MODE, CRUD, 1..nPeriod} >= 0 ; # Amount of crude supplied
var Distill_X{D_MODE, 1..nPeriod} binary ; # Additional binary variable for selecting the operating mode of the equipment
## Reforming
var Distill_to_Reforming{R_MODE, DIST_R, 1..nPeriod} >= 0 ; # Quantity of distillation products used for Reforming
var Reform_X{R_MODE, 1..nPeriod} binary ; # Additional binary variable for selecting the operating mode of the equipment
## Cracking
var Distill_to_Cracking{CR_MODE, DIST_CR, 1..nPeriod} >= 0 ;# Quantity of distillation products used for Cracking
var Cracking_X{CR_MODE, 1..nPeriod} binary ; # Additional binary variable for selecting the operating mode of the equipment
## Lubricating
var Distill_to_Lubricating{L_MODE, DIST_L, 1..nPeriod} >= 0 ;# Quantity of distillation products used for Lubricating
var Lubricating_X{L_MODE, 1..nPeriod} binary ; # Additional binary variable for selecting the operating mode of the equipment
## Blending:
var Blending{BLENDING, 1..nPeriod} >= 0 ; # Amount of ingredients mixed to obtain final products
## Demand
var Demand{PROD, STAT, 1..nPeriod, 1..nStep} >= 0 ; # Demand for each pr oduct at each station over time
var X{PROD, STAT, 1..nPeriod, 1..nStep} binary ; # Additional binary variable for demand steps (1 if for product p in period t the price is selected at step nStep, or 0 otherwise)
## Storage
var Storage_Fraction{p in PROD, t in 1..nPeriod} = # Amount of each product in Storage each period
sum{tt in 1..t} (sum{(i,p) in BLENDING} Blending[i,p,tt]
- sum{s in STAT, n in 1..nStep} Demand[p,s,tt,n]) * (1-storage_Waste[p]) ;
## Loan
# Amount of loan taken every period
var Loan_In{l in LOANS, 1..nPeriod-1} >= 0 , <= loan[l,'Max_Money'] ;
# Amount of loan taken every period
var Loan_Out{l in LOANS, t in 2..nPeriod} = Loan_In[l,t-1] * (1+loan[l, 'interest']/nPeriodByYear);
## Pollutant emissions
var Waste_Pollutant{p in POLLUT, t in 1..nPeriod} =
# Pollution from waste disposal from the Distillation process
sum{m in D_MODE, c in CRUD} Crude_Supply[m,c,t] * (1 - sum{d in DIST}distill_Yield[m,c,d]) * distill_Pollute[m,c,p]
# Pollution from waste disposal from the Reforming process
+ sum{m in R_MODE, c in DIST_R} Distill_to_Reforming[m,c,t] * (1 - sum{d in REF} reform_Yield[m,c,d]) * reform_Pollute[m,c,p]
# Pollution from waste disposal from the Cracking process
+ sum{m in CR_MODE, c in DIST_CR} Distill_to_Cracking[m,c,t] * (1 - sum{d in CRACK} crack_Yield[m,c,d]) * crack_Pollute[m,c,p]
# Pollution from waste disposal from the Lubricating process
+ sum{m in L_MODE, c in DIST_L} Distill_to_Lubricating[m,c,t] * (1 - sum{d in LUBR} lube_Yield[m,c,d]) * lube_Pollute[m,c,p];
## Cash flow with incomes and costs
var CashFlow{t in 1..nPeriod} =
# sales income
sum{p in PROD, s in STAT, n in 1..nStep} Demand[p,s,t,n] * (seasonal_Base_Price[p,t] * price_nStep_Value[n] - delivery_Cost[p,s])
# minus the cost of purchasing crude oil + the costs of the Distillation process + costs for disposal of waste from the Distillation process
- sum{m in D_MODE, c in CRUD} Crude_Supply[m,c,t] * (crude_Cost[c,t] + distill_Cost[m,c] + (1 - sum{d in DIST}distill_Yield[m,c,d]) * distill_Waste_Cost[m,c])
# minus the costs of the Reforming process + costs for disposal of waste from the Reforming process
- sum{m in R_MODE, c in DIST_R} Distill_to_Reforming[m,c,t] * (reform_Cost[m,c] + (1 - sum{d in REF} reform_Yield[m,c,d]) * reform_Waste_Cost[m,c])
# minus the costs of the Cracking process + costs for disposal of waste from the Cracking process
- sum{m in CR_MODE, c in DIST_CR} Distill_to_Cracking[m,c,t] * (crack_Cost[m,c] + (1 - sum{d in CRACK} crack_Yield[m,c,d]) * crack_Waste_Cost[m,c])
# minus the costs of the Lubricating process + costs for disposal of waste from the Lubricating process
- sum{m in L_MODE, c in DIST_L} Distill_to_Lubricating[m,c,t] * (lube_Cost[m,c] + (1 - sum{d in LUBR} lube_Yield[m,c,d]) * lube_Waste_Cost[m,c])
# minus the costs of reconfiguring equipment (if available)
- (if t > 1 then /*Nonliner piece*/
# Distillation equipment
sum{m in D_MODE} (if Distill_X[m,t] - Distill_X[m,t-1] > 0 then distill_Equipment_Setup_Cost[m] else 0)
# Reforming equipment
+ sum{m in R_MODE} (if Reform_X[m,t] - Reform_X[m,t-1] > 0 then reform_Equipment_Setup_Cost[m] else 0)
# Cracking equipment
+ sum{m in CR_MODE} (if Cracking_X[m,t] - Cracking_X[m,t-1] > 0 then crack_Equipment_Setup_Cost[m] else 0)
# Lubricating equipment
+ sum{m in L_MODE}(if Lubricating_X[m,t] - Lubricating_X[m,t-1] > 0 then lube_Equipment_Setup_Cost[m] else 0)
else 0)
# minus the cost of the Blending
- sum{(i,p) in BLENDING} Blending[i,p,t] * blending_Cost[p]
# minus cost of shutdown
- (1 - Plant_Working[t]) * plant_Shutdown_Cost
# minus the storage cost
- sum{p in PROD} Storage_Fraction[p,t] * storage_Cost[p]
# minus fixed plant costs
- plant_Const_Cost
# plus the amount of the loan received
+ (if t = nPeriod then 0 else sum{l in LOANS} Loan_In[l,t])
# minus the amount of repaid loans with accrued interest
- (if t = 1 then 0 else sum{l in LOANS} Loan_Out[l,t]);
### OBJECTIVE FUNCTION
# Maximize the total profit considering all incomes and costs, discounted by the discount rate
maximize Total_Profit:
sum{t in 1..nPeriod} CashFlow[t] / (1 + discount_Rate/nPeriodByYear)^t ;
### CONSTRAINTS
subject to
## Distillation
# Ensure that total supply of crude oil does not exceed the maximum capacity.
Crude_Supply_Min_Max{c in CRUD, t in 1..nPeriod}:crude_Min[c] <= sum{m in D_MODE} Crude_Supply[m,c,t] <= crude_Max[c];
# Ensure distillation capacity does not exceed the maximum. Сapacity is reduced during downtime caused by equipment reconfiguring.
DistillCapacity_Max {m in D_MODE, t in 1..nPeriod}: sum{c in CRUD} Crude_Supply[m,c,t] <= distill_Cap_Max [m]
/* Nonliner piece*/ * (if t > 1 then (if Distill_X[m,t] > Distill_X[m,t-1] then 1 - distill_Equipment_Setup_Period[m] else 1) else 1) ;
# Ensure only one mode per period
ForEachPeriodOnlyOne_Distill_X { t in 1..nPeriod}: sum{m in D_MODE} Distill_X[m,t] <= 1 ;
# Ensure that Crude_Supply > 0 only when Distill_X > 0
Distill_{m in D_MODE, t in 1..nPeriod}: sum{c in CRUD} Crude_Supply[m,c,t] <= Distill_X[m,t] * 10e5;
## Reforming
# Ensure reforming capacity does not exceed the maximum. Сapacity is reduced during downtime caused by equipment reconfiguring.
Reforming_Capacity_Max {m in R_MODE, t in 1..nPeriod}: sum{c in DIST_R} Distill_to_Reforming[m,c,t] <= reform_Cap_Max[m]
/* Nonliner piece*/ * (if t > 1 then (if Reform_X[m,t] > Reform_X[m,t-1] then 1 - reform_Equipment_Setup_Period[m] else 1) else 1);
# Ensure only one mode per period
ForEachPeriodOnlyOne_Reform_X { t in 1..nPeriod}: sum{m in R_MODE} Reform_X[m,t] <= 1 ;
# Ensure that Distill_to_Reforming > 0 only when Reform_X > 0
Reform_{m in R_MODE, t in 1..nPeriod}:sum{c in DIST_R}Distill_to_Reforming[m,c,t] <= Reform_X[m,t] * 10e5;
## Cracking
# Ensure cracking capacity does not exceed the maximum. Сapacity is reduced during downtime caused by equipment reconfiguring.
CrackingCapacity_Max {m in CR_MODE, t in 1..nPeriod}: sum{c in DIST_CR} Distill_to_Cracking[m,c,t] <= crack_Cap_Max[m]
/* Nonliner piece*/ * (if t > 1 then (if Cracking_X[m,t] > Cracking_X[m,t-1] then 1 - crack_Equipment_Setup_Period[m] else 1) else 1);
# Ensure only one mode per period
ForEachPeriodOnlyOne_Cracking_X { t in 1..nPeriod}: sum{m in CR_MODE} Cracking_X[m,t] <= 1 ;
# Ensure that Distill_to_Cracking > 0 only when Cracking_X > 0
Cracking_{m in CR_MODE, t in 1..nPeriod}: sum{c in DIST_CR} Distill_to_Cracking[m,c,t] <= Cracking_X[m,t] * 10e5;
## Lubricating
# Ensure cracking does not exceed the minimum & maximum volume
Lube_Oil_Min_Max {t in 1..nPeriod}:
lube_limit_Min <= sum{(m,d,l)in LUBRICATING} Distill_to_Lubricating[m,d,t] * lube_Yield[m,d,l] <= lube_limit_Max ;
# Сapacity is reduced during downtime caused by equipment reconfiguring.
Lube_Oil_Capacity_Max {m in L_MODE, t in 1..nPeriod}: sum{c in DIST_L} Distill_to_Lubricating[m,c,t] <= lube_Cap_Max[m]
/* Nonliner piece*/ * (if t > 1 then (if Lubricating_X[m,t] > Lubricating_X[m,t-1] then 1 - lube_Equipment_Setup_Period[m] else 1) else 1); # Nonliner piece
# Ensure only one mode per period
ForEachPeriodOnlyOne_Lubricating_X { t in 1..nPeriod}: sum{m in L_MODE} Lubricating_X[m,t] <= 1 ;
# Ensure that Distill_to_Lubricating> 0 only when Lubricating_X > 0
Lubricating_{m in L_MODE, t in 1..nPeriod}: sum{c in DIST_L}Distill_to_Lubricating[m,c,t] <= Lubricating_X[m,t] * 10e5;
## Blending
PremiumRegularGasRatio {t in 1..nPeriod}: # Premium gasoline production: at least 40% of regular gasoline production
sum{(i,p) in BLENDING: p='Premium Gasoline'} Blending[i,p,t] >=
sum{(i,p) in BLENDING: p='Regular Gasoline'} Blending[i,p,t] * prod_Premium_Regular_Gas_Min ;
OctaneNumberMin {p in PROD, t in 1..nPeriod: p = 'Premium Gasoline'}:# Ensure octane number requirements for final products
sum{(i,p) in BLENDING} Blending[i,p,t] * Intermed_Octane[i] >=
sum{(ii,p) in BLENDING} Blending[ii,p,t] * prod_Octane_Min[p] ;
OctaneNumberMin_2 {p in PROD, t in 1..nPeriod: p = 'Regular Gasoline'}:# Ensure octane number requirements for final products
sum{(i,p) in BLENDING} Blending[i,p,t] * Intermed_Octane[i] >=
sum{(ii,p) in BLENDING} Blending[ii,p,t] * prod_Octane_Min[p] ;
VaporPressure_Max {p in PROD, t in 1..nPeriod: p='Jet Fuel'}:# Ensure vapor pressure limits for products
sum{(i,p) in BLENDING} Blending[i,p,t] * Intermed_VaporPressure[i] <=
sum{(i,p) in BLENDING} Blending[i,p,t] * prod_VaporPressure_Max[p] ;
FuelOilRatio {(i,p) in BLENDING, t in 1..nPeriod: p = 'Fuel Oil'}: # Maintain the correct ratio for fuel oil production
Blending['Residuum',p, t] = Blending[i,p,t] * prod_FuelOil_Ratio[i] ;
## Storage
# Ensure storage fractions are non-negative and within capacity
Storage_non_negative {p in PROD, t in 1..nPeriod}:
0 <= Storage_Fraction[p,t] <= storage_Capacity[p];
## Financial calculations
CashFlow_Balance{t in 1..nPeriod}: # Cash flow balance
initial_Cash
+ sum{tt in 1..t}CashFlow[tt] >= 0;
## Ensure sufficient distillation output
Distillation_Out {d in DIST, t in 1..nPeriod}:
sum{m in D_MODE, c in CRUD} Crude_Supply[m,c,t] * distill_Yield[m,c,d]
>=
sum{m in R_MODE, dd in DIST_R: dd=d} Distill_to_Reforming[m,dd,t]
+ sum{m in CR_MODE, dd in DIST_CR: dd=d} Distill_to_Cracking[m,dd,t]
+ sum{m in L_MODE, dd in DIST_L: dd=d} Distill_to_Lubricating[m,dd,t] ;
## Balance INTERMED products before blending
INTERMED_Balance{i in INTERMED, t in 1..nPeriod}:
sum{(i,p) in BLENDING} Blending[i,p,t] <=
sum{(m,c,d) in DISTILLATION:d=i} Crude_Supply[m,c,t] * distill_Yield[m,c,d]
- sum{m in R_MODE, d in DIST_R: d=i} Distill_to_Reforming[m,d,t]
- sum{m in CR_MODE, d in DIST_CR: d=i} Distill_to_Cracking[m,d,t]
- sum{m in L_MODE, d in DIST_L: d=i} Distill_to_Lubricating[m,d,t]
+ sum{(m,d,r) in REFORMING: r=i} Distill_to_Reforming[m,d,t] * reform_Yield[m,d,r]
+ sum{(m,d,cr) in CRACKING: cr=i} Distill_to_Cracking[m,d,t] * crack_Yield[m,d,cr]
+ sum{(m,d,l) in LUBRICATING: l=i} Distill_to_Lubricating[m,d,t] * lube_Yield[m,d,l] ;
## Prices elastisity
ForEachPeriodOnlyOne_X {p in PROD, s in STAT, t in 1..nPeriod}:
sum{i in 1..nStep} X [p,s,t,i] = 1 ; # Ensure only one price per product per period
# Double restriction. Ensure demand is within the range dictated by price steps.
# The constraint of type min must be set after solving a model without this constraint. #Use Min constraint after ensuring that it does not conflict with other model constraints.
Demand_Min {p in PROD, s in STAT, t in 1..nPeriod, n in 1..nStep}:
Demand[p,s,t,n] >= demand_nStep_Value[n] * X[p,s,t,n] * seasonal_Base_Demand[p,t];
Demand_Max {p in PROD, s in STAT, t in 1..nPeriod, n in 1..nStep}:
Demand[p,s,t,n] <= X[p,s,t,n] * demand_nStep_Value[n+1] * seasonal_Base_Demand[p,t];
## Shutdown contstraints
# The number of working periods is equal to the total number of periods under consideration minus the duration of the planned suspension
Plant_Working_nPeriods: sum{t in 1..nPeriod - plant_Shutdown_Period + 1} Plant_Working[t] = nPeriod - plant_Shutdown_Period;
# Additionally, there is a restriction in case of a longer (more than 1 period) plant shutdown.
Shutdown_Distill{t in 1..nPeriod - plant_Shutdown_Period + 1}:
sum{m in D_MODE, c in CRUD, tt in 0..plant_Shutdown_Period-1} Crude_Supply[m,c,t+tt] <= Plant_Working[t] * 10e5;
Writing oil_refining.mod
5. Solve problem#
# Download data from a repository
import requests
data_filename = "oil_refining.dat"
url = "https://raw.githubusercontent.com/ampl/colab.ampl.com/master/authors/mikhail/Petroleum_refining/oil_refining.dat"
response = requests.get(url)
if response.status_code == 200:
with open(data_filename, 'wb') as file:
file.write(response.content)
print(f"File downloaded successfully as {data_filename}")
else:
print(f"Failed to download file. Status code: {response.status_code}")
File downloaded successfully as oil_refining.dat
# Read model
ampl.read('oil_refining.mod')
# Read data
ampl.read('oil_refining.dat')
# Solve the Mixed-Integer Linear problem with Highs solver
ampl.option['highs_options'] = 'outlev=1 timelim=60'
ampl.solve(solver='highs')
HiGHS 1.7.1: tech:outlev = 1
lim:time = 60
Running HiGHS 1.7.1 (git hash: dcf3813): Copyright (c) 2024 HiGHS under MIT licence terms
Coefficient ranges:
Matrix [5e-03, 1e+06]
Cost [1e-03, 1e+05]
Bound [4e-01, 1e+07]
RHS [1e+00, 3e+06]
Presolving model
1466 rows, 1322 cols, 13150 nonzeros 0s
1399 rows, 1255 cols, 13247 nonzeros 0s
Solving MIP model with:
1399 rows
1255 cols (491 binary, 9 integer, 0 implied int., 755 continuous)
13247 nonzeros
Nodes | B&B Tree | Objective Bounds | Dynamic Constraints | Work
Proc. InQueue | Leaves Expl. | BestBound BestSol Gap | Cuts InLp Confl. | LpIters Time
0 0 0 0.00% 321884160.1052 -inf inf 0 0 0 0 0.1s
0 0 0 0.00% 990392.889203 -inf inf 0 0 6 1095 0.2s
L 0 0 0 0.00% 923417.4411 685848.771966 34.64% 213 70 56 1268 4.0s
0.2% inactive integer columns, restarting
Model after restart has 1394 rows, 1251 cols (489 bin., 9 int., 0 impl., 753 cont.), and 13197 nonzeros
0 0 0 0.00% 923359.161705 685848.771966 34.63% 43 0 0 5278 4.8s
0 0 0 0.00% 923359.161705 685848.771966 34.63% 43 37 9 5454 4.8s
0 0 0 0.00% 923359.161705 685848.771966 34.63% 74 39 221 11620 14.6s
9 0 1 0.39% 923359.161705 685848.771966 34.63% 79 39 326 19629 20.4s
Solving report
Status Optimal
Primal bound 685848.771966
Dual bound 685848.771966
Gap 0% (tolerance: 0.01%)
Solution status feasible
685848.771966 (objective)
0 (bound viol.)
9.43689570931e-11 (int. viol.)
0 (row viol.)
Timing 22.22 (total)
0.08 (presolve)
0.00 (postsolve)
Nodes 19
LP iterations 26803 (total)
9045 (strong br.)
376 (separation)
14619 (heuristics)
HiGHS 1.7.1: optimal solution; objective 685848.772
26803 simplex iterations
19 branching nodes
absmipgap=1.16415e-10, relmipgap=0
------------ WARNINGS ------------
WARNING: "Tolerance violations"
Type MaxAbs [Name] MaxRel [Name]
objective(s) 1E+05 2E-01
Documentation: mp.ampl.com/modeling-tools.html#automatic-solution-check.
6. Display the solution#
%%ampl_eval
display Plant_Working, Crude_Supply, Distill_to_Reforming, Distill_to_Cracking, Distill_to_Lubricating, Blending, OctaneNumberMin, VaporPressure_Max, Storage_Fraction, Demand, Loan_In, Loan_Out, CashFlow, Waste_Pollutant;
printf {p in PROD, t in 1..nPeriod}: "Octane number for products: %u %s %6.2f\n", t, p, sum{(i,p) in BLENDING} Blending[i,p,t] * Intermed_Octane[i] / sum{(ii,p) in BLENDING}(if Blending[ii,p,t] = 0 then 1 else Blending[ii,p,t]);
printf {p in PROD, t in 1..nPeriod: p='Jet Fue'}: "Vapor pressure limits of product Jet Fuel: %u %s %6.2f\n", t, p, sum{(i,p) in BLENDING} Blending[i,p,t] * Intermed_VaporPressure[i] / (if sum{(ii,p) in BLENDING} Blending[ii,p,t] = 0 then 1 else sum{(ii,p) in BLENDING}Blending[ii,p,t]) ;
printf {t in 1..nPeriod}: "Premium / Regular percentage: %u %6.2f\n", t,
sum{(i,p) in BLENDING: p ='Premium Gasoline'} Blending[i,p,t] / (if sum{(ii,pp) in BLENDING: pp ='Regular Gasoline'}Blending[ii,pp,t] = 0 then 1 else sum{(ii,pp) in BLENDING: pp ='Regular Gasoline'}Blending[ii,pp,t]) ;
printf {(i,p) in BLENDING, t in 1..nPeriod: p='Fuel Oil'}: "Production Fuel Oil ratio: %u %s %6.2f\n", t, i,
Blending[i,p,t] / (if Blending['Residuum',p,t] = 0 then 1 else Blending['Residuum',p,t]);
Plant_Working [*] :=
1 1
2 1
3 1
4 1
5 1
6 0
7 1
8 1
9 1
10 1
11 1
12 1
;
: Crude_Supply :=
D1 Crude1 1 0
D1 Crude1 2 0
D1 Crude1 3 0
D1 Crude1 4 0
D1 Crude1 5 7.27963e-11
D1 Crude1 6 -1.31266e-09
D1 Crude1 7 9497.48
D1 Crude1 8 10039.4
D1 Crude1 9 5225.87
D1 Crude1 10 0
D1 Crude1 11 0
D1 Crude1 12 0
D1 Crude2 1 0
D1 Crude2 2 0
D1 Crude2 3 0
D1 Crude2 4 0
D1 Crude2 5 0
D1 Crude2 6 -2.58296e-10
D1 Crude2 7 25000
D1 Crude2 8 25000
D1 Crude2 9 25000
D1 Crude2 10 25000
D1 Crude2 11 23925.5
D1 Crude2 12 25000
D2 Crude1 1 25711.8
D2 Crude1 2 25849.3
D2 Crude1 3 25711.8
D2 Crude1 4 40000
D2 Crude1 5 40000
D2 Crude1 6 -1.28057e-10
D2 Crude1 7 3.63798e-11
D2 Crude1 8 0
D2 Crude1 9 0
D2 Crude1 10 0
D2 Crude1 11 0
D2 Crude1 12 0
D2 Crude2 1 0
D2 Crude2 2 0
D2 Crude2 3 0
D2 Crude2 4 2083.63
D2 Crude2 5 7000
D2 Crude2 6 1.39423e-10
D2 Crude2 7 2.18279e-11
D2 Crude2 8 2.18279e-11
D2 Crude2 9 1.45519e-11
D2 Crude2 10 -7.27596e-12
D2 Crude2 11 0
D2 Crude2 12 -7.27596e-12
;
# $1 = Distill_to_Reforming
# $2 = Distill_to_Cracking
: $1 $2 :=
CR1 'Heavy Oil' 1 . 0
CR1 'Heavy Oil' 2 . 0
CR1 'Heavy Oil' 3 . 0
CR1 'Heavy Oil' 4 . 0
CR1 'Heavy Oil' 5 . 0
CR1 'Heavy Oil' 6 . 0
CR1 'Heavy Oil' 7 . 0
CR1 'Heavy Oil' 8 . 0
CR1 'Heavy Oil' 9 . 0
CR1 'Heavy Oil' 10 . 0
CR1 'Heavy Oil' 11 . 0
CR1 'Heavy Oil' 12 . 0
CR1 'Light Oil' 1 . 0
CR1 'Light Oil' 2 . 0
CR1 'Light Oil' 3 . 0
CR1 'Light Oil' 4 . 0
CR1 'Light Oil' 5 . 0
CR1 'Light Oil' 6 . 0
CR1 'Light Oil' 7 . 0
CR1 'Light Oil' 8 . 0
CR1 'Light Oil' 9 . 0
CR1 'Light Oil' 10 . 0
CR1 'Light Oil' 11 . 0
CR1 'Light Oil' 12 . 0
CR2 'Heavy Oil' 1 . 0
CR2 'Heavy Oil' 2 . 0
CR2 'Heavy Oil' 3 . 0
CR2 'Heavy Oil' 4 . 0
CR2 'Heavy Oil' 5 . 0
CR2 'Heavy Oil' 6 . 0
CR2 'Heavy Oil' 7 . 0
CR2 'Heavy Oil' 8 . 0
CR2 'Heavy Oil' 9 . 0
CR2 'Heavy Oil' 10 . 0
CR2 'Heavy Oil' 11 . 0
CR2 'Heavy Oil' 12 . 0
CR2 'Light Oil' 1 . 1167.61
CR2 'Light Oil' 2 . 1035.18
CR2 'Light Oil' 3 . 1167.61
CR2 'Light Oil' 4 . 4932.84
CR2 'Light Oil' 5 . 3912.38
CR2 'Light Oil' 6 . 0
CR2 'Light Oil' 7 . 2877.14
CR2 'Light Oil' 8 . 2883.48
CR2 'Light Oil' 9 . 2431.72
CR2 'Light Oil' 10 . 1433.34
CR2 'Light Oil' 11 . 503.968
CR2 'Light Oil' 12 . 598.348
R1 'Heavy Naphta' 1 0 .
R1 'Heavy Naphta' 2 0 .
R1 'Heavy Naphta' 3 0 .
R1 'Heavy Naphta' 4 0 .
R1 'Heavy Naphta' 5 0 .
R1 'Heavy Naphta' 6 0 .
R1 'Heavy Naphta' 7 0 .
R1 'Heavy Naphta' 8 0 .
R1 'Heavy Naphta' 9 0 .
R1 'Heavy Naphta' 10 0 .
R1 'Heavy Naphta' 11 0 .
R1 'Heavy Naphta' 12 0 .
R1 'Light Naphta' 1 0 .
R1 'Light Naphta' 2 0 .
R1 'Light Naphta' 3 0 .
R1 'Light Naphta' 4 0 .
R1 'Light Naphta' 5 0 .
R1 'Light Naphta' 6 0 .
R1 'Light Naphta' 7 0 .
R1 'Light Naphta' 8 0 .
R1 'Light Naphta' 9 0 .
R1 'Light Naphta' 10 0 .
R1 'Light Naphta' 11 0 .
R1 'Light Naphta' 12 0 .
R1 'Medium Naphta' 1 0 .
R1 'Medium Naphta' 2 0 .
R1 'Medium Naphta' 3 0 .
R1 'Medium Naphta' 4 0 .
R1 'Medium Naphta' 5 0 .
R1 'Medium Naphta' 6 0 .
R1 'Medium Naphta' 7 0 .
R1 'Medium Naphta' 8 0 .
R1 'Medium Naphta' 9 0 .
R1 'Medium Naphta' 10 0 .
R1 'Medium Naphta' 11 0 .
R1 'Medium Naphta' 12 0 .
R2 'Heavy Naphta' 1 3486.33 .
R2 'Heavy Naphta' 2 3531.92 .
R2 'Heavy Naphta' 3 3486.33 .
R2 'Heavy Naphta' 4 5887.8 .
R2 'Heavy Naphta' 5 5659.97 .
R2 'Heavy Naphta' 6 -2.20109e-10 .
R2 'Heavy Naphta' 7 4475.33 .
R2 'Heavy Naphta' 8 4730.96 .
R2 'Heavy Naphta' 9 4037.92 .
R2 'Heavy Naphta' 10 3437.19 .
R2 'Heavy Naphta' 11 3531.93 .
R2 'Heavy Naphta' 12 3528.82 .
R2 'Light Naphta' 1 0 .
R2 'Light Naphta' 2 0 .
R2 'Light Naphta' 3 0 .
R2 'Light Naphta' 4 0 .
R2 'Light Naphta' 5 0 .
R2 'Light Naphta' 6 0 .
R2 'Light Naphta' 7 0 .
R2 'Light Naphta' 8 0 .
R2 'Light Naphta' 9 0 .
R2 'Light Naphta' 10 0 .
R2 'Light Naphta' 11 0 .
R2 'Light Naphta' 12 0 .
R2 'Medium Naphta' 1 0 .
R2 'Medium Naphta' 2 0 .
R2 'Medium Naphta' 3 0 .
R2 'Medium Naphta' 4 0 .
R2 'Medium Naphta' 5 0 .
R2 'Medium Naphta' 6 0 .
R2 'Medium Naphta' 7 0 .
R2 'Medium Naphta' 8 0 .
R2 'Medium Naphta' 9 0 .
R2 'Medium Naphta' 10 0 .
R2 'Medium Naphta' 11 0 .
R2 'Medium Naphta' 12 0 .
;
# $1 = Distill_to_Lubricating
: $1 Blending :=
'Cracked gasoline' 'Premium Gasoline' 1 . 132.16
'Cracked gasoline' 'Premium Gasoline' 2 . 351.961
'Cracked gasoline' 'Premium Gasoline' 3 . 396.988
'Cracked gasoline' 'Premium Gasoline' 4 . 0
'Cracked gasoline' 'Premium Gasoline' 5 . 0
'Cracked gasoline' 'Premium Gasoline' 6 . 0
'Cracked gasoline' 'Premium Gasoline' 7 . 978.228
'Cracked gasoline' 'Premium Gasoline' 8 . 0
'Cracked gasoline' 'Premium Gasoline' 9 . 826.785
'Cracked gasoline' 'Premium Gasoline' 10 . 487.337
'Cracked gasoline' 'Premium Gasoline' 11 . 0
'Cracked gasoline' 'Premium Gasoline' 12 . 203.438
'Cracked gasoline' 'Regular Gasoline' 1 . 264.828
'Cracked gasoline' 'Regular Gasoline' 2 . 0
'Cracked gasoline' 'Regular Gasoline' 3 . 0
'Cracked gasoline' 'Regular Gasoline' 4 . 1677.17
'Cracked gasoline' 'Regular Gasoline' 5 . 1330.21
'Cracked gasoline' 'Regular Gasoline' 6 . 0
'Cracked gasoline' 'Regular Gasoline' 7 . 0
'Cracked gasoline' 'Regular Gasoline' 8 . 980.384
'Cracked gasoline' 'Regular Gasoline' 9 . 0
'Cracked gasoline' 'Regular Gasoline' 10 . 0
'Cracked gasoline' 'Regular Gasoline' 11 . 171.349
'Cracked gasoline' 'Regular Gasoline' 12 . 0
'Cracked oil' 'Fuel Oil' 1 . 585.634
'Cracked oil' 'Fuel Oil' 2 . 621.108
'Cracked oil' 'Fuel Oil' 3 . 585.634
'Cracked oil' 'Fuel Oil' 4 . 1136.71
'Cracked oil' 'Fuel Oil' 5 . 5.56673
'Cracked oil' 'Fuel Oil' 6 . 0
'Cracked oil' 'Fuel Oil' 7 . 656.387
'Cracked oil' 'Fuel Oil' 8 . 803.122
'Cracked oil' 'Fuel Oil' 9 . 488.458
'Cracked oil' 'Fuel Oil' 10 . 48.0192
'Cracked oil' 'Fuel Oil' 11 . 302.381
'Cracked oil' 'Fuel Oil' 12 . 359.009
'Cracked oil' 'Jet Fuel' 1 . 114.934
'Cracked oil' 'Jet Fuel' 2 . 0
'Cracked oil' 'Jet Fuel' 3 . 114.934
'Cracked oil' 'Jet Fuel' 4 . 1822.99
'Cracked oil' 'Jet Fuel' 5 . 2341.86
'Cracked oil' 'Jet Fuel' 6 . 2.99352e-12
'Cracked oil' 'Jet Fuel' 7 . 1069.9
'Cracked oil' 'Jet Fuel' 8 . 926.969
'Cracked oil' 'Jet Fuel' 9 . 970.574
'Cracked oil' 'Jet Fuel' 10 . 811.987
'Cracked oil' 'Jet Fuel' 11 . 0
'Cracked oil' 'Jet Fuel' 12 . 0
'Heavy Naphta' 'Premium Gasoline' 1 . 1398.92
'Heavy Naphta' 'Premium Gasoline' 2 . 46.5014
'Heavy Naphta' 'Premium Gasoline' 3 . 0
'Heavy Naphta' 'Premium Gasoline' 4 . 0
'Heavy Naphta' 'Premium Gasoline' 5 . 0
'Heavy Naphta' 'Premium Gasoline' 6 . 0
'Heavy Naphta' 'Premium Gasoline' 7 . 0
'Heavy Naphta' 'Premium Gasoline' 8 . 1606.58
'Heavy Naphta' 'Premium Gasoline' 9 . 1458.67
'Heavy Naphta' 'Premium Gasoline' 10 . 1062.81
'Heavy Naphta' 'Premium Gasoline' 11 . 0
'Heavy Naphta' 'Premium Gasoline' 12 . 741.18
'Heavy Naphta' 'Regular Gasoline' 1 . 0
'Heavy Naphta' 'Regular Gasoline' 2 . 1332.94
'Heavy Naphta' 'Regular Gasoline' 3 . 1398.92
'Heavy Naphta' 'Regular Gasoline' 4 . 2108.09
'Heavy Naphta' 'Regular Gasoline' 5 . 3270.03
'Heavy Naphta' 'Regular Gasoline' 6 . -8.71348e-11
'Heavy Naphta' 'Regular Gasoline' 7 . 1924.16
'Heavy Naphta' 'Regular Gasoline' 8 . 170.345
'Heavy Naphta' 'Regular Gasoline' 9 . 48.5866
'Heavy Naphta' 'Regular Gasoline' 10 . 0
'Heavy Naphta' 'Regular Gasoline' 11 . 774.668
'Heavy Naphta' 'Regular Gasoline' 12 . 230
'Heavy Oil' 'Fuel Oil' 1 . 780.845
'Heavy Oil' 'Fuel Oil' 2 . 828.144
'Heavy Oil' 'Fuel Oil' 3 . 780.845
'Heavy Oil' 'Fuel Oil' 4 . 1515.62
'Heavy Oil' 'Fuel Oil' 5 . 7.42231
'Heavy Oil' 'Fuel Oil' 6 . 0
'Heavy Oil' 'Fuel Oil' 7 . 875.183
'Heavy Oil' 'Fuel Oil' 8 . 1070.83
'Heavy Oil' 'Fuel Oil' 9 . 651.278
'Heavy Oil' 'Fuel Oil' 10 . 64.0256
'Heavy Oil' 'Fuel Oil' 11 . 403.174
'Heavy Oil' 'Fuel Oil' 12 . 478.679
'Heavy Oil' 'Jet Fuel' 1 . 4104.4
'Heavy Oil' 'Jet Fuel' 2 . 4083.22
'Heavy Oil' 'Jet Fuel' 3 . 4104.4
'Heavy Oil' 'Jet Fuel' 4 . 6459.44
'Heavy Oil' 'Jet Fuel' 5 . 8852.58
'Heavy Oil' 'Jet Fuel' 6 . -3.10085e-10
'Heavy Oil' 'Jet Fuel' 7 . 5774.31
'Heavy Oil' 'Jet Fuel' 8 . 5687.06
'Heavy Oil' 'Jet Fuel' 9 . 5143.9
'Heavy Oil' 'Jet Fuel' 10 . 4685.97
'Heavy Oil' 'Jet Fuel' 11 . 4142.67
'Heavy Oil' 'Jet Fuel' 12 . 4271.32
L1 Residuum 1 0 .
L1 Residuum 2 0 .
L1 Residuum 3 0 .
L1 Residuum 4 0 .
L1 Residuum 5 0 .
L1 Residuum 6 0 .
L1 Residuum 7 0 .
L1 Residuum 8 0 .
L1 Residuum 9 0 .
L1 Residuum 10 0 .
L1 Residuum 11 0 .
L1 Residuum 12 0 .
L2 Residuum 1 1000 .
L2 Residuum 2 875.973 .
L2 Residuum 3 1000 .
L2 Residuum 4 924.027 .
L2 Residuum 5 1000 .
L2 Residuum 6 0 .
L2 Residuum 7 533.333 .
L2 Residuum 8 666.667 .
L2 Residuum 9 800 .
L2 Residuum 10 933.333 .
L2 Residuum 11 933.333 .
L2 Residuum 12 933.333 .
'Light Naphta' 'Premium Gasoline' 1 . 755.487
'Light Naphta' 'Premium Gasoline' 2 . 3101.91
'Light Naphta' 'Premium Gasoline' 3 . 0
'Light Naphta' 'Premium Gasoline' 4 . 2913.97
'Light Naphta' 'Premium Gasoline' 5 . 5370.49
'Light Naphta' 'Premium Gasoline' 6 . 0
'Light Naphta' 'Premium Gasoline' 7 . 0
'Light Naphta' 'Premium Gasoline' 8 . 2282.56
'Light Naphta' 'Premium Gasoline' 9 . 0
'Light Naphta' 'Premium Gasoline' 10 . 1588
'Light Naphta' 'Premium Gasoline' 11 . 74.5326
'Light Naphta' 'Premium Gasoline' 12 . 0
'Light Naphta' 'Regular Gasoline' 1 . 2329.93
'Light Naphta' 'Regular Gasoline' 2 . 0
'Light Naphta' 'Regular Gasoline' 3 . 3085.42
'Light Naphta' 'Regular Gasoline' 4 . 2177.74
'Light Naphta' 'Regular Gasoline' 5 . 409.515
'Light Naphta' 'Regular Gasoline' 6 . -1.66018e-10
'Light Naphta' 'Regular Gasoline' 7 . 4699.75
'Light Naphta' 'Regular Gasoline' 8 . 2471.38
'Light Naphta' 'Regular Gasoline' 9 . 4272.59
'Light Naphta' 'Regular Gasoline' 10 . 2162
'Light Naphta' 'Regular Gasoline' 11 . 3514.29
'Light Naphta' 'Regular Gasoline' 12 . 3750
'Light Oil' 'Fuel Oil' 1 . 234.253
'Light Oil' 'Fuel Oil' 2 . 248.443
'Light Oil' 'Fuel Oil' 3 . 234.253
'Light Oil' 'Fuel Oil' 4 . 454.685
'Light Oil' 'Fuel Oil' 5 . 2.22669
'Light Oil' 'Fuel Oil' 6 . 0
'Light Oil' 'Fuel Oil' 7 . 262.555
'Light Oil' 'Fuel Oil' 8 . 321.249
'Light Oil' 'Fuel Oil' 9 . 195.383
'Light Oil' 'Fuel Oil' 10 . 19.2077
'Light Oil' 'Fuel Oil' 11 . 120.952
'Light Oil' 'Fuel Oil' 12 . 143.604
'Light Oil' 'Jet Fuel' 1 . 1940.67
'Light Oil' 'Jet Fuel' 2 . 2076.78
'Light Oil' 'Jet Fuel' 3 . 1940.67
'Light Oil' 'Jet Fuel' 4 . 0
'Light Oil' 'Jet Fuel' 5 . 1915.4
'Light Oil' 'Jet Fuel' 6 . -1.86314e-10
'Light Oil' 'Jet Fuel' 7 . 0
'Light Oil' 'Jet Fuel' 8 . 0
'Light Oil' 'Jet Fuel' 9 . 0
'Light Oil' 'Jet Fuel' 10 . 547.449
'Light Oil' 'Jet Fuel' 11 . 1289.12
'Light Oil' 'Jet Fuel' 12 . 1258.05
'Lube Oil' 'Lube Oil' 1 . 600
'Lube Oil' 'Lube Oil' 2 . 525.584
'Lube Oil' 'Lube Oil' 3 . 600
'Lube Oil' 'Lube Oil' 4 . 554.416
'Lube Oil' 'Lube Oil' 5 . 600
'Lube Oil' 'Lube Oil' 6 . 1.08497e-10
'Lube Oil' 'Lube Oil' 7 . 320
'Lube Oil' 'Lube Oil' 8 . 400
'Lube Oil' 'Lube Oil' 9 . 480
'Lube Oil' 'Lube Oil' 10 . 560
'Lube Oil' 'Lube Oil' 11 . 560
'Lube Oil' 'Lube Oil' 12 . 560
'Medium Naphta' 'Premium Gasoline' 1 . 0
'Medium Naphta' 'Premium Gasoline' 2 . 0
'Medium Naphta' 'Premium Gasoline' 3 . 2262.57
'Medium Naphta' 'Premium Gasoline' 4 . 3406.65
'Medium Naphta' 'Premium Gasoline' 5 . 0
'Medium Naphta' 'Premium Gasoline' 6 . -1.06411e-10
'Medium Naphta' 'Premium Gasoline' 7 . 3068.38
'Medium Naphta' 'Premium Gasoline' 8 . 0
'Medium Naphta' 'Premium Gasoline' 9 . 1056.35
'Medium Naphta' 'Premium Gasoline' 10 . 0
'Medium Naphta' 'Premium Gasoline' 11 . 2521.69
'Medium Naphta' 'Premium Gasoline' 12 . 1430
'Medium Naphta' 'Regular Gasoline' 1 . 4885.24
'Medium Naphta' 'Regular Gasoline' 2 . 4911.36
'Medium Naphta' 'Regular Gasoline' 3 . 2622.67
'Medium Naphta' 'Regular Gasoline' 4 . 4693.42
'Medium Naphta' 'Regular Gasoline' 5 . 9280
'Medium Naphta' 'Regular Gasoline' 6 . -2.13285e-10
'Medium Naphta' 'Regular Gasoline' 7 . 5081.11
'Medium Naphta' 'Regular Gasoline' 8 . 8257.89
'Medium Naphta' 'Regular Gasoline' 9 . 6238.83
'Medium Naphta' 'Regular Gasoline' 10 . 6250
'Medium Naphta' 'Regular Gasoline' 11 . 3459.69
'Medium Naphta' 'Regular Gasoline' 12 . 4820
'Reformed gasoline' 'Premium Gasoline' 1 . 1673.44
'Reformed gasoline' 'Premium Gasoline' 2 . 459.624
'Reformed gasoline' 'Premium Gasoline' 3 . 1300.44
'Reformed gasoline' 'Premium Gasoline' 4 . 2826.14
'Reformed gasoline' 'Premium Gasoline' 5 . 1022.95
'Reformed gasoline' 'Premium Gasoline' 6 . -7.09406e-11
'Reformed gasoline' 'Premium Gasoline' 7 . 1533.18
'Reformed gasoline' 'Premium Gasoline' 8 . 2270.86
'Reformed gasoline' 'Premium Gasoline' 9 . 1938.2
'Reformed gasoline' 'Premium Gasoline' 10 . 1261.85
'Reformed gasoline' 'Premium Gasoline' 11 . 1695.32
'Reformed gasoline' 'Premium Gasoline' 12 . 1693.83
'Reformed gasoline' 'Regular Gasoline' 1 . 0
'Reformed gasoline' 'Regular Gasoline' 2 . 1235.7
'Reformed gasoline' 'Regular Gasoline' 3 . 373
'Reformed gasoline' 'Regular Gasoline' 4 . 0
'Reformed gasoline' 'Regular Gasoline' 5 . 1693.84
'Reformed gasoline' 'Regular Gasoline' 6 . -3.47119e-11
'Reformed gasoline' 'Regular Gasoline' 7 . 614.976
'Reformed gasoline' 'Regular Gasoline' 8 . 0
'Reformed gasoline' 'Regular Gasoline' 9 . 0
'Reformed gasoline' 'Regular Gasoline' 10 . 388
'Reformed gasoline' 'Regular Gasoline' 11 . 0
'Reformed gasoline' 'Regular Gasoline' 12 . 0
Residuum 'Fuel Oil' 1 . 2342.53
Residuum 'Fuel Oil' 2 . 2484.43
Residuum 'Fuel Oil' 3 . 2342.53
Residuum 'Fuel Oil' 4 . 4546.85
Residuum 'Fuel Oil' 5 . 22.2669
Residuum 'Fuel Oil' 6 . 0
Residuum 'Fuel Oil' 7 . 2625.55
Residuum 'Fuel Oil' 8 . 3212.49
Residuum 'Fuel Oil' 9 . 1953.83
Residuum 'Fuel Oil' 10 . 192.077
Residuum 'Fuel Oil' 11 . 1209.52
Residuum 'Fuel Oil' 12 . 1436.04
Residuum 'Jet Fuel' 1 . 0
Residuum 'Jet Fuel' 2 . 0
Residuum 'Jet Fuel' 3 . 0
Residuum 'Jet Fuel' 4 . 0
Residuum 'Jet Fuel' 5 . 5087.73
Residuum 'Jet Fuel' 6 . -3.80169e-10
Residuum 'Jet Fuel' 7 . 1075.79
Residuum 'Jet Fuel' 8 . 425.974
Residuum 'Jet Fuel' 9 . 925.53
Residuum 'Jet Fuel' 10 . 1874.59
Residuum 'Jet Fuel' 11 . 728.205
Residuum 'Jet Fuel' 12 . 630.631
;
: OctaneNumberMin VaporPressure_Max Storage_Fraction :=
'Fuel Oil' 1 . . 143.195
'Fuel Oil' 2 . . 715.037
'Fuel Oil' 3 . . 1048.14
'Fuel Oil' 4 . . 5089.97
'Fuel Oil' 5 . . 2373.81
'Fuel Oil' 6 . . -4.54747e-13
'Fuel Oil' 7 . . 2043.65
'Fuel Oil' 8 . . 4789.96
'Fuel Oil' 9 . . 4943.84
'Fuel Oil' 10 . . 2038.62
'Fuel Oil' 11 . . 750.297
'Fuel Oil' 12 . . -5.83896e-10
'Jet Fuel' 1 . 0 0
'Jet Fuel' 2 . 0 -7.27596e-12
'Jet Fuel' 3 . 0 3.63798e-12
'Jet Fuel' 4 . 0 362.071
'Jet Fuel' 5 . 0 7992
'Jet Fuel' 6 . 0 -4.91127e-11
'Jet Fuel' 7 . 0 -4.00178e-11
'Jet Fuel' 8 . 0 -6.45741e-11
'Jet Fuel' 9 . 0 -4.36557e-11
'Jet Fuel' 10 . 0 -1.82192e-11
'Jet Fuel' 11 . 0 -6.45741e-11
'Jet Fuel' 12 . 0 -9.31255e-11
'Lube Oil' 1 . . 199.9
'Lube Oil' 2 . . 325.421
'Lube Oil' 3 . . 365.401
'Lube Oil' 4 . . 359.82
'Lube Oil' 5 . . 399.8
'Lube Oil' 6 . . 3.58114e-12
'Lube Oil' 7 . . 9.66338e-13
'Lube Oil' 8 . . 5.51381e-12
'Lube Oil' 9 . . 3.63798e-12
'Lube Oil' 10 . . 3.86535e-12
'Lube Oil' 11 . . 3.63798e-12
'Lube Oil' 12 . . 3.63798e-12
'Premium Gasoline' 1 0 . -2.72848e-12
'Premium Gasoline' 2 0 . -1.81899e-12
'Premium Gasoline' 3 0 . -2.72848e-12
'Premium Gasoline' 4 0 . 5171.21
'Premium Gasoline' 5 0 . 7158.66
'Premium Gasoline' 6 0 . 1017.14
'Premium Gasoline' 7 0 . 3.36513e-11
'Premium Gasoline' 8 0 . 2.63753e-11
'Premium Gasoline' 9 0 . 3.27418e-11
'Premium Gasoline' 10 0 . 2.09184e-11
'Premium Gasoline' 11 0 . 330.553
'Premium Gasoline' 12 0 . 3.09228e-11
'Regular Gasoline' 1 . . 0
'Regular Gasoline' 2 . . 1.81899e-12
'Regular Gasoline' 3 . . 1.81899e-12
'Regular Gasoline' 4 . . 2906.59
'Regular Gasoline' 5 . . 10778.4
'Regular Gasoline' 6 . . -1.27329e-11
'Regular Gasoline' 7 . . -2.72848e-11
'Regular Gasoline' 8 . . 2.00089e-11
'Regular Gasoline' 9 . . 1.81899e-11
'Regular Gasoline' 10 . . 3.63798e-11
'Regular Gasoline' 11 . . 2.72848e-11
'Regular Gasoline' 12 . . 2.72848e-11
;
Demand ['Fuel Oil',Station1,*,*]
: 1 2 3 4 5 6 :=
1 0 3800 0 0 0 0
2 0 3610 0 0 0 0
3 0 3610 0 0 0 0
4 0 3610 0 0 0 0
5 0 2755 0 0 0 0
6 0 2375 0 0 0 0
7 0 2375 -5.16758e-13 0 0 0
8 0 2660 0 0 0 0
9 0 3135 0 0 0 0
10 0 3230 0 0 0 0
11 0 3325 0 0 0 0
12 3168 0 0 0 0 0
['Jet Fuel',Station1,*,*]
: 1 2 3 4 5 6 :=
1 6160 0 0 0 0 0
2 6160 0 0 0 0 0
3 6160 0 0 0 0 0
4 7920 0 0 0 0 0
5 10560 0 0 0 0 0
6 8000 0 0 0 0 0
7 7920 0 0 0 0 0
8 7040 0 0 0 0 0
9 7040 0 0 0 0 0
10 7920 0 -9.9851e-12 0 0 0
11 6160 0 0 0 0 0
12 6160 9.46141e-12 0 0 0 0
['Lube Oil',Station1,*,*]
: 1 2 3 4 5 6 :=
1 400 0 0 0 0 0
2 400 0 0 0 0 0
3 560 0 0 0 0 0
4 560 0 0 0 0 0
5 560 0 0 0 0 0
6 400 0 0 0 0 0
7 320 0 0 0 0 0
8 400 0 0 0 0 0
9 480 0 0 0 0 0
10 560 0 0 0 0 0
11 560 0 0 0 0 0
12 560 0 0 0 0 0
['Premium Gasoline',Station1,*,*]
: 1 2 3 4 5 6 :=
1 3960 0 0 0 0 0
2 3960 0 0 0 0 0
3 3960 0 0 0 0 0
4 3960 0 0 0 0 0
5 4400 0 0 0 0 0
6 6160 0 0 0 0 0
7 6600 0 0 0 0 0
8 6160 0 0 0 0 0
9 5280 0 0 0 0 0
10 4400 0 0 0 0 0
11 3960 0 0 0 0 0
12 4400 0 0 0 0 0
['Regular Gasoline',Station1,*,*]
: 1 2 3 4 5 6 :=
1 7480 0 0 0 0 0
2 7480 0 0 0 0 0
3 7480 0 0 0 0 0
4 7744 0 0 0 0 0
5 8096 0 0 0 0 0
6 10800 0 0 0 0 0
7 12320 0 0 0 0 0
8 11880 0 0 0 0 0
9 10560 0 0 0 0 0
10 8800 0 0 0 0 0
11 7920 0 0 0 0 0
12 8800 0 0 0 0 0
;
: Loan_In Loan_Out :=
I 1 0 .
I 2 0 0
I 3 0 0
I 4 0 0
I 5 1326110 0
I 6 0 1333300
I 7 0 0
I 8 0 0
I 9 0 0
I 10 0 0
I 11 0 0
I 12 . 0
;
CashFlow [*] :=
1 80369.8
2 51996
3 46748.7
4 -1588420
5 -590698
6 2134110
7 14722.9
8 -232698
9 73064.3
10 345713
11 93547.6
12 200758
;
Waste_Pollutant [*,*] (tr)
: hydrocarbon 'sulfur dioxide' :=
1 290583 430374
2 288496 425586
3 290583 430374
4 480456 703234
5 482872 698860
6 -1.55711e-08 -2.25528e-08
7 324788 479531
8 340582 506003
9 291768 437185
10 240317 365653
11 233689 357689
12 237640 362257
;
Octane number for products: 1 Premium Gasoline 93.98
Octane number for products: 2 Premium Gasoline 93.98
Octane number for products: 3 Premium Gasoline 93.95
Octane number for products: 4 Premium Gasoline 93.98
Octane number for products: 5 Premium Gasoline 93.96
Octane number for products: 6 Premium Gasoline -0.00
Octane number for products: 7 Premium Gasoline 93.97
Octane number for products: 8 Premium Gasoline 93.97
Octane number for products: 9 Premium Gasoline 93.98
Octane number for products: 10 Premium Gasoline 93.98
Octane number for products: 11 Premium Gasoline 93.96
Octane number for products: 12 Premium Gasoline 93.98
Octane number for products: 1 Regular Gasoline 83.98
Octane number for products: 2 Regular Gasoline 83.98
Octane number for products: 3 Regular Gasoline 83.99
Octane number for products: 4 Regular Gasoline 83.99
Octane number for products: 5 Regular Gasoline 84.00
Octane number for products: 6 Regular Gasoline -0.00
Octane number for products: 7 Regular Gasoline 83.99
Octane number for products: 8 Regular Gasoline 83.99
Octane number for products: 9 Regular Gasoline 83.98
Octane number for products: 10 Regular Gasoline 83.98
Octane number for products: 11 Regular Gasoline 83.99
Octane number for products: 12 Regular Gasoline 83.98
Octane number for products: 1 Jet Fuel 0.00
Octane number for products: 2 Jet Fuel 0.00
Octane number for products: 3 Jet Fuel 0.00
Octane number for products: 4 Jet Fuel 0.00
Octane number for products: 5 Jet Fuel 0.00
Octane number for products: 6 Jet Fuel 0.00
Octane number for products: 7 Jet Fuel 0.00
Octane number for products: 8 Jet Fuel 0.00
Octane number for products: 9 Jet Fuel 0.00
Octane number for products: 10 Jet Fuel 0.00
Octane number for products: 11 Jet Fuel 0.00
Octane number for products: 12 Jet Fuel 0.00
Octane number for products: 1 Fuel Oil 0.00
Octane number for products: 2 Fuel Oil 0.00
Octane number for products: 3 Fuel Oil 0.00
Octane number for products: 4 Fuel Oil 0.00
Octane number for products: 5 Fuel Oil 0.00
Octane number for products: 6 Fuel Oil 0.00
Octane number for products: 7 Fuel Oil 0.00
Octane number for products: 8 Fuel Oil 0.00
Octane number for products: 9 Fuel Oil 0.00
Octane number for products: 10 Fuel Oil 0.00
Octane number for products: 11 Fuel Oil 0.00
Octane number for products: 12 Fuel Oil 0.00
Octane number for products: 1 Lube Oil 0.00
Octane number for products: 2 Lube Oil 0.00
Octane number for products: 3 Lube Oil 0.00
Octane number for products: 4 Lube Oil 0.00
Octane number for products: 5 Lube Oil 0.00
Octane number for products: 6 Lube Oil 0.00
Octane number for products: 7 Lube Oil 0.00
Octane number for products: 8 Lube Oil 0.00
Octane number for products: 9 Lube Oil 0.00
Octane number for products: 10 Lube Oil 0.00
Octane number for products: 11 Lube Oil 0.00
Octane number for products: 12 Lube Oil 0.00
Premium / Regular percentage: 1 0.53
Premium / Regular percentage: 2 0.53
Premium / Regular percentage: 3 0.53
Premium / Regular percentage: 4 0.86
Premium / Regular percentage: 5 0.40
Premium / Regular percentage: 6 0.35
Premium / Regular percentage: 7 0.45
Premium / Regular percentage: 8 0.52
Premium / Regular percentage: 9 0.50
Premium / Regular percentage: 10 0.50
Premium / Regular percentage: 11 0.54
Premium / Regular percentage: 12 0.46
Production Fuel Oil ratio: 1 Light Oil 0.10
Production Fuel Oil ratio: 2 Light Oil 0.10
Production Fuel Oil ratio: 3 Light Oil 0.10
Production Fuel Oil ratio: 4 Light Oil 0.10
Production Fuel Oil ratio: 5 Light Oil 0.10
Production Fuel Oil ratio: 6 Light Oil 0.00
Production Fuel Oil ratio: 7 Light Oil 0.10
Production Fuel Oil ratio: 8 Light Oil 0.10
Production Fuel Oil ratio: 9 Light Oil 0.10
Production Fuel Oil ratio: 10 Light Oil 0.10
Production Fuel Oil ratio: 11 Light Oil 0.10
Production Fuel Oil ratio: 12 Light Oil 0.10
Production Fuel Oil ratio: 1 Heavy Oil 0.33
Production Fuel Oil ratio: 2 Heavy Oil 0.33
Production Fuel Oil ratio: 3 Heavy Oil 0.33
Production Fuel Oil ratio: 4 Heavy Oil 0.33
Production Fuel Oil ratio: 5 Heavy Oil 0.33
Production Fuel Oil ratio: 6 Heavy Oil 0.00
Production Fuel Oil ratio: 7 Heavy Oil 0.33
Production Fuel Oil ratio: 8 Heavy Oil 0.33
Production Fuel Oil ratio: 9 Heavy Oil 0.33
Production Fuel Oil ratio: 10 Heavy Oil 0.33
Production Fuel Oil ratio: 11 Heavy Oil 0.33
Production Fuel Oil ratio: 12 Heavy Oil 0.33
Production Fuel Oil ratio: 1 Residuum 1.00
Production Fuel Oil ratio: 2 Residuum 1.00
Production Fuel Oil ratio: 3 Residuum 1.00
Production Fuel Oil ratio: 4 Residuum 1.00
Production Fuel Oil ratio: 5 Residuum 1.00
Production Fuel Oil ratio: 6 Residuum 0.00
Production Fuel Oil ratio: 7 Residuum 1.00
Production Fuel Oil ratio: 8 Residuum 1.00
Production Fuel Oil ratio: 9 Residuum 1.00
Production Fuel Oil ratio: 10 Residuum 1.00
Production Fuel Oil ratio: 11 Residuum 1.00
Production Fuel Oil ratio: 12 Residuum 1.00
Production Fuel Oil ratio: 1 Cracked oil 0.25
Production Fuel Oil ratio: 2 Cracked oil 0.25
Production Fuel Oil ratio: 3 Cracked oil 0.25
Production Fuel Oil ratio: 4 Cracked oil 0.25
Production Fuel Oil ratio: 5 Cracked oil 0.25
Production Fuel Oil ratio: 6 Cracked oil 0.00
Production Fuel Oil ratio: 7 Cracked oil 0.25
Production Fuel Oil ratio: 8 Cracked oil 0.25
Production Fuel Oil ratio: 9 Cracked oil 0.25
Production Fuel Oil ratio: 10 Cracked oil 0.25
Production Fuel Oil ratio: 11 Cracked oil 0.25
Production Fuel Oil ratio: 12 Cracked oil 0.25
7. Further steps#
Here is a list of steps required to successfully implement the results of mathematical optimization into the refinery production:
Verify Solution Accuracy
Check Constraints
Validate Assumptions
Cross-Check with Historical Data
Sensitivity Analysis
Analyze how changes in key parameters (e.g., crude oil prices, demand forecasts) affect the solution
Scenario Analysis
Evaluate the solution under different scenarios (e.g., market fluctuations, supply disruptions)
Risk Management
Identify Potential Risks: Operational, Market, External
Monitoring and Feedback
Implementation Monitoring
Continuous Improvement
Review and Update
Post-Implementation Review