Oil refinery production optimization¶
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 decisionmaking 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 decisionsupport 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 decisionmaking, driving longterm success in a competitive and everchanging 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.
Tags: Oil production, Production optimization, Profitability, Refinery, Deterministic model, Piecewiselinear, mip, amplonly, cbc
Notebook author: Mikhail Riabtsev <mail@solverytic.com>
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, $/barrel 
Residue disposal cost, $/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, $/barrel 
Residue disposal cost, $/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, $/barrel 
Residue disposal cost, $/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, $/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, $/barrel 
Residue disposal cost, $/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.
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 
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 
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.
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.
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.
Stage 3: Blending¶
Stage 4: Storage¶
Factory restrictions¶
Demand¶
Finance¶
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 # Loading panda to work with pandas.DataFrame objects (https://pandas.pydata.org/)
import numpy as np # Loading numpy to perform multidimensional calculations numpy.matrix (https://numpy.org/)
import matplotlib.pyplot as plt # Loading library for creating static, animated, and interactive visualizations (https://matplotlib.org/)
# Google Colab & Kaggle integration
from amplpy import AMPL, ampl_notebook
ampl = ampl_notebook(
modules=["cbc", "highs"], # modules to install
license_uuid="default", # license to use
) # instantiate AMPL object and register magics
from amplpy import AMPL
ampl = AMPL() # create a new AMPL object with all default settings
3. AMPL formulation of the model¶
Use %%ampl_eval to evaluate AMPL commands and declarations
%%ampl_eval
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]) * (1storage_Waste[p]) ;
## Loan
# Amount of loan taken every period
var Loan_In{l in LOANS, 1..nPeriod1} >= 0 , <= loan[l,'Max_Money'] ;
# Amount of loan taken every period
var Loan_Out{l in LOANS, t in 2..nPeriod} = Loan_In[l,t1] * (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,t1] > 0 then distill_Equipment_Setup_Cost[m] else 0)
# Reforming equipment
+ sum{m in R_MODE} (if Reform_X[m,t]  Reform_X[m,t1] > 0 then reform_Equipment_Setup_Cost[m] else 0)
# Cracking equipment
+ sum{m in CR_MODE} (if Cracking_X[m,t]  Cracking_X[m,t1] > 0 then crack_Equipment_Setup_Cost[m] else 0)
# Lubricating equipment
+ sum{m in L_MODE}(if Lubricating_X[m,t]  Lubricating_X[m,t1] > 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,t1] 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,t1] 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,t1] 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,t1] 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 nonnegative 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_Period1} Crude_Supply[m,c,t+tt] <= Plant_Working[t] * 10e5;
4. Load data¶
%%ampl_eval
data;
### SETS
# Set of crude oil types
set CRUD = 'Crude1','Crude2' ;
# Set of distillation products
set DIST:= 'Light Naphta','Medium Naphta','Heavy Naphta','Light Oil','Heavy Oil','Residuum' ;
# Set of reforming products
set REF:= 'Reformed gasoline' ;
# Set of cracking products
set CRACK:= 'Cracked oil','Cracked gasoline' ;
# Set of Lubricating products
set LUBR:= 'Lube Oil';
# Set of final products
set PROD:= 'Premium Gasoline','Regular Gasoline','Jet Fuel','Fuel Oil','Lube Oil' ;
# Set of delivery stations
set STAT := Station1 ;
# Set of operating modes for Distillation equipment
set D_MODE := D1, D2 ;
# Set of operating modes for Reforming equipment
set R_MODE := R1, R2 ;
# Set of operating modes for Cracking equipment
set CR_MODE := CR1, CR2 ;
# Set of operating modes for Lubrication equipment
set L_MODE := L1, L2 ;
# Set of pollutants
set POLLUT := 'hydrocarbon', 'sulfur dioxide';
# Set of components and products of mixing process
set BLENDING: 'Premium Gasoline' 'Regular Gasoline' 'Jet Fuel' 'Fuel Oil' 'Lube Oil':=
'Light Naphta' + +   
'Medium Naphta' + +   
'Heavy Naphta' + +   
'Light Oil'   + + 
'Heavy Oil'   + + 
'Residuum'   + + 
'Reformed gasoline' + +   
'Cracked oil'   + + 
'Cracked gasoline' + +   
'Lube Oil'     + ;
### PARAMETERS
param nPeriod:= 12 ; # Scheduling period (weeks)
param nPeriodByYear = 12; # Number of nPeriods in the Year
## Crude Oil
# Minimum, Maximum supply of crude oil barrels per week
param: crude_Min crude_Max:=
Crude1 0 40000
Crude2 0 25000 ;
# Cost of purchasing crude oil per barrel through the period
param crude_Cost : 1 2 3 4 5 6 7 8 9 10 11 12 :=
Crude1 80 80 82 83 84 85 86 87 88 89 90 91
Crude2 85 86 87 88 89 90 90 90 90 91 91 91;
## Distillation
# Yield of products after distillation
param: DISTILLATION: distill_Yield: 'Light Naphta' 'Medium Naphta' 'Heavy Naphta' 'Light Oil' 'Heavy Oil' 'Residuum' :=
D1 Crude1 0.1 0.2 0.2 0.12 0.2 0.13
D1 Crude2 0.15 0.25 0.18 0.08 0.19 0.12
D2 Crude1 0.12 0.19 0.19 0.13 0.19 0.13
D2 Crude2 0.14 0.24 0.19 0.09 0.18 0.13 ;
# Pollutant emissions
param distill_Pollute: 'hydrocarbon' 'sulfur dioxide':=
D1 Crude1 100 120
D1 Crude2 105 116
D2 Crude1 99 115
D2 Crude2 108 111 ;
# Cost of Distillation 1 barrel of crude oil. Residue disposal cost.
param: distill_Cost, distill_Waste_Cost:=
D1 Crude1 18 2
D1 Crude2 15 3
D2 Crude1 17 1.5
D2 Crude2 16 2.2 ;
# Maximum distillation capacity. Equipment setup period
param: distill_Cap_Max, distill_Equipment_Setup_Period, distill_Equipment_Setup_Cost:=
D1 45000 0.5 50000
D2 47000 0.6 70000;
## Reforming
# Yield of products after Reforming
param: REFORMING: reform_Yield: 'Reformed gasoline':=
R1 'Light Naphta' 0.6
R1 'Medium Naphta' 0.52
R1 'Heavy Naphta' 0.45
R2 'Light Naphta' 0.6
R2 'Medium Naphta' 0.52
R2 'Heavy Naphta' 0.48 ;
# Pollutant emissions
param reform_Pollute: 'hydrocarbon' 'sulfur dioxide':=
R1 'Light Naphta' 60 180
R1 'Medium Naphta' 70 140
R1 'Heavy Naphta' 72 115
R2 'Light Naphta' 65 180
R2 'Medium Naphta' 40 150
R2 'Heavy Naphta' 70 118 ;
# Cost of Reforming 1 barrel of distilled fraction. Residue disposal cost
param: reform_Cost, reform_Waste_Cost:=
R1 'Light Naphta' 20 2
R1 'Medium Naphta' 26 1.8
R1 'Heavy Naphta' 28 2.2
R2 'Light Naphta' 22 2
R2 'Medium Naphta' 24 3
R2 'Heavy Naphta' 26 1.3;
# Maximum Reforming capacity. Equipment setup period
param: reform_Cap_Max, reform_Equipment_Setup_Period, reform_Equipment_Setup_Cost:=
R1 10000 0.5 80000
R2 12000 0.6 90000;
## Cracking
# Yield of products after Craking
param: CRACKING: crack_Yield: 'Cracked oil' 'Cracked gasoline':=
CR1 'Light Oil' 0.68 0.28
CR1 'Heavy Oil' 0.75 0.2
CR2 'Light Oil' 0.6 0.34
CR2 'Heavy Oil' 0.52 0.25 ;
# Pollutant emissions
param crack_Pollute: 'hydrocarbon' 'sulfur dioxide':=
CR1 'Light Oil' 100 200
CR1 'Heavy Oil' 150 250
CR2 'Light Oil' 120 180
CR2 'Heavy Oil' 150 240 ;
# Cost of Cracking 1 barrel of distilled fraction. Residue disposal cost
param: crack_Cost crack_Waste_Cost:=
CR1 'Light Oil' 20 1
CR1 'Heavy Oil' 22 1.2
CR2 'Light Oil' 21 1.36
CR2 'Heavy Oil' 18 1.05 ;
# Maximum Cracking capacity. Equipment setup period
param: crack_Cap_Max, crack_Equipment_Setup_Period, crack_Equipment_Setup_Cost:=
CR1 8000 0.3 25000
CR2 9000 0.2 36300;
## Lubricating
# Yield of products after Lubricating
param: LUBRICATING: lube_Yield: 'Lube Oil':=
L1 'Residuum' 0.5
L2 'Residuum' 0.6;
# Pollutant emissions
param lube_Pollute: 'hydrocarbon' 'sulfur dioxide':=
L1 'Residuum' 60 180
L2 'Residuum' 70 140 ;
# Cost of Lubricating 1 barrel of distilled fraction. Residue disposal cost
param: lube_Cost lube_Waste_Cost:=
L1 'Residuum' 21 1.2
L2 'Residuum' 22 1.4 ;
# Maximum Cracking capacity. Equipment setup period
param: lube_Cap_Max, lube_Equipment_Setup_Period, lube_Equipment_Setup_Cost:=
L1 500 0.2 5000
L2 1000 0.1 8000;
# Volume Limitations
param lube_limit_Min := 0 ;
param lube_limit_Max := 1000 ;
## INTERMED
# Octane numbers and Vapor pressure for each INTERMED fraction
param: Intermed_Octane Intermed_VaporPressure:=
'Light Naphta' 90 .
'Medium Naphta' 80 .
'Heavy Naphta' 70 .
'Light Oil' 0 1
'Heavy Oil' 0 0.6
'Residuum' 0 0.05
'Reformed gasoline' 115 .
'Cracked gasoline' 105 .
'Cracked oil' 0 1.5
'Lube Oil' 0 .;
## Blending
# Cost of processing 1 barrel of products
param blending_Cost:=
'Premium Gasoline' 2
'Regular Gasoline' 1.9
'Jet Fuel' 2.2
'Fuel Oil' 2
'Lube Oil' 2.4 ;
## Products
# Minimum octane for products
param prod_Octane_Min:=
'Regular Gasoline' 84
'Premium Gasoline' 94 ;
# Vapor pressure limits of product
param prod_VaporPressure_Max :=
'Jet Fuel' 1 ;
# Minimum percentage of premium gasoline production relative to regular gasoline
param prod_Premium_Regular_Gas_Min := 0.4 ;
# Blending ratio for fuel oil production: Light oil, Crack Oil, Fuel Oil and Residuum mix in the proportion 10:4:3:1
param prod_FuelOil_Ratio :=
'Light Oil' 10
'Cracked oil' 4
'Heavy Oil' 3
'Residuum' 1 ;
## Storage
# Storage capacity for each product. Weekly storage cost per barrel. Standard loss percentage during storage
param: storage_Capacity storage_Cost storage_Waste:=
'Premium Gasoline' 50000 3 0.003
'Regular Gasoline' 50000 5 0.002
'Jet Fuel' 30000 7 0.001
'Fuel Oil' 10000 2 0.0005
'Lube Oil' 4500 4 0.0005;
# Cost of delivering products to gas stations
param delivery_Cost: 'Station1':=
'Premium Gasoline' 2
'Regular Gasoline' 2
'Jet Fuel' 3
'Fuel Oil' 2
'Lube Oil' 4 ;
## Plant
param plant_Shutdown_Period := 1; # Equipment setup period
param plant_Shutdown_Cost = 100000; # Equipment setup cost
param plant_Const_Cost := 300000; # Plant fixed costs
param initial_Cash := 2000000 ; # Initial cash available
## Market
# Changes in demand levels during the season.
param seasonal_Base_Demand:
1 2 3 4 5 6 7 8 9 10 11 12 :=
'Premium Gasoline' 4500 4500 4500 4500 5000 7000 7500 7000 6000 5000 4500 5000
'Regular Gasoline' 8500 8500 8500 8800 9200 13500 14000 13500 12000 10000 9000 10000
'Jet Fuel' 7000 7000 7000 9000 12000 10000 9000 8000 8000 9000 7000 7000
'Fuel Oil' 4000 3800 3800 3800 2900 2500 2500 2800 3300 3400 3500 3600
'Lube Oil' 500 500 700 700 700 500 400 500 600 700 700 700;
# Changes in price levels during the season (1 barrel).
param seasonal_Base_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 ;
## Price elasticity
param nStep:= 6 ; # Number of price steps
param: price_nStep_Value demand_nStep_Value:=
1 1.06 0.8
2 1.04 0.88
3 1.02 0.95
4 1.0 1
5 0.98 1.02
6 0.96 1.05
7 0.94 1.09 ;
## Finance
param discount_Rate := 0.05 ; # Financial parameters for discount rate
# Loans
set LOANS := 'I';
set LOAN_param := 'term' 'interest' 'Max_Money';
param loan: 'term' 'interest' 'Max_Money' :=
I 1 0.065 1e7 ;
5. Solve problem¶
Use %%ampl_eval to evaluate AMPL commands and declarations
%%ampl_eval
option solver highs; # Choosing a solver
# Defining Output Settings
option show_stats 1; # (1) Show statistical information about the size of the problem. Default 0 (statistics are not displayed)
option display_1col 0; # Data Display Settings
option omit_zero_rows 1; # Hide rows with 0 values. Default (0)
solve; # Solve the model
Presolve eliminates 15 constraints.
Substitution eliminates 107 variables.
Adjusted problem:
1259 variables:
372 binary variables
96 nonlinear variables
791 linear variables
1414 constraints; 13987 nonzeros
99 nonlinear constraints
1315 linear constraints
97 equality constraints
1259 inequality constraints
58 range constraints
1 nonlinear objective; 899 nonzeros.
HiGHS 1.6.0:HiGHS 1.6.0: optimal solution; objective 685848.772
26660 simplex iterations
19 branching nodes
6. Display the solution¶
Use %%ampl_eval
%%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 4 1 5 1 6 1 7 1 8 1 9 1 10 1 11 1 12 1
;
: Crude_Supply :=
D1 Crude1 1 1302.75
D1 Crude1 2 17845.2
D1 Crude1 4 4749.83
D1 Crude1 5 8528.38
D1 Crude1 6 5394.44
D1 Crude1 7 3205.38
D1 Crude1 8 5826.38
D1 Crude1 9 5272.35
D1 Crude2 1 25000
D1 Crude2 2 25000
D1 Crude2 4 25000
D1 Crude2 5 25000
D1 Crude2 6 25000
D1 Crude2 7 25000
D1 Crude2 8 25000
D1 Crude2 9 25000
D1 Crude2 10 25000
D1 Crude2 11 23582.3
D1 Crude2 12 25000
D2 Crude1 3 2.30926e10
;
# $1 = Distill_to_Reforming
# $2 = Distill_to_Cracking
: $1 $2
:=
CR1 'Light Oil' 1 . 1.67187e13
CR2 'Heavy Oil' 5 . 5.05151e13
CR2 'Light Oil' 1 . 940.594
CR2 'Light Oil' 2 . 1787.13
CR2 'Light Oil' 3 . 2.08216e11
CR2 'Light Oil' 4 . 893.564
CR2 'Light Oil' 5 . 681.931
CR2 'Light Oil' 6 . 2506.24
CR2 'Light Oil' 7 . 2243.56
CR2 'Light Oil' 8 . 2440.41
CR2 'Light Oil' 9 . 2387.48
CR2 'Light Oil' 10 . 1433.34
CR2 'Light Oil' 11 . 684.032
CR2 'Light Oil' 12 . 808.559
R2 'Heavy Naphta' 1 4184.39 .
R2 'Heavy Naphta' 2 5779.87 .
R2 'Heavy Naphta' 3 3.30119e11 .
R2 'Heavy Naphta' 4 4921.27 .
R2 'Heavy Naphta' 5 5368.11 .
R2 'Heavy Naphta' 6 3798.97 .
R2 'Heavy Naphta' 7 3533.07 .
R2 'Heavy Naphta' 8 3875.33 .
R2 'Heavy Naphta' 9 4053.69 .
R2 'Heavy Naphta' 10 3437.19 .
R2 'Heavy Naphta' 11 3427.37 .
R2 'Heavy Naphta' 12 3505.75 .
;
# $1 = Distill_to_Lubricating
: $1 Blending :=
'Cracked gasoline' 'Premium Gasoline' 2 . 45.5924
'Cracked gasoline' 'Premium Gasoline' 4 . 303.812
'Cracked gasoline' 'Premium Gasoline' 5 . 231.856
'Cracked gasoline' 'Premium Gasoline' 6 . 558.735
'Cracked gasoline' 'Premium Gasoline' 7 . 462.559
'Cracked gasoline' 'Premium Gasoline' 9 . 232.723
'Cracked gasoline' 'Premium Gasoline' 11 . 232.571
'Cracked gasoline' 'Premium Gasoline' 12 . 274.91
'Cracked gasoline' 'Regular Gasoline' 1 . 319.802
'Cracked gasoline' 'Regular Gasoline' 2 . 562.031
'Cracked gasoline' 'Regular Gasoline' 3 . 1.95174e12
'Cracked gasoline' 'Regular Gasoline' 6 . 293.388
'Cracked gasoline' 'Regular Gasoline' 7 . 300.25
'Cracked gasoline' 'Regular Gasoline' 8 . 829.74
'Cracked gasoline' 'Regular Gasoline' 9 . 579.02
'Cracked gasoline' 'Regular Gasoline' 10 . 487.337
'Cracked oil' 'Fuel Oil' 1 . 564.356
'Cracked oil' 'Fuel Oil' 2 . 1072.28
'Cracked oil' 'Fuel Oil' 4 . 536.139
'Cracked oil' 'Fuel Oil' 5 . 409.158
'Cracked oil' 'Fuel Oil' 6 . 352.723
'Cracked oil' 'Fuel Oil' 7 . 352.723
'Cracked oil' 'Fuel Oil' 8 . 646.887
'Cracked oil' 'Fuel Oil' 9 . 613.005
'Cracked oil' 'Fuel Oil' 10 . 186.633
'Cracked oil' 'Fuel Oil' 11 . 410.419
'Cracked oil' 'Fuel Oil' 12 . 485.135
'Cracked oil' 'Jet Fuel' 6 . 1151.02
'Cracked oil' 'Jet Fuel' 7 . 993.411
'Cracked oil' 'Jet Fuel' 8 . 817.359
'Cracked oil' 'Jet Fuel' 9 . 819.483
'Cracked oil' 'Jet Fuel' 10 . 673.373
'Heavy Naphta' 'Premium Gasoline' 2 . 2289.18
'Heavy Naphta' 'Premium Gasoline' 6 . 1779.92
'Heavy Naphta' 'Premium Gasoline' 7 . 1608
'Heavy Naphta' 'Premium Gasoline' 8 . 1397.9
'Heavy Naphta' 'Regular Gasoline' 1 . 576.155
'Heavy Naphta' 'Regular Gasoline' 3 . 1.08641e11
'Heavy Naphta' 'Regular Gasoline' 4 . 528.701
'Heavy Naphta' 'Regular Gasoline' 5 . 837.565
'Heavy Naphta' 'Regular Gasoline' 8 . 392.043
'Heavy Naphta' 'Regular Gasoline' 9 . 1500.78
'Heavy Naphta' 'Regular Gasoline' 10 . 1062.81
'Heavy Naphta' 'Regular Gasoline' 11 . 817.445
'Heavy Naphta' 'Regular Gasoline' 12 . 994.249
'Heavy Oil' 'Fuel Oil' 1 . 752.475
'Heavy Oil' 'Fuel Oil' 2 . 1429.7
'Heavy Oil' 'Fuel Oil' 4 . 714.851
'Heavy Oil' 'Fuel Oil' 5 . 545.545
'Heavy Oil' 'Fuel Oil' 6 . 470.297
'Heavy Oil' 'Fuel Oil' 7 . 470.297
'Heavy Oil' 'Fuel Oil' 8 . 862.516
'Heavy Oil' 'Fuel Oil' 9 . 817.339
'Heavy Oil' 'Fuel Oil' 10 . 248.844
'Heavy Oil' 'Fuel Oil' 11 . 547.226
'Heavy Oil' 'Fuel Oil' 12 . 646.847
'Heavy Oil' 'Jet Fuel' 1 . 4258.07
'Heavy Oil' 'Jet Fuel' 2 . 6889.34
'Heavy Oil' 'Jet Fuel' 3 . 4.39297e11
'Heavy Oil' 'Jet Fuel' 4 . 4985.12
'Heavy Oil' 'Jet Fuel' 5 . 5910.13
'Heavy Oil' 'Jet Fuel' 6 . 5358.59
'Heavy Oil' 'Jet Fuel' 7 . 4920.78
'Heavy Oil' 'Jet Fuel' 8 . 5052.76
'Heavy Oil' 'Jet Fuel' 9 . 4987.13
'Heavy Oil' 'Jet Fuel' 10 . 4501.16
'Heavy Oil' 'Jet Fuel' 11 . 3933.41
'Heavy Oil' 'Jet Fuel' 12 . 4103.15
'Light Naphta' 'Premium Gasoline' 1 . 3880.28
'Light Naphta' 'Premium Gasoline' 2 . 955.602
'Light Naphta' 'Premium Gasoline' 3 . 2.77112e11
'Light Naphta' 'Premium Gasoline' 4 . 598.683
'Light Naphta' 'Premium Gasoline' 5 . 36.0166
'Light Naphta' 'Premium Gasoline' 6 . 430.376
'Light Naphta' 'Premium Gasoline' 7 . 527.363
'Light Naphta' 'Premium Gasoline' 8 . 1378.44
'Light Naphta' 'Premium Gasoline' 10 . 385.528
'Light Naphta' 'Premium Gasoline' 11 . 3441.76
'Light Naphta' 'Premium Gasoline' 12 . 3377.65
'Light Naphta' 'Regular Gasoline' 2 . 4578.92
'Light Naphta' 'Regular Gasoline' 4 . 3626.3
'Light Naphta' 'Regular Gasoline' 5 . 4566.82
'Light Naphta' 'Regular Gasoline' 6 . 3859.07
'Light Naphta' 'Regular Gasoline' 7 . 3543.18
'Light Naphta' 'Regular Gasoline' 8 . 2954.2
'Light Naphta' 'Regular Gasoline' 9 . 4277.23
'Light Naphta' 'Regular Gasoline' 10 . 3364.47
'Light Naphta' 'Regular Gasoline' 11 . 95.5879
'Light Naphta' 'Regular Gasoline' 12 . 372.352
'Light Oil' 'Fuel Oil' 1 . 225.743
'Light Oil' 'Fuel Oil' 2 . 428.911
'Light Oil' 'Fuel Oil' 4 . 214.455
'Light Oil' 'Fuel Oil' 5 . 163.663
'Light Oil' 'Fuel Oil' 6 . 141.089
'Light Oil' 'Fuel Oil' 7 . 141.089
'Light Oil' 'Fuel Oil' 8 . 258.755
'Light Oil' 'Fuel Oil' 9 . 245.202
'Light Oil' 'Fuel Oil' 10 . 74.6532
'Light Oil' 'Fuel Oil' 11 . 164.168
'Light Oil' 'Fuel Oil' 12 . 194.054
'Light Oil' 'Jet Fuel' 1 . 989.993
'Light Oil' 'Jet Fuel' 2 . 1925.39
'Light Oil' 'Jet Fuel' 3 . 3.25453e11
'Light Oil' 'Jet Fuel' 4 . 1461.96
'Light Oil' 'Jet Fuel' 5 . 2177.81
'Light Oil' 'Jet Fuel' 10 . 492.004
'Light Oil' 'Jet Fuel' 11 . 1038.39
'Light Oil' 'Jet Fuel' 12 . 997.387
'Medium Naphta' 'Premium Gasoline' 1 . 717.55
'Medium Naphta' 'Premium Gasoline' 3 . 2.45998e12
'Medium Naphta' 'Premium Gasoline' 4 . 3610.97
'Medium Naphta' 'Premium Gasoline' 5 . 4036.92
'Medium Naphta' 'Premium Gasoline' 9 . 3101.51
'Medium Naphta' 'Premium Gasoline' 10 . 2364.62
'Medium Naphta' 'Regular Gasoline' 1 . 5793
'Medium Naphta' 'Regular Gasoline' 2 . 9819.05
'Medium Naphta' 'Regular Gasoline' 3 . 4.6336e11
'Medium Naphta' 'Regular Gasoline' 4 . 3589
'Medium Naphta' 'Regular Gasoline' 5 . 3918.75
'Medium Naphta' 'Regular Gasoline' 6 . 7328.89
'Medium Naphta' 'Regular Gasoline' 7 . 6891.08
'Medium Naphta' 'Regular Gasoline' 8 . 7415.28
'Medium Naphta' 'Regular Gasoline' 9 . 4202.96
'Medium Naphta' 'Regular Gasoline' 10 . 3885.38
'Medium Naphta' 'Regular Gasoline' 11 . 5895.58
'Medium Naphta' 'Regular Gasoline' 12 . 6250
'Reformed gasoline' 'Premium Gasoline' 1 . 1217.47
'Reformed gasoline' 'Premium Gasoline' 2 . 2774.34
'Reformed gasoline' 'Premium Gasoline' 3 . 3.63833e12
'Reformed gasoline' 'Premium Gasoline' 4 . 2362.21
'Reformed gasoline' 'Premium Gasoline' 5 . 2576.69
'Reformed gasoline' 'Premium Gasoline' 6 . 1823.5
'Reformed gasoline' 'Premium Gasoline' 7 . 1695.88
'Reformed gasoline' 'Premium Gasoline' 8 . 1860.16
'Reformed gasoline' 'Premium Gasoline' 9 . 1945.77
'Reformed gasoline' 'Premium Gasoline' 10 . 1649.85
'Reformed gasoline' 'Premium Gasoline' 11 . 533.75
'Reformed gasoline' 'Premium Gasoline' 12 . 499.361
'Reformed gasoline' 'Regular Gasoline' 1 . 791.043
'Reformed gasoline' 'Regular Gasoline' 3 . 1.22074e11
'Reformed gasoline' 'Regular Gasoline' 11 . 1111.39
'Reformed gasoline' 'Regular Gasoline' 12 . 1183.4
Residuum 'Fuel Oil' 1 . 2257.43
Residuum 'Fuel Oil' 2 . 4289.11
Residuum 'Fuel Oil' 4 . 2144.55
Residuum 'Fuel Oil' 5 . 1636.63
Residuum 'Fuel Oil' 6 . 1410.89
Residuum 'Fuel Oil' 7 . 1410.89
Residuum 'Fuel Oil' 8 . 2587.55
Residuum 'Fuel Oil' 9 . 2452.02
Residuum 'Fuel Oil' 10 . 746.532
Residuum 'Fuel Oil' 11 . 1641.68
Residuum 'Fuel Oil' 12 . 1940.54
Residuum 'Jet Fuel' 1 . 911.932
Residuum 'Jet Fuel' 2 . 1030.77
Residuum 'Jet Fuel' 3 . 3.02269e11
Residuum 'Jet Fuel' 4 . 1472.92
Residuum 'Jet Fuel' 5 . 2472.06
Residuum 'Jet Fuel' 6 . 2290.39
Residuum 'Jet Fuel' 7 . 2005.81
Residuum 'Jet Fuel' 8 . 1169.88
Residuum 'Jet Fuel' 9 . 1233.39
Residuum 'Jet Fuel' 10 . 2253.47
Residuum 'Jet Fuel' 11 . 1188.2
Residuum 'Jet Fuel' 12 . 1059.46
;
: OctaneNumberMin VaporPressure_Max Storage_Fraction :=
'Fuel Oil' 1 . . 9.09495e13
'Fuel Oil' 2 . . 3608.19
'Fuel Oil' 3 . . 5.00222e12
'Fuel Oil' 4 . . 4.54747e12
'Fuel Oil' 5 . . 4.54747e12
'Fuel Oil' 6 . . 5.00222e12
'Fuel Oil' 7 . . 3.63798e12
'Fuel Oil' 8 . . 1694.86
'Fuel Oil' 9 . . 2686.93
'Fuel Oil' 10 . . 714.576
'Fuel Oil' 11 . . 153.347
'Fuel Oil' 12 . . 4.54747e13
'Jet Fuel' 1 . 0 1.81899e12
'Jet Fuel' 2 . 0 3681.82
'Jet Fuel' 3 . 0 3.63798e12
'Jet Fuel' 4 . 0 3.63798e12
'Jet Fuel' 5 . 0 3.63798e12
'Jet Fuel' 6 . 0 1.81899e12
'Jet Fuel' 7 . 0 5.45697e12
'Jet Fuel' 8 . 0 1.18234e11
'Jet Fuel' 9 . 0 3.63798e12
'Jet Fuel' 10 . 0 8.18545e12
'Jet Fuel' 11 . 0 1.81899e12
'Jet Fuel' 12 . 0 9.09495e12
'Premium Gasoline' 1 0 . 1849.73
'Premium Gasoline' 2 0 . 3948.12
'Premium Gasoline' 3 0 . 4.54747e12
'Premium Gasoline' 4 0 . 2906.92
'Premium Gasoline' 5 0 . 5380.97
'Premium Gasoline' 6 0 . 3818.21
'Premium Gasoline' 7 0 . 1518.93
'Premium Gasoline' 8 0 . 1.00044e11
'Premium Gasoline' 9 0 . 1.81899e11
'Premium Gasoline' 10 0 . 6.36646e12
'Premium Gasoline' 11 0 . 247.336
'Premium Gasoline' 12 0 . 5.45697e12
'Regular Gasoline' 2 . . 7465.04
'Regular Gasoline' 3 . . 9.09495e12
'Regular Gasoline' 4 . . 1.09139e11
'Regular Gasoline' 5 . . 1224.69
'Regular Gasoline' 6 . . 826.827
'Regular Gasoline' 7 . . 1.27329e11
'Regular Gasoline' 9 . . 1.27329e11
'Regular Gasoline' 10 . . 1.45519e11
'Regular Gasoline' 11 . . 5.45697e12
'Regular Gasoline' 12 . . 1.81899e12
;
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 5.71968e12 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 0 0 0 0
8 0 2660 5.16758e13 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 1.08674e10 3420 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 3685.5 0 0 0 0 0
4 7920 0 0 0 0 0
5 10560 0 0 0 0 0
6 8800 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 0 0 0 0
11 6160 0 0 0 0 0
12 6160 0 0 0 0 0
['Lube Oil',Station1,*,*]
: 1 2 3 4 5 6 :=
['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 11880 0 0 0 0 0
7 11563 0 0 0 0 0
8 11591.3 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 2 80858.5 0
I 3 0 81296.5
;
CashFlow [*] :=
1 124454 4 341312 7 569130 10 315474
2 1875550 5 475846 8 157371 11 98679.3
3 2204550 6 353639 9 2035.04 12 144353
;
Waste_Pollutant [*,*] (tr)
: hydrocarbon 'sulfur dioxide' :=
1 244348 361729
2 391231 568025
3 2.1948e09 3.12856e09
4 288067 427118
5 321701 474922
6 262049 379539
7 239534 347252
8 266515 386105
9 269856 393153
10 214184 313386
11 203966 299758
12 212181 310845
;
Octane number for products: 1 Premium Gasoline 93.97
Octane number for products: 2 Premium Gasoline 93.98
Octane number for products: 3 Premium Gasoline 0.00
Octane number for products: 4 Premium Gasoline 93.99
Octane number for products: 5 Premium Gasoline 93.99
Octane number for products: 6 Premium Gasoline 93.98
Octane number for products: 7 Premium Gasoline 93.98
Octane number for products: 8 Premium Gasoline 93.96
Octane number for products: 9 Premium Gasoline 93.96
Octane number for products: 10 Premium Gasoline 93.96
Octane number for products: 11 Premium Gasoline 93.96
Octane number for products: 12 Premium Gasoline 93.95
Octane number for products: 1 Regular Gasoline 83.99
Octane number for products: 2 Regular Gasoline 83.99
Octane number for products: 3 Regular Gasoline 0.00
Octane number for products: 4 Regular Gasoline 83.98
Octane number for products: 5 Regular Gasoline 83.98
Octane number for products: 6 Regular Gasoline 83.99
Octane number for products: 7 Regular Gasoline 83.98
Octane number for products: 8 Regular Gasoline 83.99
Octane number for products: 9 Regular Gasoline 83.99
Octane number for products: 10 Regular Gasoline 83.99
Octane number for products: 11 Regular Gasoline 83.99
Octane number for products: 12 Regular Gasoline 83.99
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 0.78
Premium / Regular percentage: 2 0.41
Premium / Regular percentage: 3 0.43
Premium / Regular percentage: 4 0.89
Premium / Regular percentage: 5 0.74
Premium / Regular percentage: 6 0.40
Premium / Regular percentage: 7 0.40
Premium / Regular percentage: 8 0.40
Premium / Regular percentage: 9 0.50
Premium / Regular percentage: 10 0.50
Premium / Regular percentage: 11 0.53
Premium / Regular percentage: 12 0.47
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 0.00
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 0.10
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 0.00
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 0.33
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 0.00
Production Fuel Oil ratio: 4 Residuum 1.00
Production Fuel Oil ratio: 5 Residuum 1.00
Production Fuel Oil ratio: 6 Residuum 1.00
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 0.00
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 0.25
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
CrossCheck 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
PostImplementation Review