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

0e 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. 0is paper proposes a model of mixed-integer linear programming (MILP) that seeks to minimize the total cost of the bioethanol supply chain. 0e 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. 0e 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.


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].
ere is much research that assesses the feasibility of producing biofuels from various types of biomass [9][10][11][12][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]. e 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]. e 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][19][20][21][22][23][24]. e 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. is 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. e 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). e 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. e 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]. e 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. e 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. 2 Mathematical Problems in Engineering 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. e use of bioethanol in gasoline has become a global trend to reduce CO 2 emissions to the atmosphere, increasing the octane number of gasoline and reducing dependence on petroleum products, experimentally [37]. e 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. e 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]. erefore, the use of raw materials lignocellulosic biomass is being studied intensively to develop bioethanol without using grains for human consumption. e 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. e 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. us, 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. ese 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. e 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.

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 Figure 1). e proposed model considers sites for biomass harvesting, storage facilities, biorefineries, mixing plants, and customer demand. e 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). e 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. e model considers aspects such as To determine (i) e number and location of harvest sites (ii) e amount of biomass transported from each harvest site to storage centers and biorefineries (iii) e 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) e number of storage centers, biorefineries, and mixing plants that must be opened In 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. e MILP model proposed in this case study incorporates the following characteristics for the Bio-Eth SC:

e 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][43][44][45][46][47][48] in the study region, the planted area is 247,942 and 212,414 ha for maize and barley, respectively. e average biomass yields are 1.95 t ha − 1 for corn and 1.99 t ha − 1 for barley. erefore, the biomass potential in the study region is 906,190.76 t of dry matter.

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. e 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.

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.

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 mixedinteger 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. e 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.

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

Holding Costs
is the cost of holding biomass type b ∈ B per ton at the harvest site i ∈ I

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

Capacities
is the storage capacity of the warehouse j ∈ J S P k (L) is the bioethanol production capacity per year of the biorefinery k ∈ K S B k (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

e Opening of Facilities
nb is the maximum number of biorefineries that can be opened nm is the maximum number of mixing plants that can be opened

Other Parameters
L ibt is the number of hectares of land at the harvest site i ∈ I for biomass typeb ∈ B, in the time t ∈ T P ibt is the proportion of land available at the harvest site i ∈ I with biomass type b ∈ B, in the time t ∈ T R ibt (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 nt (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

Decision Variables for Holding
kt is the amount of bioethanol stored in the biorefinery k ∈ K in the time t ∈ T Z M mt is the amount of biofuel stored in the mixing plant m ∈ M in the time t ∈ T

Decision Variables for Sent Quantities
kmt is the amount of bioethanol sent from biorefinery k ∈ K to the mixing plant m ∈ M in the time t ∈ T Y M mnt is the amount of biofuel sent from the mixing plant m ∈ M to the customer n ∈ N in the time t ∈ T

Other Decision Variables
Y RP mt is the amount of fossil fuel required in the mixing plant m ∈ M in the time t ∈ T W kbt is the amount of biomass type b ∈ B processed in the biorefinery k ∈ K in the time t ∈ T ϕ ibt is the amount of biomass type b ∈ B produced on the harvest site i ∈ I in the time t ∈ T

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. ese 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).
e objective of the proposed model is minimizing the total annual cost of Bio-Eth SC. e 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. e different components of the objective function are explained as follows.
e annual amortization cost of the distribution centers can be defined as e cost of annual amortization of biorefineries is e annual amortization cost of the mixing plants that are opened is defined as e cost of storing bioethanol in biorefineries is calculated as e cost of holding bioethanol in the mixing plant is e cost of holding a unit of biomass at the harvest site is expressed as follows: e cost of holding units in a storage center is defined as e cost of maintaining units in biorefinery k of biomass type b can be computed as e cost of transporting biomass from the harvest site i to the storage center j is e cost of transporting biomass from the harvest site i to the biorefinery k is described by e cost of transporting biomass from a storage center to the biorefinery is derived as Calculating the cost of transporting bioethanol from biorefinery to the mixing plant is given by the relation e cost of transporting biofuel from the mixing plant to the n customers is shown in e cost of fossil fuel delivered to the mixing plant is determined as e cost of processing biomass to generate bioethanol is computed as Growing and harvesting biomass at each harvest site are calculated to determine the costs of sowing: e fitness function O to be minimized is the next and considers all the above cost elements: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 8 Mathematical Problems in Engineering 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: 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: Equation (30) guarantees that the quantity of biofuel stored in the mixing plants m does not exceed its mixing capacity, for each period t: Equation (31) guarantees that the mixture of bioethanol with fossil fuel is according to the value of ψ: Equation (32) guarantees the opening of at least one storage center j: Equation (33) guarantees the opening of the biorefineries k that are indicated in parameter nb: Equation (34) guarantees the opening of the mixing plants m that are indicated in the nm parameter: e following expressions are domain restrictions of decision variables:

Case of Study
e 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.

Input Parameters.
e relevant input parameters are as follows: (1) e 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 Figure 3) 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) e 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) ere are considered 224 customers (n � 1, . . . , 224), which represent the same number of gasoline service stations in the study region (see Figure 5 Table 3. e MILP model described in Section 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.

Results
For the analysis of the proposal, three scenarios are presented considering different percentages of land availability Mathematical Problems in Engineering 9 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. e 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. e analysis of cost results for the three scenarios presented is shown in Figure 6. 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.
In scenario LA1 to produce a mixture of E5 and E8, only barley biomass is used (see Figure 7), 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. e 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 Table 4, 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. Figures 10-12 show the cost structure of the Bio-Eth SC for the three scenarios. e 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. erefore, 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. e 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. Table 5 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. Figure 13 shows the selected harvest sites, the storage center (capacity 110,000 t), biorefinery (capacity 190 MLPY), and mixing plant (555,000 MLPY).
According to Figure 13, 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. Table 6 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. e breakdown of the costs is indicated as a percentage concerning the total of the Bio-Eth SC. e proposed MILP model is sensitive to changes in the parameters indicated in Table 2.
From 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. e 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]. e 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 Cost per unit of fuel in the period ($/L) μ t � 1.00 (for all t) [2] e processing cost of a biomass unit ($/t) ω kb � 48.86 (for all b, k) Assumed e proportion of land available at the harvest site P ibt � 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 nt 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)         of biomass from the harvest sites and bioethanol production processes that generate a higher yield per unit of processed biomass (t). e 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. e 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. erefore, 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.

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. e 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. en 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     (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. erefore, 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) e 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) e biomass of agricultural barley residues is preferably selected against agricultural corn residues; this is also due to better yield in the conversion process. (iv) e 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.
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. e model is deterministic. erefore, 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.

Data Availability
e data used to support the findings of this study are included within the article in Tables 1-3 and can be obtained from the first author and corresponding author.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.