# Optimization of the Supply Chain in the Production of Ethanol from Agricultural Biomass Using Mixed-Integer Linear Programming (MILP): A Case Study

Authors: Edgar León-Olivares; Hertwin Minor-Popocatl; Omar Aguilar-Mejía; Diana Sánchez-Partida
Journal: Mathematical Problems in Engineering
 (2020)

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## Abstract

The production of biofuels from agricultural biomass has attracted much attention from researchers in recent years. Biomass residues generated from agricultural production of corn and barley represent an essential source of raw material for the production of biofuels, and a mathematical programming-based approach can be used to establish an efficient supply chain. This paper proposes a model of mixed-integer linear programming (MILP) that seeks to minimize the total cost of the bioethanol supply chain. The proposal allows determining the optimal number and location of storage centers, biorefineries, and mixing plants, as well as the flow of biomass and bioethanol between the facilities. To show the proposed approach, we present a case study developed in the region of Tulancingo, Hidalgo, in Mexico (case study), considering the potential of biomass (corn and barley residues) in the region. The results show the costs for the production of bioethanol, transportation, and refining and total cost of the bioethanol supply chain, besides a sensitivity analysis on the costs of the bioethanol supply chain which is presented by mixing different percentages of bioethanol with fossil fuel to satisfy the demand. We conclude that the proposed approach is viable in the process of configuring the supply chain within the proposed study region.


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## Body

## 1. Introduction

Countries around the world have considered and directed policies towards the increase and economic use of biomass to meet their future energy demands in order to meet polluting emissions reduction targets, as specified in the Kyoto Protocol, to reduce dependence from fossil fuels [1].Due to the energy crisis, environmental, and social problems, many researchers have focused on the development of renewable energy (RE) sources to guarantee energy consumption, protect the environment, and promote regional development. Biofuel is a type of RE that can be used in multiple ways to replace energy based on fossil fuels. Bioethanol is a type of biofuel that is currently widely used in internal combustion vehicles [2], which, when mixed with fossil fuel, has the objective of oxygenating it, thus achieving complete combustion that allows reducing toxic emissions [3].Although first-generation bioethanol production has been commercialized worldwide, it is still debatable about the consumption of food and energy used to get the biofuel. Recently, this trend has changed, and now the focus is on the use of lignocellulose and nonfood biomass products to produce biofuel and thus improve food and energy security [4]. Biomass is considered an alternative source of attractive energy to replace fossil fuels [5], if and only if it occurs without negatively affecting the environment [6] because not all agricultural residues should be used for biofuel production [7, 8].There is much research that assesses the feasibility of producing biofuels from various types of biomass [9–13] and different conversion techniques [14, 15]. Currently, many research efforts are directed towards the development of efficient conversion technologies and bioethanol supply chain (Bio-Eth SC) systems that use lignocellulosic biomass like raw materials [4]. The components of the biomass include cellulose, hemicelluloses, lignin, extracts, lipids, proteins, simple sugars, starches, water, hydrocarbons, ash, and other compounds [16]. However, not all the waste produced should be used for the production of bioenergy, since the indiscriminate disposal of waste can lead to a decrease in soil quality with adverse impacts [17].The main logistical activities in a Bio-Eth SC based on corn and barley agricultural residues include sowing, harvesting, collecting in bales for easy storage and transport, the conversion to bioethanol, and transportation of bioethanol between biorefineries and mixing plants, as well as the transportation of biofuel between mixing plants and customers. It is essential to investigate the number and optimal locations for storage facilities, biorefineries, mixing plants, and finding the optimal allocation of raw materials, as well as the estimation of costs, processing, and transportation in order to facilitate the commercialization of biofuel production [18–24].The use of the mathematical programming (MP) approach to the design of supply chains for the production of biofuels has been widely addressed in the specialized literature. In [25], a mixed-integer linear programming (MILP) model is proposed for a bioenergy supply chain. This approach proposes to minimize the total cost of the supply chain (SC) as well as to define the capacity and location of production facilities, optimal selection of quantities and sources of biomass, modes of transport, and the links that must be established for the transport of biomass and the products that are delivered to the markets. The proposed approach does not consider mixing plants with fossil fuels.In [26], a stochastic programming model of mixed integers with two steps is presented for the strategic planning of biofuel supply systems based on biological residues, including maize residues, rice straw, wheat straw, waste forestry, and municipal solid waste (wood, paper, and cotton). The model identifies refineries, size, and location of terminals; the results show that bioethanol production can be viable based on such waste; this proposal does not consider barley residues and no mixing plants.In [27], an integrated model is developed that includes strategic and tactical decisions simultaneously to optimize forest-based biomass supply chains to produce bioenergy and biofuels, the proposal considers the annual and monthly variations in the supply of biomass, the demand for bioenergy/biofuels, and losses during processing, and storage also determines the opening of conversion facilities; this paper is a case study which shows that the capacity of conversion technologies and the amount of biomass processed by the strategic model are not sufficient to meet the monthly demand for bioenergy; this approach does not consider the inclusion of mixing plants within the SC.An approach that seeks the optimization of biorefinery locations and the associated transport networks for the production of biofuel using corn stover is presented in [28] through an MILP considering the uncertainty. The case study suggests the implementation of the technology to be used, and the solution manages to meet 10% of the demand; the proposal only considers agricultural corn residues and does not imply storage centers or mixing plants with fossil fuel.A stochastic proposal that considers multiple periods in the design of the SC of biofuels based on grass, urban waste, corn stover, wheat straw, and rice is presented in [29]. The proposal considers a system of production, distribution, time stages, locations, and capacities of the technical installations and material flows; this proposal does not consider mixing facilities with fossil fuel or barley biomass.In [24], an integrated mathematical model to determine the best logistics decisions and minimize the total cost of the grass-based bioethanol SC is proposed; the case study demonstrates the economic viability of producing biofuel from biomass on a commercial scale; the model does not consider storage centers or mixing plants. In [30], an MP approach is presented, to optimize strategic decisions (location and type of facilities) and tactics (assignment) in all types of biomass-based SCs; however, for its implementation, a critical point is to identify the quantitative values for the different parameters of the model.A linear programming (LP) model is addressed to optimize the SC in [31]; this paper is considering the transport from forest biomass collection sites and corn residues to the biorefineries, but it does not consider a set of customers, barley residues, or plants of mixing with fossil fuel.In [32], it presents a mathematical model that can be used to design the SC and manage the logistics of a biorefinery, the proposed model coordinates design and logistics decisions, and it also determines the number, size, and location of the biorefineries needed to produce biofuels using biomass from corn and forest residues. The model also determines the amount of biomass sent, processed, and inventoried over some time, including mixing plants, storage centers, and a set of customers. However, it does not consider agricultural residues of barley.In [33], a conceptual design of a lignocellulosic biorefinery and its supply chain for ethanol production in India is proposed; in this proposal, it is not considered as the use of biomass from barley agricultural waste, nor is it considered in the supply chain as the use of mixing plants and not a set of customers. In [34], a comprehensive model for the design and analysis of bioethanol production and supply strategies from lignocellulosic biomass is developed, taking as a case study the island of Jeju, Korea; in this study, the use of plants mixed and a set of customers represented by regions are considered; also, the authors consider the use of barley waste; however, they do not consider corn waste.In [35], the authors present a review of 72 research articles published between 2006 and 2015 from a sustainability perspective, as well as the inclusion of uncertainty regarding the design and optimization of biorefineries supply chain management. Derived from the analysis of these publications, it is found that the main objective is an economic benefit, and most of these works develop a deterministic MILP model.Another work that makes a review of 146 publications between 1997 and 2016 related to the design of the biomass supply chain is that presented by Ghaderi et al. [20], in which they are reviewed, analyzed, and classified according to their modeling approaches, decisions, uncertainties, solution methodologies, sustainability, model characteristics, entities, data, and regions of the case studies. In the majority of the publications reviewed, the main objective is the total minimization of costs and maximizing benefits; the most widely used mathematical programming approach is the MILP and multicriteria decision-making (MCDM). However, despite the diversity of the types of biomass used in each case study, only one of them [36] uses, among other wastes, corn, and barley for bioethanol production in Northern Italy. However, the model focuses on capacity planning and the problems of selecting technology for bioethanol production in the presence of market uncertainty do not consider a set of mixing plants or customers.The use of bioethanol in gasoline has become a global trend to reduceCO2 emissions to the atmosphere, increasing the octane number of gasoline and reducing dependence on petroleum products, experimentally [37]. The effect of the use of ethanol and gasoline mixtures in the mechanical, energetic, and environmental performance of the vehicles is studied, concluding that there is a reduction in damages to human health, the ecosystem, and natural resources when the vehicles use a mixture of bioethanol and fossil fuel. According to [38], it is assumed that most engines can operate safely with a mixture of gasoline and ethanol E10 (90% gasoline and 10% ethanol). However, it can have a variation from E5 to E100.The use of bioethanol as an additive to fossil fuel has increased in recent years. However, the use of grains in the production of bioethanol is unacceptable, from the ethical point of view, in a world where there is much inequality, and a considerable part of the population goes hungry [39]. Therefore, the use of raw materials lignocellulosic biomass is being studied intensively to develop bioethanol without using grains for human consumption. The residues of corn and barley are an essential alternative to be used in the production of bioethanol.In the literature review, we observed that the use of the MP approach in the design of SCs for the production of biofuels from agricultural biomasses is widely used. The presented approaches do not show a combination of agricultural residues of corn and barley nor the inclusion of mixing plants except [32] to combine fossil fuel and biofuel and to be able to respond to the demand of biofuels at competitive prices and in the case study proposed by authors, it includes agricultural residues of corn and barley and the inclusion of mixing plants. Thus, commercial software is the tool used to solve the modeling (commercial solver LINGO 17).On the other hand, government policy within the study region is to promote sustainable development [40]. Explicitly, the region of the case of study will give impetus to the research and development of projects for the generation and use of alternative energy under sustainability criteria. These favor the use of renewable energies with social and environmental responsibility, develop studies of regional nature that determine the most appropriate form for the generation of energy, and favor the rational use of energy resources derived from the productive processes of the primary sector [41].In this paper, we study the conditions of the area of the case of study for the production of second-generation bioethanol from agricultural residues in the region (corn and barley) with a four-level Bio-Eth SC. An MILP is formulated that supports the design problem of the Bio-Eth SC proposal, due to the number of cultivation sites, available alternatives to the facilities, and interactions between each level of the Bio-Eth SC. It allows choosing the location of the storage facilities, biorefineries, and mixing plants, as well as cultivation sites and biomass quantities.The objectives of this study are (1) to determine the availability of biomass for bioethanol production in the proposed study area; (2) to determine the feasible Bio-Eth SC design; (3) to establish the total costs of the Bio-Eth SC; (4) to provide information on the production of bioethanol from corn and barley agricultural residues biomass; (5) to determine the viability of the Bio-Eth SC through a sensitivity analysis using different percentages of mixture between bioethanol and fossil biofuel to satisfy the demand.


## 2. Description of the Problem

For the Bio-Eth SC’s strategic design along with planning decisions that minimize the total cost, a model is proposed that integrates facilities for the production of bioethanol based on agricultural residues of corn and barley (see Figure1).Figure 1
Model of the proposed supply chain.The proposed model considers sites for biomass harvesting, storage facilities, biorefineries, mixing plants, and customer demand. The biomass is transported between the harvest site and storage centers or biorefineries, and the bioethanol is transported from the biorefineries to the mixing plants with fossil fuel and finally from the mixing plants to the customers (gas stations). The design problem determines the location of the facilities (storage centers, biorefineries, and mixing plants), as well as the harvest sites from where the biomass of corn and barley crops will be collected and flow between facilities.The model considers aspects such as(i)
All possible locations of the cultivation sites, storage centers, biorefineries, mixing plants, and customers(ii)
The possible supply (a type of biomass and quantity per period) of each harvest site(iii)
Cost of sowing, cultivation, and harvesting for each type of biomass(iv)
The distance between all points of the Bio-Eth SC(v)
Cost of transport mode(vi)
Cost of amortization and the annual operation of the facilities(vii)
Possible capacity values of the facilities(viii)
The conversion factors for each type of biomass in bioethanol(ix)
The demandTo determine(i)
The number and location of harvest sites(ii)
The amount of biomass transported from each harvest site to storage centers and biorefineries(iii)
The amount of bioethanol transported from biorefineries to mixing plants(iv)
Amount of product stored at harvest sites and each facility(v)
Amount of fossil fuel required for mixing with bioethanol(vi)
Amount of biofuel transported to customers(vii)
The number of storage centers, biorefineries, and mixing plants that must be openedIn order to minimize the total cost of the SC and, at the same time, satisfy the established demand, the impact of the yield of corn and barley crops, the loss of dry matter during storage, and the availability of farmland are also considered in the model.The MILP model proposed in this case study incorporates the following characteristics for the Bio-Eth SC:(i)
For the proposed model, a 75-kilometer zone around the municipality in question covers the states of Hidalgo, Mexico, Puebla, Tlaxcala, and Veracruz and totals 112 municipalities (see Figures2 and 3)(ii)
Only corn and barley residues are considered(iii)
In this study, two periods are considered: the first is spring-summer that considers harvest of the rainy season and the second is autumn-winter for harvesting in irrigated landFigure 2
Area of influence for the research study. Source: map made using Google Maps.Figure 3
Location of harvest sites. Source: map made using Google Maps.


### 2.1. Assumptions

Then, the different assumptions used in the proposed MILP model are explained.


#### 2.1.1. Location of Storage Centers, Biorefineries, and Mixing Plants

The location of storage centers, biorefineries, and mixing plants have predetermined locations.


#### 2.1.2. Harvesting Method

Harvest costs are only square bales.


#### 2.1.3. The Frequency of the Harvest of Corn and Barley

In the study region, the most important crops are corn and barley; the frequency of collection of agricultural waste derived from barley is done once a year (spring-summer period) and for corn in some places up to twice per year (spring-summer and fall-winter). According to the data obtained from [42–48] in the study region, the planted area is 247,942 and 212,414 ha for maize and barley, respectively. The average biomass yields are 1.95 t ha−1 for corn and 1.99 t ha−1 for barley. Therefore, the biomass potential in the study region is 906,190.76 t of dry matter.


#### 2.1.4. Mode of Transport of Biomass and Bioethanol

In the region of study, the mode of transport is only by road using freight trucks and tankers. The mode of transport directly affects the cost of the logistics chain [2]; in the study region, as the distances to transport the biomass and biofuel do not exceed 300 km, the mode of transport at the lowest cost is by road [49], using cargo trucks and tankers.


#### 2.1.5. Demand

In the present investigation, the demand for biofuel is known for each period; according to the combustible sales data in the study region, it is approximately 988 million litres per year (MLPY) [50]; the demands for each client were determined under a normal distribution, using an average of 4,357,025.76 and standard deviation 1,742,810.30. Also, each service station is considered like a customer located in the region for the case study.


## 2.1. Assumptions

Then, the different assumptions used in the proposed MILP model are explained.


### 2.1.1. Location of Storage Centers, Biorefineries, and Mixing Plants

The location of storage centers, biorefineries, and mixing plants have predetermined locations.


### 2.1.2. Harvesting Method

Harvest costs are only square bales.


### 2.1.3. The Frequency of the Harvest of Corn and Barley

In the study region, the most important crops are corn and barley; the frequency of collection of agricultural waste derived from barley is done once a year (spring-summer period) and for corn in some places up to twice per year (spring-summer and fall-winter). According to the data obtained from [42–48] in the study region, the planted area is 247,942 and 212,414 ha for maize and barley, respectively. The average biomass yields are 1.95 t ha−1 for corn and 1.99 t ha−1 for barley. Therefore, the biomass potential in the study region is 906,190.76 t of dry matter.


### 2.1.4. Mode of Transport of Biomass and Bioethanol

In the region of study, the mode of transport is only by road using freight trucks and tankers. The mode of transport directly affects the cost of the logistics chain [2]; in the study region, as the distances to transport the biomass and biofuel do not exceed 300 km, the mode of transport at the lowest cost is by road [49], using cargo trucks and tankers.


### 2.1.5. Demand

In the present investigation, the demand for biofuel is known for each period; according to the combustible sales data in the study region, it is approximately 988 million litres per year (MLPY) [50]; the demands for each client were determined under a normal distribution, using an average of 4,357,025.76 and standard deviation 1,742,810.30. Also, each service station is considered like a customer located in the region for the case study.


## 2.1.1. Location of Storage Centers, Biorefineries, and Mixing Plants

The location of storage centers, biorefineries, and mixing plants have predetermined locations.


## 2.1.2. Harvesting Method

Harvest costs are only square bales.


## 2.1.3. The Frequency of the Harvest of Corn and Barley

In the study region, the most important crops are corn and barley; the frequency of collection of agricultural waste derived from barley is done once a year (spring-summer period) and for corn in some places up to twice per year (spring-summer and fall-winter). According to the data obtained from [42–48] in the study region, the planted area is 247,942 and 212,414 ha for maize and barley, respectively. The average biomass yields are 1.95 t ha−1 for corn and 1.99 t ha−1 for barley. Therefore, the biomass potential in the study region is 906,190.76 t of dry matter.


## 2.1.4. Mode of Transport of Biomass and Bioethanol

In the region of study, the mode of transport is only by road using freight trucks and tankers. The mode of transport directly affects the cost of the logistics chain [2]; in the study region, as the distances to transport the biomass and biofuel do not exceed 300 km, the mode of transport at the lowest cost is by road [49], using cargo trucks and tankers.


## 2.1.5. Demand

In the present investigation, the demand for biofuel is known for each period; according to the combustible sales data in the study region, it is approximately 988 million litres per year (MLPY) [50]; the demands for each client were determined under a normal distribution, using an average of 4,357,025.76 and standard deviation 1,742,810.30. Also, each service station is considered like a customer located in the region for the case study.


## 3. Mathematical Model

### 3.1. Application of MILP

An outstanding approach in the generation and evaluation of a large number of alternatives in the design process of an SC is based on the MILP [36]. Several models have been presented so far to optimize the economic and environmental performance of the SC’s biofuel simultaneously. Zhuang and Chang [51] propose a model of mixed-integer programming (MIP) to determine a combination of products for a production process; this study is based on a cost accounting system of time-based activities. Sharifzadeh et al. [52] use an MILP to determine the optimum design and operation of the network of a supply chain under uncertainty, specifically for making systematic and centralized production decisions and distributed and mobile biofuels. Shabani and Sowlati [53] present a nonlinear mixed integer programming approach (MINLP), whose objective is to maximize the value of the supply chain for the generation of electricity from forest biomass, improving profits from the optimal solution; the model developed is a mixed-integer nonlinear programming (MINLP). Lee et al. [34] in their work develop an optimization model using MILP for the design and analysis of bioethanol production and supply strategies from lignocellulosic biomass. Venkat and Shastri [33] develop an MILP model for the conceptual design of a lignocellulosic biorefinery and its supply chain to produce ethanol from agricultural waste in the Indian context.The proposed approach in this paper is presented as an MILP, considering the framework formulated in this section and using a previously proposed mathematical model [32]. For the problem posed, the indices, parameters, and decision variables are presented in detail, as well as the objective function and restrictions of the model.


### 3.2. Models Parameters

#### 3.2.1. Sets

B denotes biomass types
I denotes harvest sites
J denotes storage centers
K denotes biorefineries in a particular location
M denotes mixed plants
N denotes customers
T denotes periods


#### 3.2.2. Amortization of Facilities

α
j($/year) is the annual cost of construction amortization and operation of the warehousej∈J
β
k($/year) is the annual amortization of construction and operation of the biorefinery k∈K
γ
m($/year) is the annual amortization of construction and operation of the mixing plant m∈M


#### 3.2.3. Harvest Costs

δ
i
b
t($/ha) is the cost of sowing and growing biomass b∈B at the harvest site i∈I, in the time t∈T
η
i
b
t($/ha) is the cost of harvesting the biomass b∈B at the harvest site i∈I, in the time t∈T


#### 3.2.4. Holding Costs

H
i
b
S($/t) is the cost of holding biomass type b∈B per ton at the harvest site i∈I
H
j
b
W($/t) is the cost of holding biomass type b∈B per ton in the warehouse j∈J
H
k
b
B($/t) is the cost of holding biomass type b∈B per ton in the biorefinery k∈K
H
k
E($/L) is the cost of holding bioethanol per litre in the biorefinery k∈K
H
m
M($/L) is the cost of holding biofuel per litre in the mixing plant m∈M


#### 3.2.5. Transport Costs

a
i
j($/t) is the cost of transporting a biomass ton from the harvest site i∈I to the warehouse j∈J
b
i
k($/t) is the cost of transporting a biomass ton from the harvest site i∈I to the biorefinery k∈K
c
j
k($/t) is the cost of transporting a biomass ton from the warehouse j∈J to the biorefinery k∈K
d
k
m($/L) is the cost of transporting a bioethanol litre from the biorefinery k∈K to the mixing plant m∈M
e
m
n($/L) is the cost of transporting a biofuel litre from the plant m∈M to the customer n∈N.


#### 3.2.6. Capacities

S
j
W(t) is the storage capacity of the warehouse j∈J
S
k
P(L) is the bioethanol production capacity per year of the biorefinery k∈K
S
k
B(t) is the capacity to store biomass per year of the biorefinery k∈K
S
m
M(L) is mixing capacity per year of the mixing plant m∈M


#### 3.2.7. The Opening of Facilities

n
b is the maximum number of biorefineries that can be opened
n
m is the maximum number of mixing plants that can be opened


#### 3.2.8. Other Costs

μ
t($/L) is the cost per litre of fuel in the period t∈T
ω
k
b($/t) is the cost of processing a biomass ton, type b∈B in the biorefinery k∈K


#### 3.2.9. Other Parameters

L
i
b
t is the number of hectares of land at the harvest site i∈I for biomass typeb∈B, in the time t∈T
P
i
b
t is the proportion of land available at the harvest site i∈I with biomass type b∈B, in the time t∈T
R
i
b
t(t/ha) is the yield of biomass type b∈B at the harvest site i∈I in the time t∈T
θ(%) is the percentage of deterioration of stored biomass
λ
b(L/t) is the conversion ratio of biomass type b∈B
D
n
t(L) is the customer’s fuel demand n∈N in the period t∈T
ψ is the percentage in which the mixture of bioethanol with fossil fuel is required
ρ is the percentage destined to store biomass in biorefinery k∈K


### 3.3. Decision Variables

#### 3.3.1. Binary Decision Variables

X
j
W is a binary variable equal to 1, if the warehouse j∈J is open, 0 otherwise
X
k
P is a binary variable equal to 1, if the biorefinery k∈K is open, 0 otherwise
X
m
M is a binary variable equal to 1, if the mixing plant m∈M is open, 0 otherwise


#### 3.3.2. Decision Variables for Holding

Z
i
b
t
S is the amount of biomass type b∈B stored on the site i∈I in the time t∈T
Z
j
b
t
W is the amount of biomass type b∈B stored on the warehouse j∈J in the time t∈T
Z
k
b
t
B is the amount of biomass type b∈B stored in the biorefinery k∈K in the time t∈T
Z
k
t
E is the amount of bioethanol stored in the biorefinery k∈K in the time t∈T
Z
m
t
M is the amount of biofuel stored in the mixing plant m∈M in the time t∈T


#### 3.3.3. Decision Variables for Sent Quantities

Y
i
j
b
t
S is the amount of biomass type b∈B sent from the site i∈I to the warehouse j∈J in the time t∈T
Y
i
k
b
t
W is the amount of biomass type b∈B sent from the site i∈I to biorefinery k∈K in the time t∈T
Y
j
k
b
t
B is the amount of biomass type b∈B sent from the site j∈J to biorefinery k∈K in the time t∈T
Y
k
m
t
E is the amount of bioethanol sent from biorefinery k∈K to the mixing plant m∈M in the time t∈T
Y
m
n
t
M is the amount of biofuel sent from the mixing plant m∈M to the customer n∈N in the time t∈T


#### 3.3.4. Other Decision Variables

Y
m
t
R
P is the amount of fossil fuel required in the mixing plant m∈M in the time t∈T
W
k
b
t is the amount of biomass type b∈B processed in the biorefinery k∈K in the time t∈T
ϕ
i
b
t is the amount of biomass type b∈B produced on the harvest site i∈I in the time t∈T


### 3.4. Objectives and Objective Function

In the harvest sites (I), the agricultural biomass of corn and barley is generated, and square bales do the collection method. These are sent to the storage centers (J) or directly to the biorefineries (K) in each period T. Once the conversion process is completed, the bioethanol is sent from the biorefineries to the mixing plants (M), where it will be combined with fossil fuel to be sent to the customers (N) finally.In order to minimize the costs of the SC in the MILP model, the decisions that are optimized are the (1) selection of sites of harvest sites (i); (2) selection of storage centers (j), which have a predetermined location; (3) selection of biorefineries (k), which have a predetermined location and capacity; (4) flow of biomass material to storage centers and biorefineries; (5) volume of bioethanol during period (t); (6) flow of bioethanol to mixing plants (m); (6) flow of biofuel from mixing plants to customers (n) during period (t).The objective of the proposed model is minimizing the total annual cost of Bio-Eth SC. The cost of the Bio-Eth SC includes the cost of annual amortization of the number of distribution centers, biorefineries, and mixing plants that will be opened, cost of storage of bioethanol in biorefineries and mixing plants, and the cost of storage of biomass in distribution centers and biorefineries. In the same way, the cost of transporting biomass from the harvest sites to distribution centers and biorefineries and from distribution centers to biorefineries is modeled, as is the cost of transporting bioethanol from biorefineries to mixing plants, the cost of transporting biofuel from mixing plants to customers, and the cost of transporting fossil fuel to the mixing plant. Finally, the cost of processing per unit of biomass and cost of sowing, cultivation, and harvesting for the production of biomass are taken into account. The different components of the objective function are explained as follows.The annual amortization cost of the distribution centers can be defined as(1)∑j=1JαjXjW.The cost of annual amortization of biorefineries is(2)∑k=1KβkXkP.The annual amortization cost of the mixing plants that are opened is defined as(3)∑m=1MγmXmM.The cost of storing bioethanol in biorefineries is calculated as(4)∑t=1T∑k=1KHkEZktE.The cost of holding bioethanol in the mixing plant is(5)∑t=1T∑m=1MHmMZmtM.The cost of holding a unit of biomass at the harvest site is expressed as follows:(6)∑t=1T∑b=1B∑i=1IHibSZibtS.The cost of holding units in a storage center is defined as(7)∑t=1T∑b=1B∑j=1JHjbWZjbtW.The cost of maintaining units in biorefineryk of biomass type b can be computed as(8)∑t=1T∑b=1B∑k=1KHkbBZkbtB.The cost of transporting biomass from the harvest sitei to the storage center j is(9)∑t=1T∑b=1B∑i=1I∑j=1JaijYijbtS.The cost of transporting biomass from the harvest sitei to the biorefinery k is described by(10)∑t=1T∑b=1B∑i=1I∑k=1KbikYikbtW.The cost of transporting biomass from a storage center to the biorefinery is derived as(11)∑t=1T∑b=1B∑j=1J∑k=1KcjkYjkbtB.Calculating the cost of transporting bioethanol from biorefinery to the mixing plant is given by the relation(12)∑t=1T∑k=1K∑m=1MdkmYkmtE.The cost of transporting biofuel from the mixing plant to then customers is shown in (13)∑t=1T∑m=1M∑n=1NemnYmntM.The cost of fossil fuel delivered to the mixing plant is determined as(14)∑t=1T∑m=1MμtYmtRP.The cost of processing biomass to generate bioethanol is computed as(15)∑t=1T∑k=1K∑b=1BωkbWkbt.Growing and harvesting biomass at each harvest site are calculated to determine the costs of sowing:(16)∑t=1T∑i=1I∑b=1Bδibt+ηibtϕibt.The fitness functionO to be minimized is the next and considers all the above cost elements:(17)minΩ=∑j=1JαjXjW+∑k=1KβkXkP+∑m=1MγjXmM+∑t=1T∑k=1KHkEZktE+∑t=1T∑m=1MHmMZmtM+∑t=1T∑b=1B∑i=1IHibSZibtS+∑t=1T∑b=1B∑j=1JHjbSZjbtS+∑t=1T∑b=1B∑k=1KHkbSZkbtS+∑t=1T∑b=1B∑i=1I∑j=1JaijYijbtS+∑t=1T∑b=1B∑i=1I∑k=1KbikYikbtW+∑t=1T∑b=1B∑j=1J∑k=1KcjkYkkbtB+∑t=1T∑k=1K∑m=1MdkmYkmtE+∑t=1T∑m=1M∑n=1NemnYmntM+∑t=1T∑m=1MμtYmtRP+∑t=1T∑k=1K∑b=1BωkmWkbt+∑t=1T∑i=1I∑b=1Bδibt+ηibtϕibt.


### 3.5. Constraints

Equation (18) guarantees that the total amount of type b biomass at harvest site i in period t depends on the number of hectares of biomass collected and the yield of production:(18)ϕibt≤RibtPibtLibt,∀i∈I,b∈B,t∈T.Equation (19) guarantees that the shipment of type b biomass from harvest site i to storage center j and biorefinery k at time t is equal to the amount of type b biomass available at harvest site i:(19)∑j=1JYijbtS+ZibtS+∑k=1KYikbtW=ϕibt+1−θZib,t−1S,∀i∈I,b∈B,t∈T.Equation (20) guarantees that the shipment of biomass type b from storage center j to biorefinery k is equal to the amount of type b biomass available in storage center j in each period t:(20)∑i=1IYijbtS+1−θZjb,t−1W=∑k=1KYjkbtB+ZjbtW,∀j∈J,b∈B,t∈T.Equation (21) guarantees that the quantity of type b biomass sent from the harvest site i and the storage center j to the biorefinery k is equal to the biomass type b processed in the biorefinery k:(21)∑j=1JYjkbtB+1−θZkb,t−1B+∑i=1IYikbtW=Wkbt+ZkbtB,∀k∈K,b∈B,t∈T.Equation (22) guarantees that the amount of bioethanol sent from the biorefinery k to the mixing plant m is equal to the amount of bioethanol available in the biorefinery k in the period t:(22)∑b=1BλbWkbt+Zk,t−1E=∑m=1MYkmtE+ZktE,∀k∈K,t∈T.Equation (23) guarantees that the amount of biofuel sent from the mixing plant m to customers n is equal to the amount of bioethanol available in the mixing plant m in the period t:(23)∑k=1KYkmtE+Zm,t−1M+YmtRP=∑n=1NYmntM+ZmtM,∀m∈M,t∈T.Equation (24) guarantees that the amount of biofuel sent from the mixing plants m to the customers n is equal to the demand of each customer n, for each period t:(24)∑m=1MYmntM=Dnt,∀n∈N,t∈T.Equation (25) ensures that the quantity of biomass type b sent from harvest sites i to storage centers j does not exceed the capacity of storage centers j:(25)∑i=1I∑b=1BYijbtS+∑b=1BZjb,t−1W≤SjWXjW,∀j∈J,t∈T.Equation (26) guarantees that the quantity of type b biomass sent from the storage centers j and the harvest sites i to the biorefinery k does not exceed the production capacity of the biorefinery k:(26)∑j=1J∑b=1BYjkbtB+∑b=1BZkb,t−1B+∑i=1I∑b=1BYikbtW≤SkPXkP,∀k∈K,t∈T.Equation (27) guarantees that the quantity of bioethanol sent from biorefinery k, plus the amount of fossil fuel that reaches the mixing plants m, does not exceed the mixing capacity of the mixing plant m, in period t:(27)∑k=1KYkmtE+Zm,t−1M+YmtRP≤SmMXmM,∀m∈M,t∈T.Equation (28) guarantees that the biomass type b in the biorefineries k does not exceed the capacity of the biorefineries k to store biomass for each period t:(28)∑b=1BZkbtB≤SkB,∀k∈K,t∈T.Equation (29) guarantees that the amount of bioethanol stored in the biorefineries k does not exceed the amount of bioethanol produced by the biorefineries k, for each period t:(29)ZktE≤SkPρ,∀k∈K,t∈T.Equation (30) guarantees that the quantity of biofuel stored in the mixing plants m does not exceed its mixing capacity, for each period t:(30)ZmM≤SmM,∀m∈M,t∈T.Equation (31) guarantees that the mixture of bioethanol with fossil fuel is according to the value of ψ:(31)∑k=1KYkmtE+Zm,t−1M1−ψψ=YmtRP,∀m∈M,t∈T.Equation (32) guarantees the opening of at least one storage centerj:(32)∑j=1JXjW≥1.Equation (33) guarantees the opening of the biorefineries k that are indicated in parameter nb:(33)∑k=1KXkP≤nb.Equation (34) guarantees the opening of the mixing plants m that are indicated in the nm parameter:(34)∑m=1MXmM≤nm.The following expressions are domain restrictions of decision variables:(35)ZjbtW,ZktE,ZmM,ZkbtB,ZibtS≥0,∀i∈I,j∈J,k∈k,b∈B,m∈M,t∈T,YijbtS,YikbtW,YjkbtB,YkmtE,YmntM≥0,∀i∈I,j∈J,k∈k,b∈B,m∈M,n∈N,t∈T,YmtRP,wkbt,ϕibt≥0,∀i∈I,k∈k,b∈B,m∈M,n∈N,t∈T,XjW,XkP,XmM∈0,1,∀j∈J,k∈K,m∈M.


## 3.1. Application of MILP

An outstanding approach in the generation and evaluation of a large number of alternatives in the design process of an SC is based on the MILP [36]. Several models have been presented so far to optimize the economic and environmental performance of the SC’s biofuel simultaneously. Zhuang and Chang [51] propose a model of mixed-integer programming (MIP) to determine a combination of products for a production process; this study is based on a cost accounting system of time-based activities. Sharifzadeh et al. [52] use an MILP to determine the optimum design and operation of the network of a supply chain under uncertainty, specifically for making systematic and centralized production decisions and distributed and mobile biofuels. Shabani and Sowlati [53] present a nonlinear mixed integer programming approach (MINLP), whose objective is to maximize the value of the supply chain for the generation of electricity from forest biomass, improving profits from the optimal solution; the model developed is a mixed-integer nonlinear programming (MINLP). Lee et al. [34] in their work develop an optimization model using MILP for the design and analysis of bioethanol production and supply strategies from lignocellulosic biomass. Venkat and Shastri [33] develop an MILP model for the conceptual design of a lignocellulosic biorefinery and its supply chain to produce ethanol from agricultural waste in the Indian context.The proposed approach in this paper is presented as an MILP, considering the framework formulated in this section and using a previously proposed mathematical model [32]. For the problem posed, the indices, parameters, and decision variables are presented in detail, as well as the objective function and restrictions of the model.


## 3.2. Models Parameters

### 3.2.1. Sets

B denotes biomass types
I denotes harvest sites
J denotes storage centers
K denotes biorefineries in a particular location
M denotes mixed plants
N denotes customers
T denotes periods


### 3.2.2. Amortization of Facilities

α
j($/year) is the annual cost of construction amortization and operation of the warehousej∈J
β
k($/year) is the annual amortization of construction and operation of the biorefinery k∈K
γ
m($/year) is the annual amortization of construction and operation of the mixing plant m∈M


### 3.2.3. Harvest Costs

δ
i
b
t($/ha) is the cost of sowing and growing biomass b∈B at the harvest site i∈I, in the time t∈T
η
i
b
t($/ha) is the cost of harvesting the biomass b∈B at the harvest site i∈I, in the time t∈T


### 3.2.4. Holding Costs

H
i
b
S($/t) is the cost of holding biomass type b∈B per ton at the harvest site i∈I
H
j
b
W($/t) is the cost of holding biomass type b∈B per ton in the warehouse j∈J
H
k
b
B($/t) is the cost of holding biomass type b∈B per ton in the biorefinery k∈K
H
k
E($/L) is the cost of holding bioethanol per litre in the biorefinery k∈K
H
m
M($/L) is the cost of holding biofuel per litre in the mixing plant m∈M


### 3.2.5. Transport Costs

a
i
j($/t) is the cost of transporting a biomass ton from the harvest site i∈I to the warehouse j∈J
b
i
k($/t) is the cost of transporting a biomass ton from the harvest site i∈I to the biorefinery k∈K
c
j
k($/t) is the cost of transporting a biomass ton from the warehouse j∈J to the biorefinery k∈K
d
k
m($/L) is the cost of transporting a bioethanol litre from the biorefinery k∈K to the mixing plant m∈M
e
m
n($/L) is the cost of transporting a biofuel litre from the plant m∈M to the customer n∈N.


### 3.2.6. Capacities

S
j
W(t) is the storage capacity of the warehouse j∈J
S
k
P(L) is the bioethanol production capacity per year of the biorefinery k∈K
S
k
B(t) is the capacity to store biomass per year of the biorefinery k∈K
S
m
M(L) is mixing capacity per year of the mixing plant m∈M


### 3.2.7. The Opening of Facilities

n
b is the maximum number of biorefineries that can be opened
n
m is the maximum number of mixing plants that can be opened


### 3.2.8. Other Costs

μ
t($/L) is the cost per litre of fuel in the period t∈T
ω
k
b($/t) is the cost of processing a biomass ton, type b∈B in the biorefinery k∈K


### 3.2.9. Other Parameters

L
i
b
t is the number of hectares of land at the harvest site i∈I for biomass typeb∈B, in the time t∈T
P
i
b
t is the proportion of land available at the harvest site i∈I with biomass type b∈B, in the time t∈T
R
i
b
t(t/ha) is the yield of biomass type b∈B at the harvest site i∈I in the time t∈T
θ(%) is the percentage of deterioration of stored biomass
λ
b(L/t) is the conversion ratio of biomass type b∈B
D
n
t(L) is the customer’s fuel demand n∈N in the period t∈T
ψ is the percentage in which the mixture of bioethanol with fossil fuel is required
ρ is the percentage destined to store biomass in biorefinery k∈K


## 3.2.1. Sets

B denotes biomass types
I denotes harvest sites
J denotes storage centers
K denotes biorefineries in a particular location
M denotes mixed plants
N denotes customers
T denotes periods


## 3.2.2. Amortization of Facilities

α
j($/year) is the annual cost of construction amortization and operation of the warehousej∈J
β
k($/year) is the annual amortization of construction and operation of the biorefinery k∈K
γ
m($/year) is the annual amortization of construction and operation of the mixing plant m∈M


## 3.2.3. Harvest Costs

δ
i
b
t($/ha) is the cost of sowing and growing biomass b∈B at the harvest site i∈I, in the time t∈T
η
i
b
t($/ha) is the cost of harvesting the biomass b∈B at the harvest site i∈I, in the time t∈T


## 3.2.4. Holding Costs

H
i
b
S($/t) is the cost of holding biomass type b∈B per ton at the harvest site i∈I
H
j
b
W($/t) is the cost of holding biomass type b∈B per ton in the warehouse j∈J
H
k
b
B($/t) is the cost of holding biomass type b∈B per ton in the biorefinery k∈K
H
k
E($/L) is the cost of holding bioethanol per litre in the biorefinery k∈K
H
m
M($/L) is the cost of holding biofuel per litre in the mixing plant m∈M


## 3.2.5. Transport Costs

a
i
j($/t) is the cost of transporting a biomass ton from the harvest site i∈I to the warehouse j∈J
b
i
k($/t) is the cost of transporting a biomass ton from the harvest site i∈I to the biorefinery k∈K
c
j
k($/t) is the cost of transporting a biomass ton from the warehouse j∈J to the biorefinery k∈K
d
k
m($/L) is the cost of transporting a bioethanol litre from the biorefinery k∈K to the mixing plant m∈M
e
m
n($/L) is the cost of transporting a biofuel litre from the plant m∈M to the customer n∈N.


## 3.2.6. Capacities

S
j
W(t) is the storage capacity of the warehouse j∈J
S
k
P(L) is the bioethanol production capacity per year of the biorefinery k∈K
S
k
B(t) is the capacity to store biomass per year of the biorefinery k∈K
S
m
M(L) is mixing capacity per year of the mixing plant m∈M


## 3.2.7. The Opening of Facilities

n
b is the maximum number of biorefineries that can be opened
n
m is the maximum number of mixing plants that can be opened


## 3.2.8. Other Costs

μ
t($/L) is the cost per litre of fuel in the period t∈T
ω
k
b($/t) is the cost of processing a biomass ton, type b∈B in the biorefinery k∈K


## 3.2.9. Other Parameters

L
i
b
t is the number of hectares of land at the harvest site i∈I for biomass typeb∈B, in the time t∈T
P
i
b
t is the proportion of land available at the harvest site i∈I with biomass type b∈B, in the time t∈T
R
i
b
t(t/ha) is the yield of biomass type b∈B at the harvest site i∈I in the time t∈T
θ(%) is the percentage of deterioration of stored biomass
λ
b(L/t) is the conversion ratio of biomass type b∈B
D
n
t(L) is the customer’s fuel demand n∈N in the period t∈T
ψ is the percentage in which the mixture of bioethanol with fossil fuel is required
ρ is the percentage destined to store biomass in biorefinery k∈K


## 3.3. Decision Variables

### 3.3.1. Binary Decision Variables

X
j
W is a binary variable equal to 1, if the warehouse j∈J is open, 0 otherwise
X
k
P is a binary variable equal to 1, if the biorefinery k∈K is open, 0 otherwise
X
m
M is a binary variable equal to 1, if the mixing plant m∈M is open, 0 otherwise


### 3.3.2. Decision Variables for Holding

Z
i
b
t
S is the amount of biomass type b∈B stored on the site i∈I in the time t∈T
Z
j
b
t
W is the amount of biomass type b∈B stored on the warehouse j∈J in the time t∈T
Z
k
b
t
B is the amount of biomass type b∈B stored in the biorefinery k∈K in the time t∈T
Z
k
t
E is the amount of bioethanol stored in the biorefinery k∈K in the time t∈T
Z
m
t
M is the amount of biofuel stored in the mixing plant m∈M in the time t∈T


### 3.3.3. Decision Variables for Sent Quantities

Y
i
j
b
t
S is the amount of biomass type b∈B sent from the site i∈I to the warehouse j∈J in the time t∈T
Y
i
k
b
t
W is the amount of biomass type b∈B sent from the site i∈I to biorefinery k∈K in the time t∈T
Y
j
k
b
t
B is the amount of biomass type b∈B sent from the site j∈J to biorefinery k∈K in the time t∈T
Y
k
m
t
E is the amount of bioethanol sent from biorefinery k∈K to the mixing plant m∈M in the time t∈T
Y
m
n
t
M is the amount of biofuel sent from the mixing plant m∈M to the customer n∈N in the time t∈T


### 3.3.4. Other Decision Variables

Y
m
t
R
P is the amount of fossil fuel required in the mixing plant m∈M in the time t∈T
W
k
b
t is the amount of biomass type b∈B processed in the biorefinery k∈K in the time t∈T
ϕ
i
b
t is the amount of biomass type b∈B produced on the harvest site i∈I in the time t∈T


## 3.3.1. Binary Decision Variables

X
j
W is a binary variable equal to 1, if the warehouse j∈J is open, 0 otherwise
X
k
P is a binary variable equal to 1, if the biorefinery k∈K is open, 0 otherwise
X
m
M is a binary variable equal to 1, if the mixing plant m∈M is open, 0 otherwise


## 3.3.2. Decision Variables for Holding

Z
i
b
t
S is the amount of biomass type b∈B stored on the site i∈I in the time t∈T
Z
j
b
t
W is the amount of biomass type b∈B stored on the warehouse j∈J in the time t∈T
Z
k
b
t
B is the amount of biomass type b∈B stored in the biorefinery k∈K in the time t∈T
Z
k
t
E is the amount of bioethanol stored in the biorefinery k∈K in the time t∈T
Z
m
t
M is the amount of biofuel stored in the mixing plant m∈M in the time t∈T


## 3.3.3. Decision Variables for Sent Quantities

Y
i
j
b
t
S is the amount of biomass type b∈B sent from the site i∈I to the warehouse j∈J in the time t∈T
Y
i
k
b
t
W is the amount of biomass type b∈B sent from the site i∈I to biorefinery k∈K in the time t∈T
Y
j
k
b
t
B is the amount of biomass type b∈B sent from the site j∈J to biorefinery k∈K in the time t∈T
Y
k
m
t
E is the amount of bioethanol sent from biorefinery k∈K to the mixing plant m∈M in the time t∈T
Y
m
n
t
M is the amount of biofuel sent from the mixing plant m∈M to the customer n∈N in the time t∈T


## 3.3.4. Other Decision Variables

Y
m
t
R
P is the amount of fossil fuel required in the mixing plant m∈M in the time t∈T
W
k
b
t is the amount of biomass type b∈B processed in the biorefinery k∈K in the time t∈T
ϕ
i
b
t is the amount of biomass type b∈B produced on the harvest site i∈I in the time t∈T


## 3.4. Objectives and Objective Function

In the harvest sites (I), the agricultural biomass of corn and barley is generated, and square bales do the collection method. These are sent to the storage centers (J) or directly to the biorefineries (K) in each period T. Once the conversion process is completed, the bioethanol is sent from the biorefineries to the mixing plants (M), where it will be combined with fossil fuel to be sent to the customers (N) finally.In order to minimize the costs of the SC in the MILP model, the decisions that are optimized are the (1) selection of sites of harvest sites (i); (2) selection of storage centers (j), which have a predetermined location; (3) selection of biorefineries (k), which have a predetermined location and capacity; (4) flow of biomass material to storage centers and biorefineries; (5) volume of bioethanol during period (t); (6) flow of bioethanol to mixing plants (m); (6) flow of biofuel from mixing plants to customers (n) during period (t).The objective of the proposed model is minimizing the total annual cost of Bio-Eth SC. The cost of the Bio-Eth SC includes the cost of annual amortization of the number of distribution centers, biorefineries, and mixing plants that will be opened, cost of storage of bioethanol in biorefineries and mixing plants, and the cost of storage of biomass in distribution centers and biorefineries. In the same way, the cost of transporting biomass from the harvest sites to distribution centers and biorefineries and from distribution centers to biorefineries is modeled, as is the cost of transporting bioethanol from biorefineries to mixing plants, the cost of transporting biofuel from mixing plants to customers, and the cost of transporting fossil fuel to the mixing plant. Finally, the cost of processing per unit of biomass and cost of sowing, cultivation, and harvesting for the production of biomass are taken into account. The different components of the objective function are explained as follows.The annual amortization cost of the distribution centers can be defined as(1)∑j=1JαjXjW.The cost of annual amortization of biorefineries is(2)∑k=1KβkXkP.The annual amortization cost of the mixing plants that are opened is defined as(3)∑m=1MγmXmM.The cost of storing bioethanol in biorefineries is calculated as(4)∑t=1T∑k=1KHkEZktE.The cost of holding bioethanol in the mixing plant is(5)∑t=1T∑m=1MHmMZmtM.The cost of holding a unit of biomass at the harvest site is expressed as follows:(6)∑t=1T∑b=1B∑i=1IHibSZibtS.The cost of holding units in a storage center is defined as(7)∑t=1T∑b=1B∑j=1JHjbWZjbtW.The cost of maintaining units in biorefineryk of biomass type b can be computed as(8)∑t=1T∑b=1B∑k=1KHkbBZkbtB.The cost of transporting biomass from the harvest sitei to the storage center j is(9)∑t=1T∑b=1B∑i=1I∑j=1JaijYijbtS.The cost of transporting biomass from the harvest sitei to the biorefinery k is described by(10)∑t=1T∑b=1B∑i=1I∑k=1KbikYikbtW.The cost of transporting biomass from a storage center to the biorefinery is derived as(11)∑t=1T∑b=1B∑j=1J∑k=1KcjkYjkbtB.Calculating the cost of transporting bioethanol from biorefinery to the mixing plant is given by the relation(12)∑t=1T∑k=1K∑m=1MdkmYkmtE.The cost of transporting biofuel from the mixing plant to then customers is shown in (13)∑t=1T∑m=1M∑n=1NemnYmntM.The cost of fossil fuel delivered to the mixing plant is determined as(14)∑t=1T∑m=1MμtYmtRP.The cost of processing biomass to generate bioethanol is computed as(15)∑t=1T∑k=1K∑b=1BωkbWkbt.Growing and harvesting biomass at each harvest site are calculated to determine the costs of sowing:(16)∑t=1T∑i=1I∑b=1Bδibt+ηibtϕibt.The fitness functionO to be minimized is the next and considers all the above cost elements:(17)minΩ=∑j=1JαjXjW+∑k=1KβkXkP+∑m=1MγjXmM+∑t=1T∑k=1KHkEZktE+∑t=1T∑m=1MHmMZmtM+∑t=1T∑b=1B∑i=1IHibSZibtS+∑t=1T∑b=1B∑j=1JHjbSZjbtS+∑t=1T∑b=1B∑k=1KHkbSZkbtS+∑t=1T∑b=1B∑i=1I∑j=1JaijYijbtS+∑t=1T∑b=1B∑i=1I∑k=1KbikYikbtW+∑t=1T∑b=1B∑j=1J∑k=1KcjkYkkbtB+∑t=1T∑k=1K∑m=1MdkmYkmtE+∑t=1T∑m=1M∑n=1NemnYmntM+∑t=1T∑m=1MμtYmtRP+∑t=1T∑k=1K∑b=1BωkmWkbt+∑t=1T∑i=1I∑b=1Bδibt+ηibtϕibt.


## 3.5. Constraints

Equation (18) guarantees that the total amount of type b biomass at harvest site i in period t depends on the number of hectares of biomass collected and the yield of production:(18)ϕibt≤RibtPibtLibt,∀i∈I,b∈B,t∈T.Equation (19) guarantees that the shipment of type b biomass from harvest site i to storage center j and biorefinery k at time t is equal to the amount of type b biomass available at harvest site i:(19)∑j=1JYijbtS+ZibtS+∑k=1KYikbtW=ϕibt+1−θZib,t−1S,∀i∈I,b∈B,t∈T.Equation (20) guarantees that the shipment of biomass type b from storage center j to biorefinery k is equal to the amount of type b biomass available in storage center j in each period t:(20)∑i=1IYijbtS+1−θZjb,t−1W=∑k=1KYjkbtB+ZjbtW,∀j∈J,b∈B,t∈T.Equation (21) guarantees that the quantity of type b biomass sent from the harvest site i and the storage center j to the biorefinery k is equal to the biomass type b processed in the biorefinery k:(21)∑j=1JYjkbtB+1−θZkb,t−1B+∑i=1IYikbtW=Wkbt+ZkbtB,∀k∈K,b∈B,t∈T.Equation (22) guarantees that the amount of bioethanol sent from the biorefinery k to the mixing plant m is equal to the amount of bioethanol available in the biorefinery k in the period t:(22)∑b=1BλbWkbt+Zk,t−1E=∑m=1MYkmtE+ZktE,∀k∈K,t∈T.Equation (23) guarantees that the amount of biofuel sent from the mixing plant m to customers n is equal to the amount of bioethanol available in the mixing plant m in the period t:(23)∑k=1KYkmtE+Zm,t−1M+YmtRP=∑n=1NYmntM+ZmtM,∀m∈M,t∈T.Equation (24) guarantees that the amount of biofuel sent from the mixing plants m to the customers n is equal to the demand of each customer n, for each period t:(24)∑m=1MYmntM=Dnt,∀n∈N,t∈T.Equation (25) ensures that the quantity of biomass type b sent from harvest sites i to storage centers j does not exceed the capacity of storage centers j:(25)∑i=1I∑b=1BYijbtS+∑b=1BZjb,t−1W≤SjWXjW,∀j∈J,t∈T.Equation (26) guarantees that the quantity of type b biomass sent from the storage centers j and the harvest sites i to the biorefinery k does not exceed the production capacity of the biorefinery k:(26)∑j=1J∑b=1BYjkbtB+∑b=1BZkb,t−1B+∑i=1I∑b=1BYikbtW≤SkPXkP,∀k∈K,t∈T.Equation (27) guarantees that the quantity of bioethanol sent from biorefinery k, plus the amount of fossil fuel that reaches the mixing plants m, does not exceed the mixing capacity of the mixing plant m, in period t:(27)∑k=1KYkmtE+Zm,t−1M+YmtRP≤SmMXmM,∀m∈M,t∈T.Equation (28) guarantees that the biomass type b in the biorefineries k does not exceed the capacity of the biorefineries k to store biomass for each period t:(28)∑b=1BZkbtB≤SkB,∀k∈K,t∈T.Equation (29) guarantees that the amount of bioethanol stored in the biorefineries k does not exceed the amount of bioethanol produced by the biorefineries k, for each period t:(29)ZktE≤SkPρ,∀k∈K,t∈T.Equation (30) guarantees that the quantity of biofuel stored in the mixing plants m does not exceed its mixing capacity, for each period t:(30)ZmM≤SmM,∀m∈M,t∈T.Equation (31) guarantees that the mixture of bioethanol with fossil fuel is according to the value of ψ:(31)∑k=1KYkmtE+Zm,t−1M1−ψψ=YmtRP,∀m∈M,t∈T.Equation (32) guarantees the opening of at least one storage centerj:(32)∑j=1JXjW≥1.Equation (33) guarantees the opening of the biorefineries k that are indicated in parameter nb:(33)∑k=1KXkP≤nb.Equation (34) guarantees the opening of the mixing plants m that are indicated in the nm parameter:(34)∑m=1MXmM≤nm.The following expressions are domain restrictions of decision variables:(35)ZjbtW,ZktE,ZmM,ZkbtB,ZibtS≥0,∀i∈I,j∈J,k∈k,b∈B,m∈M,t∈T,YijbtS,YikbtW,YjkbtB,YkmtE,YmntM≥0,∀i∈I,j∈J,k∈k,b∈B,m∈M,n∈N,t∈T,YmtRP,wkbt,ϕibt≥0,∀i∈I,k∈k,b∈B,m∈M,n∈N,t∈T,XjW,XkP,XmM∈0,1,∀j∈J,k∈K,m∈M.


## 4. Case of Study

The analysis of a case study is presented to establish the viability of the proposed approach, which considers biomass of agricultural waste of corn and barley crops in the region of the case of study.


### 4.1. Input Parameters

The relevant input parameters are as follows:(1)The modeling horizon is one year, divided into two periods (spring-summer; autumn-winter) (T=1,2)(2)It is considered that the 112 municipalities (see Figure3) that can supply the residues of corn and barley (i=1,…,112), the cropland data, and the applied yields are in [42,54](3)Locations for storage centers (j=1,…,7), biorefineries (k=1,…,3), and mixing plants (m=1,..,3) are predetermined locations to raise the economic activity in these areas (see Figure 4), of which the model should choose the best alternative(4)The considered capacities for storage centers are 110,000; 200,000; and 300,600 tons and for biorefineries 190 and 380 MLPY [55]. For the mixing plants, the capacities considered are 370 and 555 MLPY; these data are estimated from [56](5)There are considered 224 customers (n=1,…,224), which represent the same number of gasoline service stations in the study region (see Figure 5)Figure 4
Location of storage centers (red), biorefineries (green), and mixing plants (purple). Source: map made using Google Maps.Figure 5
Customer location (gasoline service stations). Source: map made using Google Maps.


### 4.2. Other Parameters

Other input parameters used in the present case are indicated in Tables1 and 2, and the geographic coordinates of the facilities and harvest sites marked in Figures 3–5 are shown in Table 3.Table 1
Input parameters,Ribt,andHibt (b = 1 corn biomass and b = 2 barley biomass).
Sitei
Municipality
Grain yieldt/h from site i for product b, for t=1,2
Yields of biomasst/h from site i for product b, for t=1,2
Hectares available for on-site cultivationi for product b at time t=1,2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
t
=
1
t
=
1
t
=
2
t
=
2
t
=
1
t
=
1
t
=
2
t
=
2
t
=
1
t
=
1
t
=
2
t
=
2
1
Acatlán, HGO
1.85
2.95
0.00
0.00
1.96
2.06
0.00
0.00
8173.00
120.00
0.00
0.00
2
Acaxochitlán, HGO
2.40
2.80
0.00
0.00
2.54
1.96
0.00
0.00
7306.00
115.00
0.00
0.00
3
Actopan, HGO
3.74
1.00
0.00
3.80
3.96
0.70
0.00
2.66
3860.00
365.00
0.00
259.00
4
Agua Blanca de Iturbide, HGO
1.60
0.00
0.00
0.00
1.69
0.00
0.00
0.00
2801.00
0.00
0.00
0.00
5
Ajacuba, HGO
4.60
3.00
0.00
3.80
4.87
2.10
0.00
2.66
6270.00
544.00
0.00
119.00
6
Almoloya, HGO
2.50
2.95
0.00
0.00
2.65
2.06
0.00
0.00
670.00
8953.00
0.00
0.00
7
Apan, HGO
2.40
1.80
0.00
0.00
2.54
1.26
0.00
0.00
800.00
22856.00
0.00
0.00
8
Atotonilco el Grande, HGO
1.99
5.20
0.00
0.00
2.10
3.64
0.00
0.00
6826.40
30.00
0.00
0.00
9
Cuautepec de Hinojosa, HGO
2.10
2.00
0.00
0.00
2.22
1.40
0.00
0.00
4717.00
10790.00
0.00
0.00
10
El Arenal, HGO
4.45
1.80
0.00
0.00
4.71
1.26
0.00
0.00
1940.00
45.00
0.00
0.00
11
Emiliano Zapata, HGO
2.20
2.15
0.00
0.00
2.33
1.50
0.00
0.00
500.00
2181.00
0.00
0.00
12
Epazoyucan, HGO
1.58
0.80
0.00
0.00
1.66
0.56
0.00
0.00
268.00
6952.00
0.00
0.00
13
Francisco I. Madero, HGO
5.43
3.00
0.00
3.80
5.75
2.10
0.00
2.66
2470.00
60.00
0.00
100.00
14
Huasca de Ocampo, HGO
1.93
1.45
0.00
0.00
2.04
1.01
0.00
0.00
6246.50
85.00
0.00
0.00
15
Huehuetla, HGO
1.00
0.00
0.80
0.00
1.06
0.00
0.84
0.00
5100.00
0.00
1730.00
0.00
16
Metepec, HGO
1.58
1.60
0.00
0.00
1.66
1.12
0.00
0.00
5070.00
2120.00
0.00
0.00
17
Metztitlán, HGO
4.08
0.00
8.00
0.00
4.31
0.00
8.48
0.00
3680.00
0.00
800.00
0.00
18
Mineral de la Reforma, HGO
2.80
2.25
0.00
4.00
2.96
1.57
0.00
2.80
385.00
2575.00
0.00
89.00
19
Mineral del Chico, HGO
2.03
1.10
0.00
0.00
2.14
0.77
0.00
0.00
1462.00
136.00
0.00
0.00
20
Mineral del Monte, HGO
0.85
1.10
0.00
0.00
0.90
0.77
0.00
0.00
370.00
66.00
0.00
0.00
21
Omitlán de Juárez, HGO
1.08
1.00
0.00
0.00
1.14
0.70
0.00
0.00
1266.00
63.00
0.00
0.00
22
Pachuca de Soto, HGO
1.80
0.90
0.00
0.00
1.90
0.63
0.00
0.00
94.75
2760.00
0.00
0.00
23
San Agustín Metzquititlán, HGO
2.78
1.80
7.50
0.00
2.94
1.26
7.95
0.00
1800.00
10.00
68.00
0.00
24
San Agustín Tlaxiaca, HGO
2.40
2.00
0.00
0.00
2.54
1.40
0.00
0.00
620.00
3964.00
0.00
0.00
25
San Bartolo Tutotepec, HGO
1.10
0.00
1.10
0.00
1.16
0.00
1.16
0.00
2215.00
0.00
1315.00
0.00
26
San Salvador, HGO
5.18
1.10
0.00
3.50
5.48
0.77
0.00
2.45
3250.00
75.00
0.00
55.00
27
Santiago de Anaya, HGO
4.93
1.10
0.00
3.50
5.22
0.77
0.00
2.45
2650.00
105.00
0.00
32.70
28
Santiago Tulantepec, HGO
2.05
2.70
0.00
0.00
2.17
1.89
0.00
0.00
2754.00
308.00
0.00
0.00
29
Singuilucan, HGO
2.60
2.90
0.00
0.00
2.75
2.03
0.00
0.00
2397.00
10809.00
0.00
0.00
30
Tenango de Doria, HGO
1.15
0.00
1.20
0.00
1.21
0.00
1.27
0.00
2759.00
0.00
800.00
0.00
31
Tepeapulco, HGO
2.85
2.25
0.00
0.00
3.02
1.57
0.00
0.00
761.00
7205.00
0.00
0.00
32
Tianguistengo, HGO
1.20
0.00
0.95
0.00
1.27
0.00
1.00
0.00
1220.00
0.00
511.00
0.00
33
Tizayuca, HGO
3.50
2.30
0.00
0.00
3.71
1.61
0.00
0.00
1220.00
1068.20
0.00
0.00
34
Tlanalapa, HGO
1.85
2.15
0.00
0.00
1.96
1.50
0.00
0.00
219.00
3340.00
0.00
0.00
35
Tolcayuca, HGO
2.43
0.90
0.00
0.00
2.57
0.63
0.00
0.00
106.00
2905.00
0.00
0.00
36
Tulancingo de Bravo, HGO
2.50
1.80
0.00
0.00
2.65
1.26
0.00
0.00
5120.00
210.00
0.00
0.00
37
Villa de Tezontepec, HGO
2.95
1.50
0.00
0.00
3.12
1.05
0.00
0.00
480.00
2381.00
0.00
0.00
38
Zacualtipán de Ángeles, HGO
0.95
1.10
1.10
0.00
1.00
0.77
1.16
0.00
612.00
14.00
88.00
0.00
39
Zapotlán de Juárez, HGO
2.34
1.00
0.00
0.00
2.48
0.70
0.00
0.00
638.00
4357.00
0.00
0.00
40
Zempoala, HGO
2.00
1.00
0.00
0.00
2.12
0.70
0.00
0.00
2309.50
13668.00
0.00
0.00
41
Axapusco, MEX
2.35
1.70
0.00
0.00
2.49
1.19
0.00
0.00
1320.00
9740.00
0.00
0.00
42
Hueypoxtla, MEX
2.93
1.70
0.00
0.00
3.10
1.19
0.00
0.00
6426.00
4200.00
0.00
0.00
43
Nopaltepec, MEX
1.30
1.80
0.00
0.00
1.37
1.26
0.00
0.00
404.00
3381.00
0.00
0.00
44
Otumba, MEX
2.67
2.00
0.00
0.00
2.82
1.40
0.00
0.00
990.00
4235.00
0.00
0.00
45
San Martín de las Pirámides, MEX
2.63
2.25
0.00
0.00
2.78
1.57
0.00
0.00
618.39
16.00
0.00
0.00
46
Tecámac, MEX
3.63
1.30
0.00
0.00
3.84
0.91
0.00
0.00
3971.00
2791.00
0.00
0.00
47
Temascalapa, MEX
1.28
1.85
0.00
0.00
1.35
1.29
0.00
0.00
1452.00
10361.00
0.00
0.00
48
Teotihuacán, MEX
3.27
2.18
0.00
0.00
3.46
1.52
0.00
0.00
1995.00
59.00
0.00
0.00
49
Tepetlaoxtoc, MEX
2.85
1.80
0.00
0.00
3.02
1.26
0.00
0.00
969.00
1303.50
0.00
0.00
50
Zumpango, MEX
3.80
1.70
0.00
0.00
4.02
1.19
0.00
0.00
10015.00
2382.00
0.00
0.00
51
Ahuacatlán, PUE
0.85
0.00
0.00
0.00
0.90
0.00
0.00
0.00
976.00
0.00
0.00
0.00
52
Ahuazotepec, PUE
1.40
0.00
0.00
1.10
1.48
0.00
0.00
0.77
1240.00
0.00
0.00
169.70
53
Amixtlán, PUE
0.87
0.00
1.08
0.00
0.91
0.00
1.14
0.00
372.00
0.00
223.00
0.00
54
Aquixtla, PUE
1.67
1.90
0.00
0.00
1.76
1.33
0.00
0.00
4336.49
20.00
9.49
0.00
55
Camocuautla, PUE
0.97
0.00
2.10
0.00
1.03
0.00
2.22
0.00
325.00
0.00
75.00
0.00
56
Chiconcuautla, PUE
1.00
0.00
1.50
0.00
1.06
0.00
1.59
0.00
857.00
0.00
149.80
0.00
57
Chignahuapan, PUE
2.01
2.10
0.00
0.00
2.12
1.47
0.00
0.00
12865.00
6800.00
0.00
0.00
58
Coatepec, PUE
0.88
0.00
1.06
0.00
0.93
0.00
1.12
0.00
200.00
0.00
68.00
0.00
59
Cuautempan, PUE
0.84
0.00
0.00
0.00
0.88
0.00
0.00
0.00
1197.00
0.00
0.00
0.00
60
Hermenegildo Galeana, PUE
1.00
0.00
1.70
0.00
1.06
0.00
1.80
0.00
360.30
0.00
80.00
0.00
61
Honey, PUE
1.90
0.00
1.70
0.00
2.01
0.00
1.80
0.00
2981.40
0.00
535.00
0.00
62
Huauchinango, PUE
1.35
0.00
1.90
0.00
1.43
0.00
2.01
0.00
2136.50
0.00
213.80
0.00
63
Hueytlalpan, PUE
0.70
0.00
1.15
0.00
0.74
0.00
1.21
0.00
480.00
0.00
435.00
0.00
64
Huitzilan de Serdán, PUE
0.70
0.00
1.00
0.00
0.74
0.00
1.06
0.00
660.00
0.00
310.00
0.00
65
Ixtacamaxtitlán, PUE
1.97
1.70
0.00
0.00
2.09
1.19
0.00
0.00
11840.00
565.00
0.00
0.00
66
Jalpan, PUE
1.40
0.00
1.80
0.00
1.48
0.00
1.90
0.00
515.00
0.00
348.00
0.00
67
Jopala, PUE
0.90
0.00
1.80
0.00
0.95
0.00
1.90
0.00
1411.00
0.00
265.00
0.00
68
Juan Galindo, PUE
0.80
0.00
1.70
0.00
0.84
0.00
1.80
0.00
35.00
0.00
51.00
0.00
69
Naupan, PUE
0.80
0.00
1.70
0.00
0.84
0.00
1.80
0.00
680.70
0.00
67.30
0.00
70
Olintla, PUE
0.65
0.00
1.00
0.00
0.68
0.00
1.06
0.00
750.00
0.00
670.00
0.00
71
Pahuatlán, PUE
0.80
0.00
1.60
0.00
0.84
0.00
1.69
0.00
341.00
0.00
70.30
0.00
72
Pantepec, PUE
1.00
0.00
1.80
0.00
1.06
0.00
1.90
0.00
1215.00
0.00
982.07
0.00
73
San Felipe Tepatlán, PUE
0.90
0.00
1.70
0.00
0.95
0.00
1.80
0.00
258.00
0.00
60.00
0.00
74
Tepango de Rodríguez, PUE
1.02
0.00
1.15
0.00
1.07
0.00
1.21
0.00
194.00
0.00
20.50
0.00
75
Tepetzintla, PUE
0.81
0.00
0.00
0.00
0.86
0.00
0.00
0.00
960.00
0.00
0.00
0.00
76
Tetela de Ocampo, PUE
1.96
0.00
0.00
0.00
2.07
0.00
0.00
0.00
3288.00
0.00
0.00
0.00
77
Tlacuilotepec, PUE
0.80
0.00
1.70
0.00
0.84
0.00
1.80
0.00
731.30
0.00
312.00
0.00
78
Tlaola, PUE
0.80
0.00
1.50
0.00
0.84
0.00
1.59
0.00
767.00
0.00
380.20
0.00
79
Tlapacoya, PUE
0.90
0.00
1.80
0.00
0.95
0.00
1.90
0.00
452.60
0.00
204.50
0.00
80
Tlaxco, PUE
0.80
0.00
1.80
0.00
0.84
0.00
1.90
0.00
446.00
0.00
148.30
0.00
81
Xicotepec, PUE
0.90
0.00
1.90
0.00
0.95
0.00
2.01
0.00
1083.00
0.00
279.30
0.00
82
Xochitlán, PUE
0.71
0.00
1.40
0.00
0.75
0.00
1.48
0.00
720.00
0.00
350.00
0.00
83
Zacatlán, PUE
1.55
1.80
0.00
0.00
1.63
1.26
0.00
0.00
11244.50
0.00
0.50
0.00
84
Zapotitlán de Méndez, PUE
0.88
0.00
2.40
0.00
0.93
0.00
2.54
0.00
500.00
0.00
44.00
0.00
85
Zihuateutla, PUE
0.80
0.00
1.80
0.00
0.84
0.00
1.90
0.00
1106.70
0.00
112.70
0.00
86
Zongozotla, PUE
0.75
0.00
1.00
0.00
0.79
0.00
1.06
0.00
400.00
0.00
130.00
0.00
87
Atlangatepec, TLAX
2.53
2.60
0.00
0.00
2.67
1.82
0.00
0.00
2025.00
2091.00
0.00
0.00
88
Benito Juárez, TLAX
2.48
2.10
0.00
0.00
2.62
1.47
0.00
0.00
530.00
1601.00
0.00
0.00
89
Calpulalpan, TLAX
2.48
2.10
0.00
0.00
2.62
1.47
0.00
0.00
1335.00
9655.00
0.00
0.00
90
Emiliano Zapata, TLAX
2.90
2.30
0.00
0.00
3.07
1.61
0.00
0.00
910.00
30.00
0.00
0.00
91
Españita, TLAX
2.53
2.10
0.00
0.00
2.67
1.47
0.00
0.00
666.00
4537.00
0.00
0.00
92
Hueyotlipan, TLAX
2.45
2.40
0.00
0.00
2.59
1.68
0.00
0.00
1235.00
4989.00
0.00
0.00
93
Lázaro Cárdenas, TLAX
4.50
2.30
0.00
0.00
4.77
1.61
0.00
0.00
542.00
119.00
0.00
0.00
94
Muñoz de Domingo Arenas, TLAX
2.76
2.50
0.00
0.00
2.92
1.75
0.00
0.00
605.00
1110.00
0.00
0.00
95
Nanacamilpa, TLAX
2.65
2.10
0.00
0.00
2.80
1.47
0.00
0.00
590.00
5059.00
0.00
0.00
96
San Lucas Tecopilco, TLAX
2.85
3.60
0.00
0.00
3.02
2.52
0.00
0.00
1436.00
718.00
0.00
0.00
97
Sanctórum, TLAX
2.65
2.10
0.00
0.00
2.80
1.47
0.00
0.00
400.00
2764.00
0.00
0.00
98
Tetla de la Solidaridad, TLAX
2.80
2.50
0.00
0.00
2.96
1.75
0.00
0.00
460.00
6101.00
0.00
0.00
99
Tlaxco, TLAX
2.58
2.20
0.00
0.00
2.72
1.54
0.00
0.00
4396.00
14264.00
0.00
0.00
100
Xaltocan, TLAX
2.95
3.60
0.00
0.00
3.12
2.52
0.00
0.00
3814.00
1120.00
0.00
0.00
101
Benito Juárez, VER
0.75
0.00
0.90
0.00
0.79
0.00
0.95
0.00
5200.00
0.00
4450.00
0.00
102
Coahuitlán, VER
1.82
0.00
1.60
0.00
1.92
0.00
1.69
0.00
1100.00
0.00
1070.00
0.00
103
Coyutla, VER
1.79
0.00
1.80
0.00
1.89
0.00
1.90
0.00
2750.00
0.00
2650.00
0.00
104
Filomeno Mata, VER
1.45
0.00
1.40
0.00
1.53
0.00
1.48
0.00
350.00
0.00
330.00
0.00
105
Huayacocotla, VER
1.40
0.95
1.20
1.10
1.48
0.66
1.27
0.77
4200.00
255.00
80.00
88.00
106
Ilamatlán, VER
1.20
0.00
1.20
0.00
1.27
0.00
1.27
0.00
2200.00
0.00
900.00
0.00
107
Ixhuatlán de Madero, VER
1.44
0.00
1.20
0.00
1.52
0.00
1.27
0.00
7050.00
0.00
5950.00
0.00
108
Mecatlán, VER
1.45
0.00
1.40
0.00
1.53
0.00
1.48
0.00
800.00
0.00
750.00
0.00
109
Texcatepec, VER
1.00
0.00
1.20
0.00
1.06
0.00
1.27
0.00
2200.00
0.00
700.00
0.00
110
Tlachichilco, VER
1.36
0.00
1.00
0.00
1.44
0.00
1.06
0.00
2720.00
0.00
1075.00
0.00
111
Zacualpan, VER
1.30
0.00
1.20
0.00
1.37
0.00
1.27
0.00
1000.00
0.00
215.00
0.00
112
Zontecomatlán, VER
1.20
0.00
1.20
0.00
1.27
0.00
1.27
0.00
4000.00
0.00
990.00
0.00Table 2
Other input parameters.
Source
Entry parameters
Value
[55]
Cost of annual amortization of construction and operation of storage centers ($/year)
α
j = [281,250; 156,250; 406,250; 156,250; 156,250; 156,250; 156,250]
[55]
Amount of annual amortization of construction and operation of the biorefinery ($/year)
β
k  = [2,437,500; 4,500,000; 2,437,500]
[56]
Cost of annual amortization of the construction and operation of the mixing plant ($/year)
γ
m = [2,191,304.34; 3,286,956.52; 2,191,304.34]
[54, 57]
Cost of planting and cultivation of biomass ($/ha)
δ
i
b
t = [238.42, 131.57] (for all b,i) and t=1δibt = [288.94, 164.47] (for all b,i) and t=2
[54, 57]
Cost of harvested biomass ($/ha)
η
i
b
t = [63.15, 31.57] (for all b,i) and t=1
η
i
b
t = [78.94, 41.05] (for all b,i) and t=2
[19, 58]
Cost of holding biomass units at harvest sites ($/t)
S
h
i
b = 6.3 (for all b,i)
[19, 58]
Cost of holding biomass units in storage centers ($/t)
A
h
j
b = 4.3 (for allb,j)
[19, 58]
Cost of holding biomass units in biorefineries ($/t)
B
h
k
b = 4.3 (for all b,k)
Assumed
Cost of holding bioethanol units in the biorefinery ($/L)
B
H
k = 0.015 (for all k)
Assumed
Cost of holding units of bioethanol in mixing plants ($/L)
M
h
m = 0.015 (for all m)
[55]
Cost of transporting a biomass unit from the harvest site to storage centers ($/t)
a
i
j = 3.85 + 0.085 ∗ distanceij (for all i,j)
[55]
Cost of transporting a biomass unit from the harvest site to biorefineries ($/t)
b
i
k = 3.85 + 0.085 ∗ distanceik (for all i.k)
[55]
Cost of transporting biomass unit storage centers to biorefineries ($/t)
c
j
k = 3.85 + 0.085 ∗ distancejk (for all j,k)
[55]
Cost of transporting a bioethanol unit from biorefineries to mixing plants ($/L × km)
d
k
m = 0.000028 (for all k,m)
[55]
Cost of transporting a bioethanol unit from mixing plants to customers ($/L × km)
e
m
n = 0.000028 (for all m,n)
[2, 55]
Storage capacity of storage centers (t)
SA
j = [110000, 200000, 300600]
[55]
Bioethanol production capacity of biorefineries (L)
SB
k = [190, 380, 190] MLPY
Assumed
Capacity to store biomass per year in biorefineries (t)
SBB
k = [0, 0, 0] (for all k)
[56]
Capacity of the mixing plants (L)
SM
m = [370000000,555000000,370000000] (for all m)
Assumed
Number of biorefineries that can be opened
n
b = 3, (for all t)
Assumed
Number of mixing plants that can be opened
n
m = 3, (for all t)
[59]
Cost per unit of fuel in the period ($/L)
μ
t = 1.00 (for all t)
[2]
The processing cost of a biomass unit ($/t)
ω
k
b = 48.86 (for all b,k)
Assumed
The proportion of land available at the harvest site
P
i
b
t = 1.00 (for all i,b,t)
[58, 60]
Reason for deterioration of stored biomass
θ
% = 0.01 (/t)
[2, 55]
Biomass conversion ratio (L/t)
λ
b = [208.93, 274.9] for all t
[55]
Demand
D
n
t is the demand that follows a normal distribution with a standard deviation of 15% of the mean
Assumed
Percentage destined to store biomass in a biorefinery
ρ = 0.26 (for all j)Table 3
Geographical coordinates.
Harvest sites (i)
Customers (n)
1
Acatlán, HGO
20.1404043, −98.4450531
48
6262620-13
19.82661012, −98.9775187
2
Acaxochitlán, HGO
20.1520077, −98.1909943
49
6263159-13
19.83591093, −98.98033248
3
Actopan, HGO
20.2987486, −98.9782333
50
1598437-13
20.07419562, −98.35160175
4
Agua Blanca de Iturbide, HGO
20.3394764, −98.3568192
51
6262645-13
20.12329479, −98.73474466
5
Ajacuba, HGO
20.0959165, −99.119339
52
6740313-13
20.04649645, −98.79130317
6
Almoloya, HGO
19.709829, −98.406601
53
1621660-13
20.11721674, −98.78123335
7
Apan, HGO
19.7040111, −98.4399033
54
6335388-13
20.26118942, −98.94301898
8
Atotonilco el Grande, HGO
20.2850629, −98.6824608
55
1621474-13
20.1242314, −98.775894
9
Cuautepec de Hinojosa, HGO
20.0235164, −98.3107281
56
1621095-13
20.12485259, −98.75948145
10
El Arenal, HGO
20.2201604, −98.9181519
57
1617639-13
20.12630144, −98.74515474
11
Emiliano Zapata, HGO
19.6674831, −98.5477066
58
1534402-13
20.0960579, −98.36573475
12
Epazoyucan, HGO
20.0207745, −98.6423779
59
6205904-13
20.07958387, −98.38479625
13
Francisco I. Madero, HGO
20.2312746, −99.1032028
60
1600012-13
20.09195465, −98.75451949
14
Huasca de Ocampo, HGO
20.2040916, −98.5725117
61
1539674-13
20.06446449, −98.36362082
15
Huehuetla, HGO
20.4554836, −98.0729771
62
1554609-13
20.0684327, −98.36396313
16
Metepec, HGO
20.2477835, −98.312273
63
1599977-13
20.09458374, −98.76079014
17
Metztitlán, HGO
20.5921342, −98.7703514
64
6740993-13
19.97945331, −98.51887974
18
Mineral de la Reforma, HGO
20.0406116, −98.7353325
65
1608382-13
20.24632181, −99.09955346
19
Mineral del Chico, HGO
20.2134753, −98.7344742
66
6262729-13
20.28812662, −98.67235631
20
Mineral del Monte, HGO
20.1323459, −98.6602306
67
1608392-13
20.24287894, −99.08429399
21
Omitlán de Juárez, HGO
20.1724325, −98.6513042
68
1599140-13
20.037941, −98.31412473
22
Pachuca de Soto, HGO
20.077215, −98.7566185
69
1569036-13
20.05524019, −98.78057667
23
San Agustín Metzquititlán, HGO
20.5296116, −98.6427212
70
1535971-13
20.10715881, −98.74712817
24
San Agustín Tlaxiaca, HGO
20.1226752, −98.8809013
71
1539895-13
20.07733171, −98.37286078
25
San Bartolo Tutotepec, HGO
20.3929053, −98.1869602
72
1522614-13
20.08003779, −98.74534313
26
San Salvador, HGO
20.2840163, −99.0279293
73
1526786-13
20.1586768, −98.20283419
27
Santiago de Anaya, HGO
20.3781015, −98.9691353
74
1524903-13
20.34212311, −98.35927666
28
Santiago Tulantepec de Lugo Guerrero, HGO
20.0438369, −98.3662605
75
1521604-13
20.09596989, −98.71567676
29
Singuilucan, HGO
19.969154, −98.5313988
76
1598897-13
20.07360652, −98.35076155
30
Tenango de Doria, HGO
20.3341848, −98.2233524
77
1595031-13
20.11110651, −98.72523034
31
Tepeapulco, HGO
19.7975156, −98.5589504
78
6335903-13
20.27999636, −98.96093552
32
Tianguistengo, HGO
20.723284, −98.6386013
79
1620940-13
20.03455212, −98.79921647
33
Tizayuca, HGO
19.8884631, −98.9345455
80
6335945-13
19.8339404, −98.94186277
34
Tlanalapa, HGO
19.8313091, −98.5988617
81
6335902-13
20.2856335, −99.01319879
35
Tolcayuca, HGO
19.952293, −98.9093113
82
1555860-13
20.01385899, −98.6385266
36
Tulancingo de Bravo, HGO
20.0986571, −98.4009361
83
6762186-13
19.66603204, −98.55074321
37
Villa de Tezontepec, HGO
19.8965341, −98.8326645
84
1538923-13
20.10591305, −98.75064516
38
Zacualtipán de Ángeles, HGO
20.6435475, −98.642292
85
6262726-13
20.03290592, −98.30909565
39
Zapotlán de Juárez, HGO
19.9717354, −98.8762665
86
6263199-13
20.06539773, −98.34350094
40
Zempoala, HGO
19.9207444, −98.6840057
87
1555405-13
20.0328635, −98.30902557
41
Axapusco, MEX
19.7351988, −98.7664032
88
1521678-13
20.08542351, −98.7193632
42
Hueypoxtla, MEX
19.9013764, −99.0860367
89
6735744-13
20.3746293, −99.05216038
43
Nopaltepec, MEX
19.7837458, −98.7245178
90
1596483-13
20.10452107, −98.74505785
44
Otumba, MEX
19.7091826, −98.7348175
91
1597383-13
20.09837895, −98.7613604
45
San Martín de las Pirámides, MEX
19.7069201, −98.8124084
92
6336069-13
19.83060211, −98.97878862
46
Tecámac, MEX
19.730513, −98.9758301
93
6336067-13
20.09833665, −98.76131585
47
Temascalapa, MEX
19.8170981, −98.8851929
94
6335919-13
20.21798028, −98.91084482
48
Teotihuacán, MEX
19.6594005, −98.8419342
95
6335882-13
19.77797253, −98.5807555
49
Tepetlaoxtoc, MEX
19.5722448, −98.8036537
96
6709345-13
20.08941813, −98.34905726
50
Zumpango, MEX
19.7822113, −99.0850067
97
1602424-13
19.78370454, −98.57802137
51
Ahuacatlán, PUE
20.0077903, −97.8598595
98
1614387-13
19.7035096, −98.46552883
52
Ahuazotepec, PUE
20.0403697, −98.1574345
99
6262785-13
20.08400245, −98.72474423
53
Amixtlán, PUE
20.051658, −97.7990055
100
1580536-13
19.80990315, −98.59875873
54
Aquixtla, PUE
19.7986866, −97.93612
101
6434004-13
20.1405897, −98.69136054
55
Camocuautla, PUE
20.0360961, −97.7580643
102
6262651-13
20.10395531, −98.76725522
56
Chiconcuautla, PUE
20.085639, −97.9413986
103
6263077-13
20.11468896, −98.76232766
57
Chignahuapan, PUE
19.8149987, −98.0056
104
1536452-13
19.97331851, −98.52315017
58
Coatepec, PUE
20.0561731, −97.7322292
105
6262609-13
20.0946648, −98.36282552
59
Cuautempan, PUE
19.9108993, −97.7914524
106
6263141-13
20.09469545, −98.36277611
60
Hermenegildo Galeana, PUE
20.1154218, −97.7491379
107
6741127-13
20.34702497, −99.03073337
61
Honey, PUE
20.2421465, −98.2128167
108
6335877-13
19.91021142, −98.67579737
62
Huauchinango, PUE
20.1864906, −98.048172
109
6336081-13
20.08969037, −98.7715266
63
Hueytlalpan, PUE
20.0250486, −97.7016735
110
6335909-13
19.75428933, −98.588776
64
Huitzilan de Serdán, PUE
19.9690733, −97.6893139
111
6434025-13
20.10238345, −98.71881908
65
Ixtacamaxtitlán, PUE
19.6214879, −97.8187466
112
6263013-13
20.06923509, −98.36501259
66
Jalpan, PUE
20.4750844, −97.9430079
113
1539450-13
20.10114731, −98.74675649
67
Jopala, PUE
20.1675582, −97.6928329
114
6335912-13
19.78847457, −98.55422289
68
Juan Galindo, PUE
20.2059039, −98.0024242
115
1536575-13
19.9731704, −98.52329416
69
Naupan, PUE
20.2340531, −98.1076097
116
1616878-13
20.1174499, −98.89376353
70
Olintla, PUE
20.1091352, −97.6866531
117
1571974-13
20.09383484, −99.12531276
71
Pahuatlán, PUE
20.2785417, −98.1446457
118
1556421-13
20.06768121, −98.41469264
72
Pantepec, PUE
20.5216538, −97.9353046
119
6262701-13
20.65042693, −98.64842803
73
San Felipe Tepatlán, PUE
20.0892362, −97.7964735
120
6205976-13
19.84031009, −98.97275088
74
Tepango de Rodríguez, PUE
20.0028705, −97.7874613
121
6335360-13
20.1100385, −98.75335167
75
Tepetzintla, PUE
19.9646162, −97.8445172
122
1620830-13
20.04193946, −98.79443138
76
Tetela de Ocampo, PUE
19.8114457, −97.8171158
123
1607307-13
20.27346352, −98.9503825
77
Tlacuilotepec, PUE
20.3274443, −98.0664539
124
E00684-13
20.120477, −98.740764
78
Tlaola, PUE
20.1335547, −97.9192543
125
E00719-13
19.984757, −98.62337
79
Tlapacoya, PUE
20.1190485, −97.8497314
126
E00723-13
19.788618, −98.55419
80
Tlaxco, PUE
20.4193312, −98.0314136
127
E03499-13
20.148356, −98.440038
81
Xicotepec, PUE
20.2628413, −97.9676628
128
E04488-13
20.135759, −98.88477
82
Xochitlán de Vicente Suárez, PUE
19.9625389, −97.6282883
129
E04911-13
20.147214, −98.294567
83
Zacatlán, PUE
19.9289751, −97.9427719
130
E05105-13
20.101092, −98.747201
84
Zapotitlán de Méndez, PUE
19.9989588, −97.7088833
131
E05712-13
19.989644, −98.706489
85
Zihuateutla, PUE
20.2555541, −97.8935051
132
E07143-13
19.6689, −98.3736
86
Zongozotla, PUE
19.9726631, −97.7253628
133
E07168-13
19.879804, −98.947654
87
Atlangatepec, TLAX
19.5321276, −98.2013798
134
E07373-13
20.253956, −98.99411
88
Benito Juárez, TLAX
19.5832429, −98.4103775
135
E07425-13
20.092882, −98.762251
89
Calpulalpan, TLAX
19.585022, −98.5506248
136
E07555-13
19.834483, −98.94162
90
Emiliano Zapata, TLAX
19.5532389, −97.9195118
137
E07857-13
20.0002, −98.3003
91
Españita, TLAX
19.4551006, −98.4193897
138
E07928-13
20.0381, −98.3141
92
Hueyotlipan, TLAX
19.4686558, −98.3388805
139
E08197-13
20.28471, −98.944501
93
Lázaro Cárdenas, TLAX
19.5432094, −97.9921246
140
E08798-13
20.085281, −98.718168
94
Muñoz de Domingo Arenas, TLAX
19.4747654, −98.2139111
141
E08812-13
20.07401, −98.35171
95
Nanacamilpa de Mariano Arista, TLAX
19.4862556, −98.5553455
142
E09581-13
20.010591, −98.821619
96
San Lucas Tecopilco, TLAX
19.4870648, −98.2511616
143
E09784-13
19.850734, −98.974847
97
Sanctórum de Lázaro Cárdenas, TLAX
19.4869839, −98.4641075
144
E12016-13
20.0802139, −98.7874528
98
Tetla de la Solidaridad, TLAX
19.4615749, −98.0677414
145
2197248-15
19.70193184, −98.75508293
99
Tlaxco, TLAX
19.6306234, −98.1286812
146
2014301-15
19.86693441, −99.04652651
100
Xaltocan, TLAX
19.4285129, −98.2227945
147
6346818-15
19.72031508, −98.97158131
101
Benito Juárez, VER
20.8727669, −98.1990623
148
2197269-15
19.79278912, −99.0755245
102
Coahuitlán, VER
20.2572451, −97.7290964
149
2197251-15
19.68797719, −98.98854169
103
Coyutla, VER
20.2521319, −97.6707745
150
6207947-15
19.9653928, −99.0418919
104
Filomeno Mata, VER
20.205622, −97.709012
151
6207948-15
19.91509476, −99.07476651
105
Huayacocotla, VER
20.5440793, −98.4877968
152
2197255-15
19.56755307, −98.81903485
106
Ilamatlán, VER
20.7772208, −98.4431648
153
2197252-15
19.74904928, −98.94827453
107
Ixhuatlán de Madero, VER
20.6904469, −98.0195045
154
2197253-15
19.68168016, −98.97692368
108
Mecatlán, VER
20.2060248, −97.6806021
155
2197254-15
19.65975096, −99.00496648
109
Texcatepec, VER
20.5797603, −98.360424
156
2197250-15
19.70223242, −98.76409917
110
Tlachichilco, VER
20.6238679, −98.1966805
157
2267640-15
19.66808917, −99.00412379
111
Zacualpan, VER
20.4345332, −98.3421421
158
2244535-15
19.82544515, −99.0893007
112
Zontecomatlán de López y Fuentes, VER
20.7610699, −98.3384728
159
6698477-15
19.82165512, −99.08128257
Storage centersj
160
6757467-15
19.81995999, −99.11503166
1
San Agustín Tlaxiaca
20.1275913, −98.9911079
161
6346751-15
19.80429001, −99.10600887
2
Zempoala
19.9731069, −98.701172
162
2197249-15
19.70159876, −98.75514275
3
Apan
19.6783131, −98.391838
163
2244511-15
19.81314884, −99.1096896
4
Tlaola
20.1092159, −97.8980541
164
6207949-15
19.6659576, −99.01491448
5
San Agustín Metzquititlán
20.4334477, −98.6826325
165
6727603-15
19.65450225, −99.01940473
6
Tulancingo
20.2029237, −98.3159637
166
6711512-15
19.77085433, −98.9783269
7
Zacatlán
19.9322026, −98.0739212
167
6712662-15
19.65768324, −99.01904667
Biorefineriesk
168
6348476−15
19.66849959, −99.0040818
1
Zempoala
19.89299, −98.66667
169
6207760-15
19.88531279, −98.865927
2
Santa Ana Hueytlalpan
20.15845, −98.28231
170
6705119-15
19.67291216, −99.02770086
3
Actopan
20.26992, −98.85772
171
1974519-15
19.67362317, −99.02787736
Mixing plantsm
172
6265433-15
19.68830299, −98.82640382
1
Tolacayuca
19.93496, −98.89119
173
6265464-15
19.65220143, −99.00490701
2
Sahagún
19.74763, −98.58444
174
6730375-15
19.82697719, −98.89847154
3
Tulancingo
20.14878, −98.36059
175
6348771-15
19.81263783, −99.10890691
Customersn
176
6347662-15
19.96500515, −99.04159129
1
6701141-13
20.07655101, −98.38707515
177
E08836-15
19.775684, −99.014942
2
1615495-13
19.70987382, −98.3977008
178
E10339-15
19.704131, −98.945184
3
6720392-13
20.12422462, −98.77604748
179
E10524-15
19.650044, −98.90331
4
6335409-13
20.10793091, −98.71701937
180
E12702-15
19.7073, −98.70479
5
6336448-13
20.12485355, −98.75951003
181
6380203-21
19.97722214, −98.05722221
6
6263019-13
20.05575529, −98.78654483
182
6380204-21
19.94760996, −97.96174374
7
6740451-13
20.09373122, −98.7564247
183
6377502-21
19.92502054, −97.97023985
8
6263079-13
20.10597482, −98.75783492
184
6725338-21
20.00717687, −97.85922537
9
6516088-13
20.0809349, −98.38392419
185
3278184-21
20.18189292, −98.03584042
10
1513628-13
20.6628722, −98.66316875
186
6710748-21
19.62174176, −97.81312585
11
1601800-13
19.91033841, −98.67584542
187
6377024-21
19.94185103, −97.96607548
12
6335272-13
20.26979962, −98.94978937
188
6379891-21
19.89416659, −97.97277779
13
1620330-13
20.0543211, −98.78778484
189
6448431-21
20.17338613, −98.05862044
14
6336345-13
20.07531934, −98.78202543
190
6710369-21
19.91936676, −97.96005073
15
1600594-13
20.06303633, −98.77364756
191
3417636-21
20.38523593, −97.88377247
16
6335700-13
20.07754875, −98.37119607
192
3284800-21
20.20412811, −97.98910088
17
6263097-13
20.08406802, −98.37592946
193
6379274-21
20.13753714, −98.09779566
18
6263098-13
20.05705164, −98.75920889
194
6741034-21
20.17512032, −98.06730308
19
6418291-13
20.04763493, −98.35911669
195
6271508-21
20.26676393, −97.9601726
20
1546866-13
20.27901369, −98.64926589
196
6271865-21
20.26195257, −97.96239184
21
1532906-13
20.12054938, −98.74042411
197
3502442-21
19.81856774, −97.81079527
22
1619576-13
19.95534078, −98.91790267
198
3297403-21
19.84155845, −98.03226973
23
1539469-13
19.8483681, −98.97330671
199
6378263-21
20.27395137, −97.96405384
24
1539471-13
19.88013765, −98.94654865
200
3287035-21
20.00394441, −97.80046494
25
1539473-13
19.83932874, −98.97307341
201
E00751-21
20.173404, −98.059527
26
1539476-13
19.85091693, −98.97516152
202
6311273-29
19.55175573, −98.49455764
27
1539453-13
20.07313391, −98.79250195
203
6311274-29
19.54532657, −98.49260474
28
6336611-13
20.06621245, −98.77011166
204
6459714-29
19.43025706, −98.13472193
29
6335523-13
20.11312044, −98.74341589
205
6756853-29
19.48422352, −98.11410177
30
6719681-13
20.11237991, −98.4051467
206
4168017-29
19.58633359, −98.42847233
31
6740924-13
20.07298533, −98.37668807
207
4168020-29
19.59175344, −98.56376007
32
1539449-13
20.11643541, −98.72615811
208
4168027-29
19.48210098, −98.29439608
33
6205931-13
19.88237884, −98.8220836
209
6406157-29
19.49502059, −98.53402659
34
1539479-13
20.07678617, −98.38717142
210
4165224-29
19.49905295, −98.05346502
35
1539429-13
20.28485082, −98.94467205
211
4209484-29
19.42156402, −98.21178823
36
6434169-13
20.11524358, −98.40865361
212
4202637-29
19.4757085, −98.11284982
37
6205930-13
20.09476731, −98.71836192
213
4202660-29
19.46469034, −98.1132248
38
6335577-13
20.09923999, −98.71605545
214
6421897-29
19.58582813, −98.54359179
39
1539440-13
20.06872425, −98.71708094
215
4161233-29
19.47311459, −98.20562485
40
6335571-13
20.27545886, −98.94117179
216
6406128-29
19.59257433, −98.57695318
41
1539442-13
20.08646088, −98.71297338
217
6405983-29
19.58675979, −98.54644898
42
1539465-13
19.78297162, −98.54409519
218
4207147-29
19.59273099, −98.57614489
43
1539462-13
20.28324963, −99.01676083
219
6406051-29
19.61164624, −98.11998572
44
6262874-13
20.08409757, −98.3759223
220
4168036-29
19.47516948, −98.11276603
45
1539444-13
20.0583287, −98.76038144
221
E09430-29
19.5916714, −98.563885
46
1539455-13
20.10272155, −98.74669701
222
4442880-30
20.52882643, −98.49111013
47
6205973-13
19.83658241, −98.9548442
223
4459848-30
20.5829879, −98.36571903
224
4460757-30
20.77874, −98.44443The MILP model described inSection 3 ((1)–(34)) together with the parameters indicated in this section has 1698 constraints and 7156 variables (13 binary) and was solved with the commercial solver LINGO 17, using a server with an Intel ® Xeon ® E3-1220V2@ 3.10 GHz processor, 8.00 GB in RAM, and Windows 7.0 OS; each value of ψ (mix percentage) was solved with, on average, 2091 iterations in a time of three seconds.


## 4.1. Input Parameters

The relevant input parameters are as follows:(1)The modeling horizon is one year, divided into two periods (spring-summer; autumn-winter) (T=1,2)(2)It is considered that the 112 municipalities (see Figure3) that can supply the residues of corn and barley (i=1,…,112), the cropland data, and the applied yields are in [42,54](3)Locations for storage centers (j=1,…,7), biorefineries (k=1,…,3), and mixing plants (m=1,..,3) are predetermined locations to raise the economic activity in these areas (see Figure 4), of which the model should choose the best alternative(4)The considered capacities for storage centers are 110,000; 200,000; and 300,600 tons and for biorefineries 190 and 380 MLPY [55]. For the mixing plants, the capacities considered are 370 and 555 MLPY; these data are estimated from [56](5)There are considered 224 customers (n=1,…,224), which represent the same number of gasoline service stations in the study region (see Figure 5)Figure 4
Location of storage centers (red), biorefineries (green), and mixing plants (purple). Source: map made using Google Maps.Figure 5
Customer location (gasoline service stations). Source: map made using Google Maps.


## 4.2. Other Parameters

Other input parameters used in the present case are indicated in Tables1 and 2, and the geographic coordinates of the facilities and harvest sites marked in Figures 3–5 are shown in Table 3.Table 1
Input parameters,Ribt,andHibt (b = 1 corn biomass and b = 2 barley biomass).
Sitei
Municipality
Grain yieldt/h from site i for product b, for t=1,2
Yields of biomasst/h from site i for product b, for t=1,2
Hectares available for on-site cultivationi for product b at time t=1,2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
b
=
1
b
=
2
t
=
1
t
=
1
t
=
2
t
=
2
t
=
1
t
=
1
t
=
2
t
=
2
t
=
1
t
=
1
t
=
2
t
=
2
1
Acatlán, HGO
1.85
2.95
0.00
0.00
1.96
2.06
0.00
0.00
8173.00
120.00
0.00
0.00
2
Acaxochitlán, HGO
2.40
2.80
0.00
0.00
2.54
1.96
0.00
0.00
7306.00
115.00
0.00
0.00
3
Actopan, HGO
3.74
1.00
0.00
3.80
3.96
0.70
0.00
2.66
3860.00
365.00
0.00
259.00
4
Agua Blanca de Iturbide, HGO
1.60
0.00
0.00
0.00
1.69
0.00
0.00
0.00
2801.00
0.00
0.00
0.00
5
Ajacuba, HGO
4.60
3.00
0.00
3.80
4.87
2.10
0.00
2.66
6270.00
544.00
0.00
119.00
6
Almoloya, HGO
2.50
2.95
0.00
0.00
2.65
2.06
0.00
0.00
670.00
8953.00
0.00
0.00
7
Apan, HGO
2.40
1.80
0.00
0.00
2.54
1.26
0.00
0.00
800.00
22856.00
0.00
0.00
8
Atotonilco el Grande, HGO
1.99
5.20
0.00
0.00
2.10
3.64
0.00
0.00
6826.40
30.00
0.00
0.00
9
Cuautepec de Hinojosa, HGO
2.10
2.00
0.00
0.00
2.22
1.40
0.00
0.00
4717.00
10790.00
0.00
0.00
10
El Arenal, HGO
4.45
1.80
0.00
0.00
4.71
1.26
0.00
0.00
1940.00
45.00
0.00
0.00
11
Emiliano Zapata, HGO
2.20
2.15
0.00
0.00
2.33
1.50
0.00
0.00
500.00
2181.00
0.00
0.00
12
Epazoyucan, HGO
1.58
0.80
0.00
0.00
1.66
0.56
0.00
0.00
268.00
6952.00
0.00
0.00
13
Francisco I. Madero, HGO
5.43
3.00
0.00
3.80
5.75
2.10
0.00
2.66
2470.00
60.00
0.00
100.00
14
Huasca de Ocampo, HGO
1.93
1.45
0.00
0.00
2.04
1.01
0.00
0.00
6246.50
85.00
0.00
0.00
15
Huehuetla, HGO
1.00
0.00
0.80
0.00
1.06
0.00
0.84
0.00
5100.00
0.00
1730.00
0.00
16
Metepec, HGO
1.58
1.60
0.00
0.00
1.66
1.12
0.00
0.00
5070.00
2120.00
0.00
0.00
17
Metztitlán, HGO
4.08
0.00
8.00
0.00
4.31
0.00
8.48
0.00
3680.00
0.00
800.00
0.00
18
Mineral de la Reforma, HGO
2.80
2.25
0.00
4.00
2.96
1.57
0.00
2.80
385.00
2575.00
0.00
89.00
19
Mineral del Chico, HGO
2.03
1.10
0.00
0.00
2.14
0.77
0.00
0.00
1462.00
136.00
0.00
0.00
20
Mineral del Monte, HGO
0.85
1.10
0.00
0.00
0.90
0.77
0.00
0.00
370.00
66.00
0.00
0.00
21
Omitlán de Juárez, HGO
1.08
1.00
0.00
0.00
1.14
0.70
0.00
0.00
1266.00
63.00
0.00
0.00
22
Pachuca de Soto, HGO
1.80
0.90
0.00
0.00
1.90
0.63
0.00
0.00
94.75
2760.00
0.00
0.00
23
San Agustín Metzquititlán, HGO
2.78
1.80
7.50
0.00
2.94
1.26
7.95
0.00
1800.00
10.00
68.00
0.00
24
San Agustín Tlaxiaca, HGO
2.40
2.00
0.00
0.00
2.54
1.40
0.00
0.00
620.00
3964.00
0.00
0.00
25
San Bartolo Tutotepec, HGO
1.10
0.00
1.10
0.00
1.16
0.00
1.16
0.00
2215.00
0.00
1315.00
0.00
26
San Salvador, HGO
5.18
1.10
0.00
3.50
5.48
0.77
0.00
2.45
3250.00
75.00
0.00
55.00
27
Santiago de Anaya, HGO
4.93
1.10
0.00
3.50
5.22
0.77
0.00
2.45
2650.00
105.00
0.00
32.70
28
Santiago Tulantepec, HGO
2.05
2.70
0.00
0.00
2.17
1.89
0.00
0.00
2754.00
308.00
0.00
0.00
29
Singuilucan, HGO
2.60
2.90
0.00
0.00
2.75
2.03
0.00
0.00
2397.00
10809.00
0.00
0.00
30
Tenango de Doria, HGO
1.15
0.00
1.20
0.00
1.21
0.00
1.27
0.00
2759.00
0.00
800.00
0.00
31
Tepeapulco, HGO
2.85
2.25
0.00
0.00
3.02
1.57
0.00
0.00
761.00
7205.00
0.00
0.00
32
Tianguistengo, HGO
1.20
0.00
0.95
0.00
1.27
0.00
1.00
0.00
1220.00
0.00
511.00
0.00
33
Tizayuca, HGO
3.50
2.30
0.00
0.00
3.71
1.61
0.00
0.00
1220.00
1068.20
0.00
0.00
34
Tlanalapa, HGO
1.85
2.15
0.00
0.00
1.96
1.50
0.00
0.00
219.00
3340.00
0.00
0.00
35
Tolcayuca, HGO
2.43
0.90
0.00
0.00
2.57
0.63
0.00
0.00
106.00
2905.00
0.00
0.00
36
Tulancingo de Bravo, HGO
2.50
1.80
0.00
0.00
2.65
1.26
0.00
0.00
5120.00
210.00
0.00
0.00
37
Villa de Tezontepec, HGO
2.95
1.50
0.00
0.00
3.12
1.05
0.00
0.00
480.00
2381.00
0.00
0.00
38
Zacualtipán de Ángeles, HGO
0.95
1.10
1.10
0.00
1.00
0.77
1.16
0.00
612.00
14.00
88.00
0.00
39
Zapotlán de Juárez, HGO
2.34
1.00
0.00
0.00
2.48
0.70
0.00
0.00
638.00
4357.00
0.00
0.00
40
Zempoala, HGO
2.00
1.00
0.00
0.00
2.12
0.70
0.00
0.00
2309.50
13668.00
0.00
0.00
41
Axapusco, MEX
2.35
1.70
0.00
0.00
2.49
1.19
0.00
0.00
1320.00
9740.00
0.00
0.00
42
Hueypoxtla, MEX
2.93
1.70
0.00
0.00
3.10
1.19
0.00
0.00
6426.00
4200.00
0.00
0.00
43
Nopaltepec, MEX
1.30
1.80
0.00
0.00
1.37
1.26
0.00
0.00
404.00
3381.00
0.00
0.00
44
Otumba, MEX
2.67
2.00
0.00
0.00
2.82
1.40
0.00
0.00
990.00
4235.00
0.00
0.00
45
San Martín de las Pirámides, MEX
2.63
2.25
0.00
0.00
2.78
1.57
0.00
0.00
618.39
16.00
0.00
0.00
46
Tecámac, MEX
3.63
1.30
0.00
0.00
3.84
0.91
0.00
0.00
3971.00
2791.00
0.00
0.00
47
Temascalapa, MEX
1.28
1.85
0.00
0.00
1.35
1.29
0.00
0.00
1452.00
10361.00
0.00
0.00
48
Teotihuacán, MEX
3.27
2.18
0.00
0.00
3.46
1.52
0.00
0.00
1995.00
59.00
0.00
0.00
49
Tepetlaoxtoc, MEX
2.85
1.80
0.00
0.00
3.02
1.26
0.00
0.00
969.00
1303.50
0.00
0.00
50
Zumpango, MEX
3.80
1.70
0.00
0.00
4.02
1.19
0.00
0.00
10015.00
2382.00
0.00
0.00
51
Ahuacatlán, PUE
0.85
0.00
0.00
0.00
0.90
0.00
0.00
0.00
976.00
0.00
0.00
0.00
52
Ahuazotepec, PUE
1.40
0.00
0.00
1.10
1.48
0.00
0.00
0.77
1240.00
0.00
0.00
169.70
53
Amixtlán, PUE
0.87
0.00
1.08
0.00
0.91
0.00
1.14
0.00
372.00
0.00
223.00
0.00
54
Aquixtla, PUE
1.67
1.90
0.00
0.00
1.76
1.33
0.00
0.00
4336.49
20.00
9.49
0.00
55
Camocuautla, PUE
0.97
0.00
2.10
0.00
1.03
0.00
2.22
0.00
325.00
0.00
75.00
0.00
56
Chiconcuautla, PUE
1.00
0.00
1.50
0.00
1.06
0.00
1.59
0.00
857.00
0.00
149.80
0.00
57
Chignahuapan, PUE
2.01
2.10
0.00
0.00
2.12
1.47
0.00
0.00
12865.00
6800.00
0.00
0.00
58
Coatepec, PUE
0.88
0.00
1.06
0.00
0.93
0.00
1.12
0.00
200.00
0.00
68.00
0.00
59
Cuautempan, PUE
0.84
0.00
0.00
0.00
0.88
0.00
0.00
0.00
1197.00
0.00
0.00
0.00
60
Hermenegildo Galeana, PUE
1.00
0.00
1.70
0.00
1.06
0.00
1.80
0.00
360.30
0.00
80.00
0.00
61
Honey, PUE
1.90
0.00
1.70
0.00
2.01
0.00
1.80
0.00
2981.40
0.00
535.00
0.00
62
Huauchinango, PUE
1.35
0.00
1.90
0.00
1.43
0.00
2.01
0.00
2136.50
0.00
213.80
0.00
63
Hueytlalpan, PUE
0.70
0.00
1.15
0.00
0.74
0.00
1.21
0.00
480.00
0.00
435.00
0.00
64
Huitzilan de Serdán, PUE
0.70
0.00
1.00
0.00
0.74
0.00
1.06
0.00
660.00
0.00
310.00
0.00
65
Ixtacamaxtitlán, PUE
1.97
1.70
0.00
0.00
2.09
1.19
0.00
0.00
11840.00
565.00
0.00
0.00
66
Jalpan, PUE
1.40
0.00
1.80
0.00
1.48
0.00
1.90
0.00
515.00
0.00
348.00
0.00
67
Jopala, PUE
0.90
0.00
1.80
0.00
0.95
0.00
1.90
0.00
1411.00
0.00
265.00
0.00
68
Juan Galindo, PUE
0.80
0.00
1.70
0.00
0.84
0.00
1.80
0.00
35.00
0.00
51.00
0.00
69
Naupan, PUE
0.80
0.00
1.70
0.00
0.84
0.00
1.80
0.00
680.70
0.00
67.30
0.00
70
Olintla, PUE
0.65
0.00
1.00
0.00
0.68
0.00
1.06
0.00
750.00
0.00
670.00
0.00
71
Pahuatlán, PUE
0.80
0.00
1.60
0.00
0.84
0.00
1.69
0.00
341.00
0.00
70.30
0.00
72
Pantepec, PUE
1.00
0.00
1.80
0.00
1.06
0.00
1.90
0.00
1215.00
0.00
982.07
0.00
73
San Felipe Tepatlán, PUE
0.90
0.00
1.70
0.00
0.95
0.00
1.80
0.00
258.00
0.00
60.00
0.00
74
Tepango de Rodríguez, PUE
1.02
0.00
1.15
0.00
1.07
0.00
1.21
0.00
194.00
0.00
20.50
0.00
75
Tepetzintla, PUE
0.81
0.00
0.00
0.00
0.86
0.00
0.00
0.00
960.00
0.00
0.00
0.00
76
Tetela de Ocampo, PUE
1.96
0.00
0.00
0.00
2.07
0.00
0.00
0.00
3288.00
0.00
0.00
0.00
77
Tlacuilotepec, PUE
0.80
0.00
1.70
0.00
0.84
0.00
1.80
0.00
731.30
0.00
312.00
0.00
78
Tlaola, PUE
0.80
0.00
1.50
0.00
0.84
0.00
1.59
0.00
767.00
0.00
380.20
0.00
79
Tlapacoya, PUE
0.90
0.00
1.80
0.00
0.95
0.00
1.90
0.00
452.60
0.00
204.50
0.00
80
Tlaxco, PUE
0.80
0.00
1.80
0.00
0.84
0.00
1.90
0.00
446.00
0.00
148.30
0.00
81
Xicotepec, PUE
0.90
0.00
1.90
0.00
0.95
0.00
2.01
0.00
1083.00
0.00
279.30
0.00
82
Xochitlán, PUE
0.71
0.00
1.40
0.00
0.75
0.00
1.48
0.00
720.00
0.00
350.00
0.00
83
Zacatlán, PUE
1.55
1.80
0.00
0.00
1.63
1.26
0.00
0.00
11244.50
0.00
0.50
0.00
84
Zapotitlán de Méndez, PUE
0.88
0.00
2.40
0.00
0.93
0.00
2.54
0.00
500.00
0.00
44.00
0.00
85
Zihuateutla, PUE
0.80
0.00
1.80
0.00
0.84
0.00
1.90
0.00
1106.70
0.00
112.70
0.00
86
Zongozotla, PUE
0.75
0.00
1.00
0.00
0.79
0.00
1.06
0.00
400.00
0.00
130.00
0.00
87
Atlangatepec, TLAX
2.53
2.60
0.00
0.00
2.67
1.82
0.00
0.00
2025.00
2091.00
0.00
0.00
88
Benito Juárez, TLAX
2.48
2.10
0.00
0.00
2.62
1.47
0.00
0.00
530.00
1601.00
0.00
0.00
89
Calpulalpan, TLAX
2.48
2.10
0.00
0.00
2.62
1.47
0.00
0.00
1335.00
9655.00
0.00
0.00
90
Emiliano Zapata, TLAX
2.90
2.30
0.00
0.00
3.07
1.61
0.00
0.00
910.00
30.00
0.00
0.00
91
Españita, TLAX
2.53
2.10
0.00
0.00
2.67
1.47
0.00
0.00
666.00
4537.00
0.00
0.00
92
Hueyotlipan, TLAX
2.45
2.40
0.00
0.00
2.59
1.68
0.00
0.00
1235.00
4989.00
0.00
0.00
93
Lázaro Cárdenas, TLAX
4.50
2.30
0.00
0.00
4.77
1.61
0.00
0.00
542.00
119.00
0.00
0.00
94
Muñoz de Domingo Arenas, TLAX
2.76
2.50
0.00
0.00
2.92
1.75
0.00
0.00
605.00
1110.00
0.00
0.00
95
Nanacamilpa, TLAX
2.65
2.10
0.00
0.00
2.80
1.47
0.00
0.00
590.00
5059.00
0.00
0.00
96
San Lucas Tecopilco, TLAX
2.85
3.60
0.00
0.00
3.02
2.52
0.00
0.00
1436.00
718.00
0.00
0.00
97
Sanctórum, TLAX
2.65
2.10
0.00
0.00
2.80
1.47
0.00
0.00
400.00
2764.00
0.00
0.00
98
Tetla de la Solidaridad, TLAX
2.80
2.50
0.00
0.00
2.96
1.75
0.00
0.00
460.00
6101.00
0.00
0.00
99
Tlaxco, TLAX
2.58
2.20
0.00
0.00
2.72
1.54
0.00
0.00
4396.00
14264.00
0.00
0.00
100
Xaltocan, TLAX
2.95
3.60
0.00
0.00
3.12
2.52
0.00
0.00
3814.00
1120.00
0.00
0.00
101
Benito Juárez, VER
0.75
0.00
0.90
0.00
0.79
0.00
0.95
0.00
5200.00
0.00
4450.00
0.00
102
Coahuitlán, VER
1.82
0.00
1.60
0.00
1.92
0.00
1.69
0.00
1100.00
0.00
1070.00
0.00
103
Coyutla, VER
1.79
0.00
1.80
0.00
1.89
0.00
1.90
0.00
2750.00
0.00
2650.00
0.00
104
Filomeno Mata, VER
1.45
0.00
1.40
0.00
1.53
0.00
1.48
0.00
350.00
0.00
330.00
0.00
105
Huayacocotla, VER
1.40
0.95
1.20
1.10
1.48
0.66
1.27
0.77
4200.00
255.00
80.00
88.00
106
Ilamatlán, VER
1.20
0.00
1.20
0.00
1.27
0.00
1.27
0.00
2200.00
0.00
900.00
0.00
107
Ixhuatlán de Madero, VER
1.44
0.00
1.20
0.00
1.52
0.00
1.27
0.00
7050.00
0.00
5950.00
0.00
108
Mecatlán, VER
1.45
0.00
1.40
0.00
1.53
0.00
1.48
0.00
800.00
0.00
750.00
0.00
109
Texcatepec, VER
1.00
0.00
1.20
0.00
1.06
0.00
1.27
0.00
2200.00
0.00
700.00
0.00
110
Tlachichilco, VER
1.36
0.00
1.00
0.00
1.44
0.00
1.06
0.00
2720.00
0.00
1075.00
0.00
111
Zacualpan, VER
1.30
0.00
1.20
0.00
1.37
0.00
1.27
0.00
1000.00
0.00
215.00
0.00
112
Zontecomatlán, VER
1.20
0.00
1.20
0.00
1.27
0.00
1.27
0.00
4000.00
0.00
990.00
0.00Table 2
Other input parameters.
Source
Entry parameters
Value
[55]
Cost of annual amortization of construction and operation of storage centers ($/year)
α
j = [281,250; 156,250; 406,250; 156,250; 156,250; 156,250; 156,250]
[55]
Amount of annual amortization of construction and operation of the biorefinery ($/year)
β
k  = [2,437,500; 4,500,000; 2,437,500]
[56]
Cost of annual amortization of the construction and operation of the mixing plant ($/year)
γ
m = [2,191,304.34; 3,286,956.52; 2,191,304.34]
[54, 57]
Cost of planting and cultivation of biomass ($/ha)
δ
i
b
t = [238.42, 131.57] (for all b,i) and t=1δibt = [288.94, 164.47] (for all b,i) and t=2
[54, 57]
Cost of harvested biomass ($/ha)
η
i
b
t = [63.15, 31.57] (for all b,i) and t=1
η
i
b
t = [78.94, 41.05] (for all b,i) and t=2
[19, 58]
Cost of holding biomass units at harvest sites ($/t)
S
h
i
b = 6.3 (for all b,i)
[19, 58]
Cost of holding biomass units in storage centers ($/t)
A
h
j
b = 4.3 (for allb,j)
[19, 58]
Cost of holding biomass units in biorefineries ($/t)
B
h
k
b = 4.3 (for all b,k)
Assumed
Cost of holding bioethanol units in the biorefinery ($/L)
B
H
k = 0.015 (for all k)
Assumed
Cost of holding units of bioethanol in mixing plants ($/L)
M
h
m = 0.015 (for all m)
[55]
Cost of transporting a biomass unit from the harvest site to storage centers ($/t)
a
i
j = 3.85 + 0.085 ∗ distanceij (for all i,j)
[55]
Cost of transporting a biomass unit from the harvest site to biorefineries ($/t)
b
i
k = 3.85 + 0.085 ∗ distanceik (for all i.k)
[55]
Cost of transporting biomass unit storage centers to biorefineries ($/t)
c
j
k = 3.85 + 0.085 ∗ distancejk (for all j,k)
[55]
Cost of transporting a bioethanol unit from biorefineries to mixing plants ($/L × km)
d
k
m = 0.000028 (for all k,m)
[55]
Cost of transporting a bioethanol unit from mixing plants to customers ($/L × km)
e
m
n = 0.000028 (for all m,n)
[2, 55]
Storage capacity of storage centers (t)
SA
j = [110000, 200000, 300600]
[55]
Bioethanol production capacity of biorefineries (L)
SB
k = [190, 380, 190] MLPY
Assumed
Capacity to store biomass per year in biorefineries (t)
SBB
k = [0, 0, 0] (for all k)
[56]
Capacity of the mixing plants (L)
SM
m = [370000000,555000000,370000000] (for all m)
Assumed
Number of biorefineries that can be opened
n
b = 3, (for all t)
Assumed
Number of mixing plants that can be opened
n
m = 3, (for all t)
[59]
Cost per unit of fuel in the period ($/L)
μ
t = 1.00 (for all t)
[2]
The processing cost of a biomass unit ($/t)
ω
k
b = 48.86 (for all b,k)
Assumed
The proportion of land available at the harvest site
P
i
b
t = 1.00 (for all i,b,t)
[58, 60]
Reason for deterioration of stored biomass
θ
% = 0.01 (/t)
[2, 55]
Biomass conversion ratio (L/t)
λ
b = [208.93, 274.9] for all t
[55]
Demand
D
n
t is the demand that follows a normal distribution with a standard deviation of 15% of the mean
Assumed
Percentage destined to store biomass in a biorefinery
ρ = 0.26 (for all j)Table 3
Geographical coordinates.
Harvest sites (i)
Customers (n)
1
Acatlán, HGO
20.1404043, −98.4450531
48
6262620-13
19.82661012, −98.9775187
2
Acaxochitlán, HGO
20.1520077, −98.1909943
49
6263159-13
19.83591093, −98.98033248
3
Actopan, HGO
20.2987486, −98.9782333
50
1598437-13
20.07419562, −98.35160175
4
Agua Blanca de Iturbide, HGO
20.3394764, −98.3568192
51
6262645-13
20.12329479, −98.73474466
5
Ajacuba, HGO
20.0959165, −99.119339
52
6740313-13
20.04649645, −98.79130317
6
Almoloya, HGO
19.709829, −98.406601
53
1621660-13
20.11721674, −98.78123335
7
Apan, HGO
19.7040111, −98.4399033
54
6335388-13
20.26118942, −98.94301898
8
Atotonilco el Grande, HGO
20.2850629, −98.6824608
55
1621474-13
20.1242314, −98.775894
9
Cuautepec de Hinojosa, HGO
20.0235164, −98.3107281
56
1621095-13
20.12485259, −98.75948145
10
El Arenal, HGO
20.2201604, −98.9181519
57
1617639-13
20.12630144, −98.74515474
11
Emiliano Zapata, HGO
19.6674831, −98.5477066
58
1534402-13
20.0960579, −98.36573475
12
Epazoyucan, HGO
20.0207745, −98.6423779
59
6205904-13
20.07958387, −98.38479625
13
Francisco I. Madero, HGO
20.2312746, −99.1032028
60
1600012-13
20.09195465, −98.75451949
14
Huasca de Ocampo, HGO
20.2040916, −98.5725117
61
1539674-13
20.06446449, −98.36362082
15
Huehuetla, HGO
20.4554836, −98.0729771
62
1554609-13
20.0684327, −98.36396313
16
Metepec, HGO
20.2477835, −98.312273
63
1599977-13
20.09458374, −98.76079014
17
Metztitlán, HGO
20.5921342, −98.7703514
64
6740993-13
19.97945331, −98.51887974
18
Mineral de la Reforma, HGO
20.0406116, −98.7353325
65
1608382-13
20.24632181, −99.09955346
19
Mineral del Chico, HGO
20.2134753, −98.7344742
66
6262729-13
20.28812662, −98.67235631
20
Mineral del Monte, HGO
20.1323459, −98.6602306
67
1608392-13
20.24287894, −99.08429399
21
Omitlán de Juárez, HGO
20.1724325, −98.6513042
68
1599140-13
20.037941, −98.31412473
22
Pachuca de Soto, HGO
20.077215, −98.7566185
69
1569036-13
20.05524019, −98.78057667
23
San Agustín Metzquititlán, HGO
20.5296116, −98.6427212
70
1535971-13
20.10715881, −98.74712817
24
San Agustín Tlaxiaca, HGO
20.1226752, −98.8809013
71
1539895-13
20.07733171, −98.37286078
25
San Bartolo Tutotepec, HGO
20.3929053, −98.1869602
72
1522614-13
20.08003779, −98.74534313
26
San Salvador, HGO
20.2840163, −99.0279293
73
1526786-13
20.1586768, −98.20283419
27
Santiago de Anaya, HGO
20.3781015, −98.9691353
74
1524903-13
20.34212311, −98.35927666
28
Santiago Tulantepec de Lugo Guerrero, HGO
20.0438369, −98.3662605
75
1521604-13
20.09596989, −98.71567676
29
Singuilucan, HGO
19.969154, −98.5313988
76
1598897-13
20.07360652, −98.35076155
30
Tenango de Doria, HGO
20.3341848, −98.2233524
77
1595031-13
20.11110651, −98.72523034
31
Tepeapulco, HGO
19.7975156, −98.5589504
78
6335903-13
20.27999636, −98.96093552
32
Tianguistengo, HGO
20.723284, −98.6386013
79
1620940-13
20.03455212, −98.79921647
33
Tizayuca, HGO
19.8884631, −98.9345455
80
6335945-13
19.8339404, −98.94186277
34
Tlanalapa, HGO
19.8313091, −98.5988617
81
6335902-13
20.2856335, −99.01319879
35
Tolcayuca, HGO
19.952293, −98.9093113
82
1555860-13
20.01385899, −98.6385266
36
Tulancingo de Bravo, HGO
20.0986571, −98.4009361
83
6762186-13
19.66603204, −98.55074321
37
Villa de Tezontepec, HGO
19.8965341, −98.8326645
84
1538923-13
20.10591305, −98.75064516
38
Zacualtipán de Ángeles, HGO
20.6435475, −98.642292
85
6262726-13
20.03290592, −98.30909565
39
Zapotlán de Juárez, HGO
19.9717354, −98.8762665
86
6263199-13
20.06539773, −98.34350094
40
Zempoala, HGO
19.9207444, −98.6840057
87
1555405-13
20.0328635, −98.30902557
41
Axapusco, MEX
19.7351988, −98.7664032
88
1521678-13
20.08542351, −98.7193632
42
Hueypoxtla, MEX
19.9013764, −99.0860367
89
6735744-13
20.3746293, −99.05216038
43
Nopaltepec, MEX
19.7837458, −98.7245178
90
1596483-13
20.10452107, −98.74505785
44
Otumba, MEX
19.7091826, −98.7348175
91
1597383-13
20.09837895, −98.7613604
45
San Martín de las Pirámides, MEX
19.7069201, −98.8124084
92
6336069-13
19.83060211, −98.97878862
46
Tecámac, MEX
19.730513, −98.9758301
93
6336067-13
20.09833665, −98.76131585
47
Temascalapa, MEX
19.8170981, −98.8851929
94
6335919-13
20.21798028, −98.91084482
48
Teotihuacán, MEX
19.6594005, −98.8419342
95
6335882-13
19.77797253, −98.5807555
49
Tepetlaoxtoc, MEX
19.5722448, −98.8036537
96
6709345-13
20.08941813, −98.34905726
50
Zumpango, MEX
19.7822113, −99.0850067
97
1602424-13
19.78370454, −98.57802137
51
Ahuacatlán, PUE
20.0077903, −97.8598595
98
1614387-13
19.7035096, −98.46552883
52
Ahuazotepec, PUE
20.0403697, −98.1574345
99
6262785-13
20.08400245, −98.72474423
53
Amixtlán, PUE
20.051658, −97.7990055
100
1580536-13
19.80990315, −98.59875873
54
Aquixtla, PUE
19.7986866, −97.93612
101
6434004-13
20.1405897, −98.69136054
55
Camocuautla, PUE
20.0360961, −97.7580643
102
6262651-13
20.10395531, −98.76725522
56
Chiconcuautla, PUE
20.085639, −97.9413986
103
6263077-13
20.11468896, −98.76232766
57
Chignahuapan, PUE
19.8149987, −98.0056
104
1536452-13
19.97331851, −98.52315017
58
Coatepec, PUE
20.0561731, −97.7322292
105
6262609-13
20.0946648, −98.36282552
59
Cuautempan, PUE
19.9108993, −97.7914524
106
6263141-13
20.09469545, −98.36277611
60
Hermenegildo Galeana, PUE
20.1154218, −97.7491379
107
6741127-13
20.34702497, −99.03073337
61
Honey, PUE
20.2421465, −98.2128167
108
6335877-13
19.91021142, −98.67579737
62
Huauchinango, PUE
20.1864906, −98.048172
109
6336081-13
20.08969037, −98.7715266
63
Hueytlalpan, PUE
20.0250486, −97.7016735
110
6335909-13
19.75428933, −98.588776
64
Huitzilan de Serdán, PUE
19.9690733, −97.6893139
111
6434025-13
20.10238345, −98.71881908
65
Ixtacamaxtitlán, PUE
19.6214879, −97.8187466
112
6263013-13
20.06923509, −98.36501259
66
Jalpan, PUE
20.4750844, −97.9430079
113
1539450-13
20.10114731, −98.74675649
67
Jopala, PUE
20.1675582, −97.6928329
114
6335912-13
19.78847457, −98.55422289
68
Juan Galindo, PUE
20.2059039, −98.0024242
115
1536575-13
19.9731704, −98.52329416
69
Naupan, PUE
20.2340531, −98.1076097
116
1616878-13
20.1174499, −98.89376353
70
Olintla, PUE
20.1091352, −97.6866531
117
1571974-13
20.09383484, −99.12531276
71
Pahuatlán, PUE
20.2785417, −98.1446457
118
1556421-13
20.06768121, −98.41469264
72
Pantepec, PUE
20.5216538, −97.9353046
119
6262701-13
20.65042693, −98.64842803
73
San Felipe Tepatlán, PUE
20.0892362, −97.7964735
120
6205976-13
19.84031009, −98.97275088
74
Tepango de Rodríguez, PUE
20.0028705, −97.7874613
121
6335360-13
20.1100385, −98.75335167
75
Tepetzintla, PUE
19.9646162, −97.8445172
122
1620830-13
20.04193946, −98.79443138
76
Tetela de Ocampo, PUE
19.8114457, −97.8171158
123
1607307-13
20.27346352, −98.9503825
77
Tlacuilotepec, PUE
20.3274443, −98.0664539
124
E00684-13
20.120477, −98.740764
78
Tlaola, PUE
20.1335547, −97.9192543
125
E00719-13
19.984757, −98.62337
79
Tlapacoya, PUE
20.1190485, −97.8497314
126
E00723-13
19.788618, −98.55419
80
Tlaxco, PUE
20.4193312, −98.0314136
127
E03499-13
20.148356, −98.440038
81
Xicotepec, PUE
20.2628413, −97.9676628
128
E04488-13
20.135759, −98.88477
82
Xochitlán de Vicente Suárez, PUE
19.9625389, −97.6282883
129
E04911-13
20.147214, −98.294567
83
Zacatlán, PUE
19.9289751, −97.9427719
130
E05105-13
20.101092, −98.747201
84
Zapotitlán de Méndez, PUE
19.9989588, −97.7088833
131
E05712-13
19.989644, −98.706489
85
Zihuateutla, PUE
20.2555541, −97.8935051
132
E07143-13
19.6689, −98.3736
86
Zongozotla, PUE
19.9726631, −97.7253628
133
E07168-13
19.879804, −98.947654
87
Atlangatepec, TLAX
19.5321276, −98.2013798
134
E07373-13
20.253956, −98.99411
88
Benito Juárez, TLAX
19.5832429, −98.4103775
135
E07425-13
20.092882, −98.762251
89
Calpulalpan, TLAX
19.585022, −98.5506248
136
E07555-13
19.834483, −98.94162
90
Emiliano Zapata, TLAX
19.5532389, −97.9195118
137
E07857-13
20.0002, −98.3003
91
Españita, TLAX
19.4551006, −98.4193897
138
E07928-13
20.0381, −98.3141
92
Hueyotlipan, TLAX
19.4686558, −98.3388805
139
E08197-13
20.28471, −98.944501
93
Lázaro Cárdenas, TLAX
19.5432094, −97.9921246
140
E08798-13
20.085281, −98.718168
94
Muñoz de Domingo Arenas, TLAX
19.4747654, −98.2139111
141
E08812-13
20.07401, −98.35171
95
Nanacamilpa de Mariano Arista, TLAX
19.4862556, −98.5553455
142
E09581-13
20.010591, −98.821619
96
San Lucas Tecopilco, TLAX
19.4870648, −98.2511616
143
E09784-13
19.850734, −98.974847
97
Sanctórum de Lázaro Cárdenas, TLAX
19.4869839, −98.4641075
144
E12016-13
20.0802139, −98.7874528
98
Tetla de la Solidaridad, TLAX
19.4615749, −98.0677414
145
2197248-15
19.70193184, −98.75508293
99
Tlaxco, TLAX
19.6306234, −98.1286812
146
2014301-15
19.86693441, −99.04652651
100
Xaltocan, TLAX
19.4285129, −98.2227945
147
6346818-15
19.72031508, −98.97158131
101
Benito Juárez, VER
20.8727669, −98.1990623
148
2197269-15
19.79278912, −99.0755245
102
Coahuitlán, VER
20.2572451, −97.7290964
149
2197251-15
19.68797719, −98.98854169
103
Coyutla, VER
20.2521319, −97.6707745
150
6207947-15
19.9653928, −99.0418919
104
Filomeno Mata, VER
20.205622, −97.709012
151
6207948-15
19.91509476, −99.07476651
105
Huayacocotla, VER
20.5440793, −98.4877968
152
2197255-15
19.56755307, −98.81903485
106
Ilamatlán, VER
20.7772208, −98.4431648
153
2197252-15
19.74904928, −98.94827453
107
Ixhuatlán de Madero, VER
20.6904469, −98.0195045
154
2197253-15
19.68168016, −98.97692368
108
Mecatlán, VER
20.2060248, −97.6806021
155
2197254-15
19.65975096, −99.00496648
109
Texcatepec, VER
20.5797603, −98.360424
156
2197250-15
19.70223242, −98.76409917
110
Tlachichilco, VER
20.6238679, −98.1966805
157
2267640-15
19.66808917, −99.00412379
111
Zacualpan, VER
20.4345332, −98.3421421
158
2244535-15
19.82544515, −99.0893007
112
Zontecomatlán de López y Fuentes, VER
20.7610699, −98.3384728
159
6698477-15
19.82165512, −99.08128257
Storage centersj
160
6757467-15
19.81995999, −99.11503166
1
San Agustín Tlaxiaca
20.1275913, −98.9911079
161
6346751-15
19.80429001, −99.10600887
2
Zempoala
19.9731069, −98.701172
162
2197249-15
19.70159876, −98.75514275
3
Apan
19.6783131, −98.391838
163
2244511-15
19.81314884, −99.1096896
4
Tlaola
20.1092159, −97.8980541
164
6207949-15
19.6659576, −99.01491448
5
San Agustín Metzquititlán
20.4334477, −98.6826325
165
6727603-15
19.65450225, −99.01940473
6
Tulancingo
20.2029237, −98.3159637
166
6711512-15
19.77085433, −98.9783269
7
Zacatlán
19.9322026, −98.0739212
167
6712662-15
19.65768324, −99.01904667
Biorefineriesk
168
6348476−15
19.66849959, −99.0040818
1
Zempoala
19.89299, −98.66667
169
6207760-15
19.88531279, −98.865927
2
Santa Ana Hueytlalpan
20.15845, −98.28231
170
6705119-15
19.67291216, −99.02770086
3
Actopan
20.26992, −98.85772
171
1974519-15
19.67362317, −99.02787736
Mixing plantsm
172
6265433-15
19.68830299, −98.82640382
1
Tolacayuca
19.93496, −98.89119
173
6265464-15
19.65220143, −99.00490701
2
Sahagún
19.74763, −98.58444
174
6730375-15
19.82697719, −98.89847154
3
Tulancingo
20.14878, −98.36059
175
6348771-15
19.81263783, −99.10890691
Customersn
176
6347662-15
19.96500515, −99.04159129
1
6701141-13
20.07655101, −98.38707515
177
E08836-15
19.775684, −99.014942
2
1615495-13
19.70987382, −98.3977008
178
E10339-15
19.704131, −98.945184
3
6720392-13
20.12422462, −98.77604748
179
E10524-15
19.650044, −98.90331
4
6335409-13
20.10793091, −98.71701937
180
E12702-15
19.7073, −98.70479
5
6336448-13
20.12485355, −98.75951003
181
6380203-21
19.97722214, −98.05722221
6
6263019-13
20.05575529, −98.78654483
182
6380204-21
19.94760996, −97.96174374
7
6740451-13
20.09373122, −98.7564247
183
6377502-21
19.92502054, −97.97023985
8
6263079-13
20.10597482, −98.75783492
184
6725338-21
20.00717687, −97.85922537
9
6516088-13
20.0809349, −98.38392419
185
3278184-21
20.18189292, −98.03584042
10
1513628-13
20.6628722, −98.66316875
186
6710748-21
19.62174176, −97.81312585
11
1601800-13
19.91033841, −98.67584542
187
6377024-21
19.94185103, −97.96607548
12
6335272-13
20.26979962, −98.94978937
188
6379891-21
19.89416659, −97.97277779
13
1620330-13
20.0543211, −98.78778484
189
6448431-21
20.17338613, −98.05862044
14
6336345-13
20.07531934, −98.78202543
190
6710369-21
19.91936676, −97.96005073
15
1600594-13
20.06303633, −98.77364756
191
3417636-21
20.38523593, −97.88377247
16
6335700-13
20.07754875, −98.37119607
192
3284800-21
20.20412811, −97.98910088
17
6263097-13
20.08406802, −98.37592946
193
6379274-21
20.13753714, −98.09779566
18
6263098-13
20.05705164, −98.75920889
194
6741034-21
20.17512032, −98.06730308
19
6418291-13
20.04763493, −98.35911669
195
6271508-21
20.26676393, −97.9601726
20
1546866-13
20.27901369, −98.64926589
196
6271865-21
20.26195257, −97.96239184
21
1532906-13
20.12054938, −98.74042411
197
3502442-21
19.81856774, −97.81079527
22
1619576-13
19.95534078, −98.91790267
198
3297403-21
19.84155845, −98.03226973
23
1539469-13
19.8483681, −98.97330671
199
6378263-21
20.27395137, −97.96405384
24
1539471-13
19.88013765, −98.94654865
200
3287035-21
20.00394441, −97.80046494
25
1539473-13
19.83932874, −98.97307341
201
E00751-21
20.173404, −98.059527
26
1539476-13
19.85091693, −98.97516152
202
6311273-29
19.55175573, −98.49455764
27
1539453-13
20.07313391, −98.79250195
203
6311274-29
19.54532657, −98.49260474
28
6336611-13
20.06621245, −98.77011166
204
6459714-29
19.43025706, −98.13472193
29
6335523-13
20.11312044, −98.74341589
205
6756853-29
19.48422352, −98.11410177
30
6719681-13
20.11237991, −98.4051467
206
4168017-29
19.58633359, −98.42847233
31
6740924-13
20.07298533, −98.37668807
207
4168020-29
19.59175344, −98.56376007
32
1539449-13
20.11643541, −98.72615811
208
4168027-29
19.48210098, −98.29439608
33
6205931-13
19.88237884, −98.8220836
209
6406157-29
19.49502059, −98.53402659
34
1539479-13
20.07678617, −98.38717142
210
4165224-29
19.49905295, −98.05346502
35
1539429-13
20.28485082, −98.94467205
211
4209484-29
19.42156402, −98.21178823
36
6434169-13
20.11524358, −98.40865361
212
4202637-29
19.4757085, −98.11284982
37
6205930-13
20.09476731, −98.71836192
213
4202660-29
19.46469034, −98.1132248
38
6335577-13
20.09923999, −98.71605545
214
6421897-29
19.58582813, −98.54359179
39
1539440-13
20.06872425, −98.71708094
215
4161233-29
19.47311459, −98.20562485
40
6335571-13
20.27545886, −98.94117179
216
6406128-29
19.59257433, −98.57695318
41
1539442-13
20.08646088, −98.71297338
217
6405983-29
19.58675979, −98.54644898
42
1539465-13
19.78297162, −98.54409519
218
4207147-29
19.59273099, −98.57614489
43
1539462-13
20.28324963, −99.01676083
219
6406051-29
19.61164624, −98.11998572
44
6262874-13
20.08409757, −98.3759223
220
4168036-29
19.47516948, −98.11276603
45
1539444-13
20.0583287, −98.76038144
221
E09430-29
19.5916714, −98.563885
46
1539455-13
20.10272155, −98.74669701
222
4442880-30
20.52882643, −98.49111013
47
6205973-13
19.83658241, −98.9548442
223
4459848-30
20.5829879, −98.36571903
224
4460757-30
20.77874, −98.44443The MILP model described inSection 3 ((1)–(34)) together with the parameters indicated in this section has 1698 constraints and 7156 variables (13 binary) and was solved with the commercial solver LINGO 17, using a server with an Intel ® Xeon ® E3-1220V2@ 3.10 GHz processor, 8.00 GB in RAM, and Windows 7.0 OS; each value of ψ (mix percentage) was solved with, on average, 2091 iterations in a time of three seconds.


## 5. Results

For the analysis of the proposal, three scenarios are presented considering different percentages of land availability at harvest sites (LA1 land availability of 100%, LA2 land availability 95%, and LA3 land availability 90%), as well as different proportions of bioethanol and gasoline mixture in each scenario to evaluate which bioethanol use policy is economically adequate for the study region. The ethanol blending policy is that ethanol and gasoline should be mixed according to a certain proportion, such as E5 (5% ethanol and 95% gasoline), E8 (8% ethanol and 92% gasoline), E11 (11% ethanol and 89% gasoline), E14 (14% ethanol and 86% gasoline), E17 (17% ethanol and 83% gasoline), and E20 (20% ethanol and 80% gasoline). With these three scenarios, we design and analyze the proposed Bio-Eth SC to identify the optimal configuration and the required costs.The analysis of cost results for the three scenarios presented is shown in Figure6. We can see that the best cost is obtained for an E8 mixture in the LA1 scenario; we can also observe that in the LA3 scenario the total cost of the Bio-Eth SC for an E20 mixture is the highest, since, with the total biomass available in the region [54], it would not be possible to meet the demand if only 90% of the biomass is used, which would imply the importation of biomass from other regions which would significantly increase the cost of transport and therefore the total cost of the supply chain. Figures 7–9 show the amounts of the biomass of each type used in each scenario. Unlike the E20 mix for scenarios LA1 and LA2, in scenario LA3, the amount of biomass used is beyond the maximum amount available.Figure 6
The total cost of Bio-Eth SC for three scenarios.Figure 7
Used biomass for scenario LA1.Figure 8
Used biomass for scenario LA2.Figure 9
Used biomass for scenario LA3.In scenario LA1 to produce a mixture of E5 and E8, only barley biomass is used (see Figure7), as in scenarios LA2 and LA3 for a mixture E5 (see Figures 8 and 9), in all other mixtures. It is necessary to use both types of biomass. The strategy to select between corn and barley biomass is obvious. Barley biomass has a better yield in the conversion process than corn biomass; in addition, the harvest sites that produce more barley residues are concentrated around where the biorefinery is selected.In all scenarios, the number and opening of facilities, as well as the volume of bioethanol produced, are those indicated in Table4, and only in case of producing an E20 mixture in the three scenarios the opening of two biorefineries would be required, since one is insufficient to produce the amount required to meet demand.Table 4
Percentage of annual gasoline demand that can be met with bioethanol.
Decision variables of the Bio-Eth SC
Percentage of gasoline demand satisfied with bioethanol
5%
8%
11%
14%
17%
20%
Annual volume of bioethanol production (MLPY)
49.40
79.04
108.68
138.32
167.96
197.6
Number of storage centers with capacity 110,000 t
1
1
1
1
1
1
Number of storage centers with capacity 300,600 t
0
0
0
0
0
0
Number of biorefineries with capacity 190 MLPY
1
1
1
1
1
2
Number of biorefineries with capacity 380 MLPY
0
0
0
0
0
0
Number of mixing plants with capacity 370 MLPY
0
0
0
0
0
0
Number of mixing plants with capacity 555 MLPY
1
1
1
1
1
1Figures10–12 show the cost structure of the Bio-Eth SC for the three scenarios. The total cost consists of annual amortization cost for the opening of facilities, biomass harvesting cost, storage cost (biomass and biofuel), transportation cost (biomass and biofuel), gasoline cost, and biomass-processing cost in biorefineries. In the case of the LA3 scenario and a mixture of E20, there is an excess cost due to the shortage of biomass to meet demand. First, it can be seen that the main cost driver of Bio-Eth SC is the cost of supplying liquid fuel due to the huge cost of buying gasoline. As the proportion of ethanol mixture increases, the required amount of gasoline decreases proportionally. Therefore, the purchase cost of gasoline also decreases. However, the high mixing ratio of bioethanol leads directly to the increase in the cost of biomass, transportation, and processing. Because the decrease in the cost of gasoline supply cannot compensate for the increase in the cost of biomass supply, the total cost of the Bio-Eth SC is increased.Figure 10
The cost breakdown of the Bio-Eth SC for scenario LA1.Figure 11
The cost breakdown of the Bio-Eth SC for scenario LA2.Figure 12
The cost breakdown of the Bio-Eth SC for scenario LA3.The unit cost of mixed biofuel (UCMB) in the three scenarios and for each mixture is calculated by dividing the total cost of the Bio-Eth SC with the total amount of the demand satisfied; the calculated amount varies between 0.99 and $ 1.08/L. It is noted that the unit cost of gasoline is obtained according to [59].In all scenarios, the biomass supply cost and processing cost are the largest contributors to the total cost of the Bio-Eth SC except for the cost of gasoline.Next, numerical data are detailed only for the LA1 scenario, because, in this scenario, the best total cost of the Bio-Eth SC has been obtained. Table5 provides the optimal allocation of harvest sites, storage center, biorefinery, and mixing plant to meet the demand of 988 MLPY with a mixture of 8% bioethanol.Table 5
Optimal allocation of harvest sites, storage centers, biorefineries, and mixing plants.
Scenario
Assigned harvest sites1 (i)
Assigned storage center (j)
Location of biorefinery (k)
Mixed plant assigned (m)
Assigned customers
LA1
1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 54, 57, 65, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 105
2
1
2
1, …, 224
1The names of municipalities of each location are presented in Table 1.Figure13 shows the selected harvest sites, the storage center (capacity 110,000 t), biorefinery (capacity 190 MLPY), and mixing plant (555,000 MLPY).Figure 13
Location of harvest sites (blue), storage center (red), biorefinery (yellow), and mixing plant (green). Source: map made using Google Maps.According to Figure13, the locations for the storage center, the biorefinery, and the mixing plant are selected by the model relative to the center where the greatest amount of agricultural residues of corn and barley is located.Table6 shows a breakdown of the costs (opening of facilities, harvest, transport, storage, processing, and fossil fuel) that would be necessary for the solution of the problem when there is a mixture of fossil fuel and bioethanol of E5, E8, E11, E14, E17, and E20. The breakdown of the costs is indicated as a percentage concerning the total of the Bio-Eth SC. The proposed MILP model is sensitive to changes in the parameters indicated in Table 2.Table 6
Breakdown of the total annual cost of the bioethanol supply chain based on corn and barley agricultural waste for mixing percentages of the E5, E8, E11, E14, E17, and E20 ($M).
Cost ($M)
% concerning the total cost of the Bio-Eth SC
E5
E8
E11
E14
E17
E20
E5
E8
E11
E14
E17
E20
Opening of facilities
5.88
5.88
5.88
5.88
5.88
8.32
0.6
0.6
0.6
0.6
0.6
0.8
Harvest cost
29.32
46.90
89.25
132.25
175.25
217.54
3.0
4.8
8.9
13.0
16.9
20.5
Transportation costs
8.33
9.63
10.89
12.45
14.24
16.53
0.8
1.0
1.1
1.2
1.4
1.6
Holding cost
0.37
0.59
0.85
1.19
1.53
1.48
0.0
0.1
0.1
0.1
0.1
0.1
Fossil fuel
938.62
908.98
879.34
849.70
820.06
790.42
95
92.7
88.1
83.5
79.0
74.6
Processing cost
5.19
8.29
12.37
16.47
20.57
24.65
0.5
0.8
1.2
1.6
2.0
2.3From the case of study, it is determined that only the opening one storage center, one biorefinery, and one mixing plant are required. From the analysis of results, it is observed that the best cost of the Bio-Eth SC is for a production of E8. The cost per litre would be according to the mathematical model and the parameters provided of USD 0.99 to produce a bioethanol mixture E8, which for the case of the study region would be a price that could not compete with the current cost of the available fuel (USD 0.95) [61, 62]. The difference in costs of 4.2% leaves bioethanol produced from corn and barley residues biomass in the study region at a disadvantage. It leads us to the reflection that, in order to be profitable, it would be necessary to guarantee a higher yield of biomass from the harvest sites and bioethanol production processes that generate a higher yield per unit of processed biomass (t).The design of the entire SC and its operational planning is always one of the most critical challenges that make the commercialization of cellulosic biofuels possible. The strategic and operational decisions that have to do with storage facilities, biorefinery, mixing plants, biomass management, transportation, and distribution are essential for the success of the biofuels industry. Therefore, quantitative models are necessary, since they help in the decision-making of investors, government, and social agencies to understand the impact of the SC on the generation of biofuels.


## 6. Conclusions and Future Research

In this study, a decision model based on optimization is presented using mixed-integer mathematical programming (MILP) for the design of the bioethanol supply chain (Bio-Eth SC), which includes four stages for the production of mixed fuel with bioethanol. The proposed optimization model minimizes the total cost required to build and operate the Bio-Eth SC and identifies the main decision variables, such as the types and quantities of the biomass used, quantities, and locations of the installed facilities, biomass flows, bioethanol, and mixed liquid fuel. Then we carried out the case study of the design problem of a Bio-Eth SC in the region of Tulancingo, Hidalgo, in Mexico (case study), using three scenarios (LA1 100% land availability, LA2 land availability 95%, and LA3 90% land availability) and six different mixing policies E5 (5% ethanol and 95% gasoline), E8 (8% ethanol and 92% gasoline), E11 (11% ethanol and 89% gasoline), E14 (ethanol 14% and 86% gasoline), E17 (17% ethanol and 83% gasoline), and E20 (20% ethanol and 80% gasoline).The main findings of the case study are as follows:(i)
In the E8 low ethanol blending policy in scenario LA1, the mixing of liquid fuels is produced with the lowest total cost of Bio-Eth SC at the cost of $ 0.99 per litre. On the other hand, in the E20 high-mix ethanol policy, in scenarios LA1 and LA2, Bio-Eth SC must work with two biorefineries to meet demand, which implies the highest cost per litre of mixed fuel (1.07 $/L). However, in the LA3 scenario, additional biomass would be required to meet the demand. Therefore, the cost per unit of mixed fuel would be 1.08 $/L in addition to an additional cost not calculated in this work for being out of the scope of it.(ii)
The facilities (storage centers, biorefinery, and mixing plant) tend to be installed in regions where the biomass of agricultural barley waste is more abundant to reduce the best total cost of Bio-Eth SC.(iii)
The biomass of agricultural barley residues is preferably selected against agricultural corn residues; this is also due to better yield in the conversion process.(iv)
The main contribution to the total cost of Bio-Eth SC is the purchase cost of gasoline to produce the mixed fuel, while the cost of processing biomass for bioethanol production and biomass costs are also triggers for raising the cost of bioethanol supply.(v)
We found that the unit cost of the mixture (UCMB) is not significantly sensitive to the amount of bioethanol; for example, in the LA1 scenario, only 6.7% of the total Bio-Eth SC was increased for an E20 mixture with respect to the E5 mixture. Therefore, the policy of encouraging the generation and use of alternative energy is applicable; however, the amount of energy resources derived from the productive processes of the primary sector for the production of biofuels is questionable.(vi)
Finally, the results provided by the proposed MILP model are considered adequate for the given conditions. Therefore, we can establish that the proposed approach is robust and can be used with other parameters and types of biomass.Assumptions have been made in this study, which allows some suggestions about future work. Some assumptions that were considered by default are the locations of the facilities and the maximum number that can be opened, the maintenance costs, and the percentage of facilities used to store the product. One such opportunity for future work is the question of determining the location and number of facilities that must be opened, as well as its capabilities, such as environmental impact or sustainability analysis. The model is deterministic. Therefore, a problem to consider would be a model that incorporates uncertainty, for example, the amount of biomass and demand, to make the model more realistic. Other biomass residues and more final products could be incorporated to have a better representation of the SC.



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*Source: 6029507-2020-03-11.xml*