Supply Chain Optimization for Energy Cogeneration Using Sugarcane Crop Residues (SCR)
Abstract
:1. Introduction
1.1. Background and Motivation
1.2. Literature Review—Bioenergy Supply Chain Optimization
2. Model
2.1. Problem Description
2.2. The Process
- Distance from the plot to the factory;
- Sucrose contents in the crop;
- Availability of vehicles, harvesting equipment, and crews;
- In-factory waiting time for raw materials (the sugar contents in the canes start decreasing the moment they are cut, a process called inversion).
2.3. Using Crop Residue to Generate Electricity
- Crop residue generates less CO2 equivalent than coal;
- Sugar cane mills have to purchase coal or exchange it for post-production byproducts. Crop residue is basically free.
2.4. Mathematical Model
2.4.1. Parameters
- Tons of crop residue available on plot i.
- : Energy value of the crop residue from plot i (kw*h/ton).
- : Pollution caused by burning the crop residue from plot i (CO2 tons/ton of crop residue burned).
- : Rectilinear distance (km) from plot i to the factory.
- : Fixed cost of collecting the crop residue from plot i ($).
- : Transportation cost ($/(ton*km)).
- : Baseline level of coal consumption (tons).
- : Cost of coal ($/ton).
- : Energy value of coal (kw*h/ton).
- : Pollution caused by burning coal (CO2 tons/ton of coal burned).
- : Value of carbon bonds ($/tons of CO2 removed) [33].
- : Sales price of energy.
- : Vehicles and crews available today for collection and transportation of crop residue.
2.4.2. Detailed Information about the Parameters
- : These are the tons of sugar cane crop residue that can be obtained from lot i. On average, it is possible to harvest 110 tons of sugar cane from a hectare of crop. From that, it has been estimated that the crop residue lies between 19% and 37% of that total weight [18]. The TCR from a given plot depends on its area, the variety of sugar cane grown, and the harvesting tools that are in use.
- : This represents the energy that can be obtained from a ton of crop residue. Reference [18] shows that sugar cane residue has a calorific potential of 16 kilojoules per ton. Converting this potential into kilowatts-hour, we get that on average sugar cane crop residue may generate 0.00444 kwh/ton.
- : Pollution caused by burning the crop residue from plot i. This parameter has been estimated as an average of 35.1 kg of CO2 equivalent per ton of crop residue burned [34].
- : Rectilinear distance from a plot to the sugar cane mill. The structure of plots and roadways is predominantly rectilinear. For a factory located at the distance to a plot with coordinates would be (Figure 3).
- : Fixed cost of collecting the crop residue from plot i ($). This is the cost related to fixed salary of the driver of the vehicle and the cost of ownership of said vehicle. It depends neither on the tons transported nor on the distance. We have calculated this cost at $32 USD per trip, assuming three trips per day per crew. We calculated this cost considering the fixed salaries of the crews, assuming full utilization of their work, and also considering the cost of ownership of the vehicles required for the transportation of the sugarcane crop residue. The cost of operation of the vehicles is included in the parameter COST.
- : This is the variable transportation cost. We have calculated its value at $0.115 USD per ton-km.
- : This is a user-supplied value. For our exercise we will use a value of 100 ton/day as a baseline (obtained from an actual sugar cane mill).
- : Cost of acquisition of coal in $/ton USD. This cost may vary according to the sources the individual company uses to acquire its coal. There are different acquisition strategies, including long-term contracts, open market contracts and the exchange of bagasse for coal with the paper mills. For this model, we used $75/ton USD.
- : Energy value of coal (kwh/ton). The coal used by sugar cane mills has a calorific power of 0.00666 kwh/ton on average.
- : Pollution caused by burning coal (CO2 tons/ton of coal burned). This value has been estimated as 2.66 tons of CO2 per ton of coal burned [34].
- : Value of carbon bonds ($/tons of CO2 removed). We will use $25 USD per ton of equivalent CO2, as this is close to the average in the first part of 2019 [33].
- : Sales price of energy. In Colombia, this price is currently $0.028 USD/kwh [35].
- : Trips for residue collection and transportation available today. In our example, VAV ranges between 15 and 25 for any given day.
2.4.3. Variables
- : Binary: 1 if the residue from plot i is collected, 0 if not.
- : Amount of tons of crop residue collected from plot i.
- : Tons of coal burned today.
- Income obtained through the sale of green bonds.
- Electricity sold.
- Savings realized if the coal purchased is less than the baseline.
- Total fixed transportation costs.
- Total variable transportation costs.
2.4.4. Objective Function:
2.4.5. Constraints
3. Results
4. Discussion
5. Conclusions
- SCR releases less equivalent CO2 than coal when burned for electricity generation;
- SCR is basically free. It is a byproduct of the harvesting of the sugarcane. CO2 is a raw material that has to be acquired through private contracts or the commodities market;
- SCR can be collected using crews, equipment, and vehicles that are similar to those used for the harvesting and transportation of sugarcanes.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
Julia Code
using JuMP using GLPK using MathOptInterface using CSV
# Read data from file data = CSV.read("Model-Data.csv")
# Create indexed parameters TCR = data.TCR CP = data.CP P = data.P D = data.D
# Create constants FCOST = 32; COST = 0.115; COAL = 100 CCL = 75; CPC = 0.00666; POL = 2.66 CBOND = 25; SPE = 0.028; VAV = 18
# Count the number of plots plots = size(TCR)[1]
# Create optimization model m = Model(with_optimizer(GLPK.Optimizer))
# Declare decision variables @variable(m, y[1:plots], Bin) @variable(m, x[1:plots] >= 0) @variable(m, cpur >= 0)
# Declare cost variables for the objective function @variable(m, bond_income >= 0) @variable(m, elec_sold >= 0) @variable(m, coal_savings >= 0) @variable(m, fixed_transp >= 0) @variable(m, var_transp >= 0)
# Declare the objective function @objective(m, Max, bond_income + elec_sold + coal_savings - fixed_transp - var_transp)
# The new level of pollution must not exceed the baseline @constraint(m, pol_base, cpur*POL + sum(x[i]*P[i] for i in 1:plots) <= COAL*POL)
# The electricity generated must not be less than the baseline @constraint(m, elec_gen, sum(x[i]*CP[i] for i in 1:plots) + (cpur*CPC) >= COAL*CPC)
# The number of plots to collect crop residue is limited by # the number of trips available per day @constraint(m, collect_plots, sum(y[i] for i in 1:plots) <= VAV)
# If a plot is not selected, no crop residue can be collected from it @constraint(m, residue[i=1:plots], x[i] <= TCR[i]*y[i])
# Assign value to the cost variables of the objective function @constraint(m, bondincome, bond_income == (COAL*POL - sum(x[i]*P[i] for i in 1:plots) - cpur*POL) * CBOND) @constraint(m, elecsold, elec_sold == (sum(x[i]*CP[i] for i in 1:plots) + ((cpur-COAL)*CPC))*SPE) @constraint(m, coalsavings, coal_savings == (COAL - cpur)*CCL) @constraint(m, fixedtransp, fixed_transp == sum(y[i]*FCOST for i in 1:plots)) @constraint(m, vartransp, var_transp == sum(x[i]*D[i]*COST for i in 1:plots))
print(m)
status = optimize!(m)
println("Profit: ", JuMP.objective_value(m)) println("Plots to collect: ", JuMP.value.(y)) println("Crop residue: ", JuMP.value.(x)) println("Coal to buy: ", JuMP.value(cpur)) println("Bond Income: ", JuMP.value(bond_income)) println("Electricity Sold: ", JuMP.value(elec_sold)) println("Coal Savings: ", JuMP.value(coal_savings)) println("Fixed Transp: ", JuMP.value(fixed_transp)) println("Variable Transp: ", JuMP.value(var_transp)) println("Residue Collected: ", sum(JuMP.value.(x)))
Appendix B
Instance Data
Plot. | TCR | CP | P | D |
---|---|---|---|---|
P1 | 37 | 0.0030336 | 0.0352 | 17.14 |
P2 | 30 | 0.0032734 | 0.0334 | 3.42 |
P3 | 26 | 0.0058655 | 0.0363 | 21.16 |
P4 | 39 | 0.0041573 | 0.0331 | 15.65 |
P5 | 26 | 0.0032552 | 0.0361 | 3.24 |
P6 | 35 | 0.0032061 | 0.0338 | 15.31 |
P7 | 37 | 0.0057260 | 0.0347 | 22.56 |
P8 | 33 | 0.0040761 | 0.0345 | 21.03 |
P9 | 21 | 0.0059792 | 0.0336 | 5.55 |
P10 | 33 | 0.0037543 | 0.036 | 24.73 |
P11 | 33 | 0.0052091 | 0.0354 | 17.78 |
P12 | 32 | 0.0044785 | 0.0333 | 22.54 |
P13 | 27 | 0.0030945 | 0.0343 | 11.12 |
P14 | 27 | 0.0044857 | 0.0363 | 16.47 |
P15 | 30 | 0.0046803 | 0.0353 | 22.67 |
P16 | 36 | 0.0054730 | 0.0367 | 13.91 |
P17 | 24 | 0.0042343 | 0.034 | 22.60 |
P18 | 23 | 0.0039274 | 0.0349 | 14.76 |
P19 | 30 | 0.0044093 | 0.0341 | 22.49 |
P20 | 26 | 0.0055547 | 0.0353 | 16.93 |
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Variety | Total |
---|---|
(t SCR/t cane) | |
CC 01–1940 | 0.2657 |
CC 85–92 | 0.2479 |
CC 93–4418 | 0.2624 |
Others | 0.2587 |
Total Profit | $13,708.04 USD | ||||
Plots collected | P2 | P5 | P9 | P11 | P16 |
Tons collected | 30.0 | 26.0 | 21.0 | 30.8 | 36.0 |
Coal to buy | 0.0 | ||||
Bond Income | $6523.53 USD | ||||
Electricity Sold | 0.0 | ||||
Coal Savings | $7500 (USD | ||||
Fixed Transp. | 160.0 | ||||
Variable Transp. | 155.50 | ||||
Residue Collected | 143.823 |
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Rivera-Cadavid, L.; Manyoma-Velásquez, P.C.; Manotas-Duque, D.F. Supply Chain Optimization for Energy Cogeneration Using Sugarcane Crop Residues (SCR). Sustainability 2019, 11, 6565. https://doi.org/10.3390/su11236565
Rivera-Cadavid L, Manyoma-Velásquez PC, Manotas-Duque DF. Supply Chain Optimization for Energy Cogeneration Using Sugarcane Crop Residues (SCR). Sustainability. 2019; 11(23):6565. https://doi.org/10.3390/su11236565
Chicago/Turabian StyleRivera-Cadavid, Leonardo, Pablo Cesar Manyoma-Velásquez, and Diego F. Manotas-Duque. 2019. "Supply Chain Optimization for Energy Cogeneration Using Sugarcane Crop Residues (SCR)" Sustainability 11, no. 23: 6565. https://doi.org/10.3390/su11236565