A hybrid multi-objective robust possibilistic programming approach to

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A hybrid multi-objective robust possibilistic programming approach to sustainable bioethanol supply chain network design Parisa Mousavi Ahranjani, Seyed Farid Ghaderi, Ali Azadeh, and Reza Babazadeh Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b02869 • Publication Date (Web): 16 Oct 2018 Downloaded from http://pubs.acs.org on October 22, 2018

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Industrial & Engineering Chemistry Research

A hybrid multi-objective robust possibilistic programming approach to a sustainable bioethanol supply chain network design Parisa Mousavi Ahranjania, Seyed Farid Ghaderia, Ali Azadeha, Reza Babazadehb, aSchool

of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran

bFaculty

of Engineering, Urmia University, Urmia, West Azerbaijan Province, Iran

Abstract This work proposes a multi-objective robust possibilistic programming (MORPP) model for the design and planning of a multi-period multi-feedstock lignocellulosic biofuel supply chain (LBSC) network under the epistemic uncertainty of the input data. The objective simultaneously considers economic, environmental, and social aspects. The proposed model determines the optimal location, capacity and conversion technology of biorefineries, appropriate transportation modes, material flow and production planning. In order to deal with the inherent uncertainty of input parameters a hybrid robust possibilistic programming (HRPP) approach is applied. A real case study located in Iran is conducted to demonstrate the performance of the model. Based on the DMs' preferences HRPP-I(c) version of the robust model is recognized as the most suitable one. Also, a number of scenarios are defined and some valuable managerial implications are drawn. Keywords: Bioethanol supply chain, Lignocellulosic biomass, Sustainability, Mixed integer linear programming, Multi-objective optimization, Robust possibilistic programming

1 Introduction Energy crisis due to fossil fuels depletion, environmental issues due to greenhouse gas (GHG) emissions and social issues such as job deficiencies specially in under developed rural areas have attracted researchers to develop sources of renewable energies.1 Biofuel is one of the renewable energies that could be either a substitute for, or a complement to, fossil fuels in several ways. Transportation sector has the greatest share of energy demand among other energy demanding sectors.2 Bioethanol and biodiesel, two types of transport biofuels, account for more than 90% of total world biofuel consumption. Bioethanol can be blended with gasoline in any proportion up to 10% without the necessity of engine modifications.3 Bioethanol can be produced from various raw materials which could be categorized as (i) sucrose-containing feedstock (sugarcane, sugar beet and sweet sorghum), (ii) starch-containing feedstock (wheat, corn and cassava) and (iii) lignocellulosic feedstock (straw, grasses, wood, stovers, agricultural wastes, paper, etc.). Bioethanol produced from sucrose- and starch-containing feedstock is called as first-generation bioethanol and bioethanol produced from lignocellulosic feedstock is called as second-generation bioethanol.4 Although the first-generation bioethanol production has been commercialized worldwide, there are obstacles as well, most notably conflict with the food supply chain. Since the majority of the feedstock used in production of firstgeneration bioethanol can also be consumed as food and feed, first-generation bioethanol Corresponding

Author’s E-mail: [email protected]

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production endangers food supply. But, second-generation bioethanol production while economically practical, overcomes this obstacle. Moreover, it positively impacts the environment through net reduction in GHG emissions.1 Economic dimension is usually the first and most important aspect of almost all human affairs in today's competitive world. This is also true for biofuel supply chain network design (BSCND). In addition, the concerns about negative impacts of human activities on environment and society, have led to a greater focus on environmental and social aspects of sustainabilty.1 Since BSCND directly affects the society and environment, optimizing all three aspects of sustainability is essential in BSCND.5 On the other hand, there exist different uncertainties in biofuel supply chains due to their dynamic and complicated nature, impacting their performance. Uncertainties in strategic level decision-making affect the performance of supply chains more than those in tactical/operational level decision-making.6 Therefore, it is of great importance to consider both sustainability and uncertainty in BSCND. The uncertainty in data can be classified into two main types: (i) randomness in the parameters due to the random nature of events and (ii) epistemic uncertainty due to lack of sufficient historical data and/or knowledge about parameters. Stochastic and possibilistic programming approaches are usually used to model randomness and epistemic uncertainty, respectively.7 Most studies have applied stochastic programming models to deal with the uncertainties in design of biofuel supply chain networks (BSCNs). However, due to the uncertainty variety in biofuel supply chains, it seems that stochastic programming methods have some inevitable drawbacks.8 One drawback is the need to define a large number of scenarios which results in model complexity especially in large size problems. The other is lack of reliable and sufficient data to define suitable scenarios.9 To overcome these disadvantages, some researchers have developed possibilistic programming approaches in designing BSCNs. In possibilistic programming approaches, solutions are obtained based on the average value of uncertain parameters. But they do not control deviations from expected or mean value of the objective function.10 Therefore, robust possibilistic programming (RPP) methods have been introduced and applied to provide feasibility and/or optimality robustness of the solution in BSCND. In this paper, to design a robust and sustainable bioethanol supply chain network, a multiobjective mixed-integer linear programming (MILP) model is developed. The objective involves all economic, environmental and social aspects. In order to cope with the inherent uncertainty of parameters a hybrid RPP (HRPP) approach is applied. A real-world case study in Iran is performed to assess the performance and validity of the model. Also a number of scenarios are conducted in order to provide some applicable managerial implications. The following specific features differentiates this model from other models in the literature: 



There are epistemically uncertain parameters in all three objective functions and constraints including biomass yield, bioethanol demand, bioethanol and byproducts prices, export price of bioethanol, different costs involving investment, biomass purchase, production, transportation and import costs as well as environmental impacts and job creation coefficients. Capacity is considered as a continuous variable and capacity expansion is taken into account in the model to allow for increase in blending percentage of bioethanol with gasoline during the planning horizon. 2 ACS Paragon Plus Environment

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 



 

In order to answer managerial questions, bioethanol imports to demand zones and exports from biorefineries are involved in the model as tactical decisions. Reduction in GHG emissions due to avoiding open-field burning of lignocellulosic biomass is incorporated in the environmental objective function. Since, if lignocellulosic biomass is not used for bioethanol production, a great deal of it is burned in fields, leading to GHG emissions (especially in the under-studied case). Four variants of a hybrid robust possibilistic programming (HRPP) approach are applied in design of a BSCN. The HRPP approach is developed based on Me measure (the most flexible fuzzy measure) and decision makers' (DMs') risk attitudes, which the most suitable one could be chosen based on DMs' preferences. To the best of our knowledge, this is the first research to implement HRPP approach in designing a BSCN. It should be noted that both Me measure and HRPP approach provide DMs with greater flexibility in their choice.

A real-world case study is performed to evaluate the reliability and applicability of the proposed model. Different policies on blending percentage of bioethanol into gasoline are defined and investigated to obtain managerial implications.

The rest of the paper is organized as follows. Section 2 provides a comprehensive overview of recent papers on design of BSCNs. Section 3 defines the problem and presents the model formulation. Section 4 describes RPP approach and applies the HRPP approach to solve the model. Section 5, implements the model in a real case study, summarizes the results and presents some useful managerial implications by policy analyses. Finally, Section 6 concludes the paper and suggests some future research directions.

2 Literature review Since there is a large volume of literature on design of BSCNs, we put our focus on recent papers. For more information, especially on earlier papers, interested reader could refer to Ghaderi et al.,5 Zandi Atashbar et al.,11 Sharma et al.,12 Yue et al.13 and Awudu and Zhang.14 Ghaderi et al.5 in their review paper on BSCND optimization showed that 79% of the papers by 2016 were deterministic models. Also their paper demonstrated that 76% of the papers had a single economic objective. Since then, some other deterministic papers with an economic objective have been published. For example, Babazadeh2 developed a multi-period multi-product second-generation biodiesel supply chain network. He considered Jatropha seeds and waste cooking oil as non-edible feedstocks. His proposed model identified the optimum location and capacity of facilities, suitable transportation modes, appropriate technology of biorefineries, material flow and production planning. Lee et al.15 proposed an MILP model to minimize the total required cost to establish and operate a bioethanol supply chain network. They determined variables such as types and amounts of the consumed biomass, technology configuration of biorefineries, types, capacities, and locations of major facilities and regional and seasonal flows of biomass, bioethanol and blended liquid fuels. Mutenure et al.16 presented an economic optimization model of a supply chain network to produce sugar, bioethanol, heat and electricity from the first- and second-generation biomass. An MILP model integrated with Google Earth® 3 ACS Paragon Plus Environment


and ArcGIS was presented to account for sugar demand, different feedstocks and products, together with their distribution, tax subsidies and different processing technologies. Some papers take into account environmental aspect of sustainability as well as economic aspect.17-29 Majority of these papers consider minimizing GHG emissions or environmental impact as environmental objective function. For example, Ng and Maravelias23 developed a mixed-integer non-linear programming (MINLP) model for design and planning of a cellulosic bioethanol supply chain with regional depots. Their financial and environmental model accounted for technology selection, capacity planning decisions, farm and biomass feedstock selection, biomass allocation to depots and biorefineries, as well as inventory planning decisions. Duarte et al.24 presented an MILP model for designing a sustainable supply chain of bioethanol from coffee cut stem. Single objective function of their model maximized economic benefits and positive environmental balance. Wheeler et al.25 proposed a method to address design of a sugar-ethanol supply chain both economically and environmentally. They applied an MINLP algorithm based on AHP to obtain the weighting factors for an aggregated objective function. Wheeler et al.26 in another paper combined four different multi-attribute decision-making (MADM) methods with multi-objective optimization model to identify a unique Pareto solution of the multi-objective problem. Ghasemi Nodooshan27 optimized design and configuration of an algal BSCN under economic and environmental objectives. Their MILP model included multiple production pathways and time periods, seasonality factors, water evaporation, recycling opportunities and other major features of the algal BSCN. There are some other papers that involve all three aspects of sustainability, i.e. economic, environmental and social.1, 8, 10, 30-34 Ghaderi et al.5 showed that only 5% of BSCND models cover all three aspects of sustainability. In most of these papers, maximizing the number of job opportunities created is taken as social objective function. For example, Yue et al.30 proposed a multi-objective, mixed-integer linear fractional programming (MILFP) model for design and operation of bioelectricity supply chains, considering economic, environmental, and social aspects. Objective functions include minimizing costs, minimizing GHG emissions and maximizing job opportunities. Roni et al. 31 developed a hub-and-spoke network structure for cellulosic ethanol supply chain. Optimizing total cost, CO2 emissions and number of new jobs created were economic, environmental and social objectives of their MILP model. Miret et al.32 presented a multi-objective MILP model for design of a biomass supply chain considering all three aspects of sustainability. In their model, the economic objective was minimizing total annual costs. The environmental impact was assessed via Eco-costs method. And the social impact was measured through two indicators: total number of local created jobs and the competition between energy and food. Cambero and Sowlati33 formulated a multi-objective MILP model to maximize net present value, GHG emission savings and social benefit of a forest-based biorefinery supply chain. The job-related social benefit was measured through an indicator considering different impacts of newly created jobs based on their type and location. In order to make models more realistic, uncertainty is taken into account in a number of studies. The main uncertain parameters included in papers are biomass supply, biofuel demand, biomass price and biofuel price.1, 6, 8-10, 21, 28-29, 34-50 Some papers account for uncertainty in different cost parameters such as cultivation, harvest, investment, production, inventory and transportation costs.6, 9-10, 28, 41, 43, 51 A few papers include other uncertain parameters such as carbon trading cost,17, 52 environmental impact parameters,8, 10 technological related parameters40-41, 44-45, biomass quality53 and job creation coefficients.10 4 ACS Paragon Plus Environment

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Most of the papers considering uncertainty of parameters, apply scenario-based and especially two-stage stochastic programming to deal with uncertainty. 1, 21, 29, 34-35, 37, 40, 42, 45, 48, 5455 For instance, Santibanez-Aguilar et al.21 presented a stochastic MILP model for the optimal design of a biomass conversion system involving both economic and environmental issues. The economic aspect was evaluated through net annual profit and the environmental impact was assessed via Eco-indicator 99 method. Gonela et al.34 developed a stochastic MILP model to design an optimal hybrid (first and second) generation bioethanol supply chain. They considered total expected profit of the bioethanol supply chain as the economic objective. They also accounted for environmental and social aspects in the constraints of their model, such as limitations on GHG emissions, land usage and first generation bioethanol production. Gao and You48 addressed both economic and environmental issues in addition to uncertainty impacts in their proposed supply chain optimization model. They presented a hydrocarbon biofuel supply chain case study and solved the corresponding stochastic MILFP model using a tailored solution algorithm. Li and Hu40 formulated a two-stage stochastic MILP model for bio-oil supply chain considering uncertainty in biomass availability, technology advancement, and biofuel price. Osmani and Zhang1 proposed a multi-objective stochastic MILP model for a multi-feedstock sustainable bioethanol supply chain under bioethanol demand and bioethanol sale price uncertainties. Castillo-Villar et al.53 proposed a two-stage stochastic programming model and assessed the impacts of biomass quality and variability on the design and management of a biofuel supply chain. Their proposed model minimized the total cost of location, transportation, technology selection, and biomass quality. They proposed and applied different algorithms including L-shaped, L-shaped with trust region cuts and algorithmic improvements, and multi-cut L-shaped algorithm to solve the proposed stochastic model. Ghelichi et al.50 presented an extended two-stage stochastic programming model to the design of an integrated biodiesel supply chain network from Jatropha feedstock. Their single-objective, multi-period and multi-product MILP model also put a constraint on GHG emissions. The min-max relative regret approach in a soft-worst case framework was developed to address demand and supply uncertainties. Xie and Huang49 developed a multi-stage stochastic MILP model to support biofuel supply chain expansion under evolving uncertainties. By utilizing the block-separable recourse property, they reformulated the model in an equivalent two-stage program and solved it using an enhanced nested decomposition method. Some papers use possibilistic approach in order to cope with epistemic uncertainty of the input data.6, 41 For example, Tong et al.41 proposed a multi-period MILP model for advanced dropin hydrocarbon biofuel supply chain integrated with existing petroleum refineries. They applied fuzzy possibilistic programming approach to handle the uncertain parameters including conversion rate, operation cost associated with insertion points in petroleum refinery, biomass availability and product demand. Recently robust programming including robust possibilistic programming (RPP), scenariobased robust programming and robust convex programming is used in the biomass literature to provide feasibility and/or optimality robustness of the optimal solution.8-10, 28, 36-38, 42-44, 47, 49-50, 53 For instance, Azadeh et al.37 developed a dynamic stochastic MILP model with some varying parameters during the planning horizon. In order to handle market and disruption risks as well as uncertainties in supply and demand, they employed two-stage stochastic programming and scenario-based robust programming. Tong et al.36 addressed robust design and planning of an advanced hydrocarbon biofuel supply chain integrating with existing petroleum infrastructure considering the unit cost objective. They adopted two customized algorithms to solve the resulting MILFP model. Bairamzadeh et al.8 introduced a novel MORPP approach to address the optimal 5 ACS Paragon Plus Environment


design and planning of an LBSC. They considered all three aspects of sustainability. Babazadeh et al.28 developed a new formulation of possibilistic programming approach, or better to say, robust possibilistic programming approach for designing a second-generation biodiesel supply chain. They used possibilistic mean value and absolute deviation of fuzzy numbers to deal with the inherent uncertainty in different parameters. Bairamzadeh et al.44 presented a hybrid robust optimization model to handle multiple types of uncertainty in a multi-feedstock LBSC. They applied robust scenario-based stochastic programming, robust possibilistic programming and robust convex programming approaches to cope with randomness, epistemic and deep uncertainties, respectively. Ghaderi et al.10 developed a novel MORPP model for design of a sustainable switchgrass-based bioethanol supply chain network considering economic, environmental and social objectives. Zhang and Jiang47 proposed a robust MILP model under price uncertainty for design and planning of a waste cooking oil-to-biodiesel supply chain. Their multiobjective model addressed the number, sizes and locations of biorefineries, the sites and amount of WCO collected and the transportation plans of WCO and biodiesel. Mohseni et al.43 formulated a robust MILP model for a microalgae-based biodiesel supply chain. Their model provided a tradeoff between supply chain total costs and reliability to determine the value of strategic and tactical decisions. Babazadeh9 proposed a set-induced robust optimization method to cope with the deep uncertainty of a green biomass-to-biodiesel supply chain design. His single-objective MILP model minimized total cost and maximized carbon trade. Among the above mentioned papers, there are really few ones which take into account all three aspects of sustainability (in their objective functions) together with uncertainty considerations.1, 8, 10, 47 Table 1 summarizes the characteristics of the recent studies on BSCND that consider uncertainty. It also shows the features of the model proposed in this paper compared to other studies. Reviewing Table 1 shows that a large number of researches only consider randomness uncertainty related to random nature of input parameters and use scenario-based and especially two-stage stochastic programming approach to cope with uncertainties. However, stochastic programming models suffer from some drawbacks reducing their applicability in real-world problems. In majority of real-life problems, it is impossible to elaborate the probability distribution of uncertain parameters according to lack of enough knowledge or historical data. On the other hand, due to the wide range of uncertainties in the biofuel supply chain models, utilizing scenariobased stochastic programming approaches may result in complexity caused by large number of scenarios in the case of increasing number of possible values for different uncertain parameters.44 In order to avoid such difficulties, a few studies have applied fuzzy programming6, 41 and others, robust possibilistic approaches to provide feasibility and/or optimality robustness of the optimal solution. Azadeh et al.37 and Azadeh and Arani42 only considered optimality robustness of a scenario-based stochastic biofuel supply chain with the aim of maximizing the expected profit of the supply chain along with profit variance minimization. Babazadeh et al.28 minimized possibilistic mean value of the biodiesel supply chain cost and its absolute deviation to provide optimality robustness only. Others accounted for both feasibility and optimality robustness. Bairamzadeh et al. 8, 44 utilized Necessity (Nec) fuzzy measure to cope with the existing epistemic uncertainty in a lignocellulosic supply chain. Shabani and Sowlati38 and Zhang and Jiang47 applied the robust convex programming approach proposed by Ben-Tal et al.56 to address deep uncertainty of parameters in the supply chain of a forest-based biomass power plant. In parameters with deep uncertainty, historical data and knowledge are very limited so that forming probability or even 6 ACS Paragon Plus Environment

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possibility distribution is impossible.9 However, the most major disadvantage of Ben-Tal et al. approach is that it transforms a linear programming model to a nonlinear robust convex counterpart causing more complexity in the model. Tong et al.,36 Mohseni et al.43 and Bairamzadeh et al.44 utilized the robust convex programming approach proposed by Bertsimas and Sim57 to cope with deep uncertainties in their models. In this approach the robust counterpart of the model remains linear. Babazadeh9 tackled the deep uncertainty of parameters employing set-induced robust optimization approach. Ren et al. 51 considered uncertain parameters as interval numbers. They presented an interval linear programming and developed a method for solving interval linear programming. Ghaderi et al.10 proposed a robust possibilistic programming approach which maximizes the supply chain performance, optimality robustness, and feasibility robustness based on possibilistic mean value and absolute deviation of fuzzy input parameters. The literature review of recent research on BSCD demonstrates that really few papers have considered epistemic uncertainty in the input data. To bridge this gap, this research proposes a multi-objective RPP model for the design and planning of a multi-period multi-feedstock LBSC considering the epistemic uncertainty of the input data. A hybrid RPP approach based on fuzzy Me measure is employed to provide the DMs with more flexibility in their choice according to their risk attitude.


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Table 1. Review of recent BSCND studies considering uncertainty in the input data Modeling approach

Eco. obj.

Env. obj.

MILP MILP MILP MILP

* * * *

*

37

MILP

*

36

MINLP

*

34

MILP

*

*

*

29

MILP

*

*

6

MILP

*

8

MILP

*

51

LP

*

*

42

MILP, SD

*

*

*

*

*

*

21

MILP

*

*

*

*

*

38

MILP

*

*

*

*

Ref. 54 41 40 45

43 28 1

MILP, GIS MINLP MILP

Soc. obj.

Multiperiod

Source of uncertainty

Uncertainty modelling approach

*

*

BS, BD, BP BS, BD, C, T BS, BP, T BS, T

Two-stage stochastic programming Fuzzy possibilistic programming Two-stage stochastic programming Two-stage stochastic programming

*

*

BD, BP

Two-stage stochastic programming, Scenario-based robust programming

BS, BD

Robust convex Programming (Bertsimas & sim’s approach)

LA

CF

TT

FM

IP

*

*

*

*

*

*

*

*

TM

IE

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

*

BS, BD, BP

Scenario-based stochastic programming

*

*

*

*

*

BS, BD, BP


*

*

*

*

*

BS, C

Fuzzy modeling approach

*

*

*

*

*

BD, BP, EI

Robust possibilistic programming

BS, BD, C

Interval linear programming approach

*

BS

Scenario-based stochastic programming, Scenario-based robust programming

*

*

BP


*

*

*

BS

Multi-stage stochastic & robust convex programming (Ben-Tal et al. approach)

*

*

*

*

BS, BD, BP, C

*

*

*

*

*

BS, BD, C, EI

*

*

*

BS, BD, BP

*

*

*

*

*

*

*

*


Robust convex programming (Bertsimas & sim’s approach) (Robust) possibilistic programming Scenario-based stochastic programming

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Ref.

Modeling approach

Eco. obj.

Env. obj.

Soc. obj.

LA

CF

47

MILP

*

*

*

*

*

48

MILFP

*

*

*

*

*

*

*

*

BS, BD

44

MILP

*

*

*

*

*

*

*

BS, BD, T

10

MINLP

*

*

*

*

*

*

*

BS, BD, C, EI, SP

9

MILP

*

*

*

*

*

*

*

*

BS, BD, C

50

MILP

*

*

*

*

*

*

*

*

BS, BD

49

MILP MILP

* *

* *

* *

* *

*

*

*

BD BQ

MILP

*

*

*

*

*

*

*

53

This paper

*

*

*

*

TT

FM

IP

TM

IE

Multiperiod

*

Source of uncertainty BP

*

BS, BD, BP, C, EI, SP

Uncertainty modelling approach Robust optimization (Ben-Tal et al. approach) Scenario-based stochastic programming Hybrid (scenario-based stochastic, possibilistic and convex) robust programming Robust possibilistic programming Set-induced robust optimization Extended two-stage stochastic programming Multi-stage stochastic programming Two-stage stochastic programming Robust possibilistic programming

Abbreviations: SD: System dynamics, LA: Location/allocation, CF: Capacity of facilities, TT: Type of Technology, FM: Flow of material, IP: Inventory planning, TM: Transportation mode, IE: Import/Export of biomass/biofuel, BS: Biomass supply, BD: Biofuel demand, BP: Biomass/biofuel price, C: Costs, T: Technology, EI: Environmental impacts, SP: Social parameters, BQ: Biomass quality



3 Problem definition and formulation 3.1 Problem statement This article studies a multi-period long-term multi-feedstock LBSC network design and planning while accounting for epistemic uncertainties in various parameters. Fig. 1 illustrates main elements of the considered LBSC network. Harvested biomass feedstock from supply zones is transported to biorefineries. There, it is converted into bioethanol using either thermochemical or biochemical conversion technologies. These technologies produce mixed alcohols and bioelectricity as byproducts, respectively. The produced bioethanol is transported from biorefineries to oil refineries (i.e., demand zones) where it is blended into gasoline. Two transportation modes, road and rail, are considered for transporting biomass and bioethanol across the network. Bioethanol exports from biorefineries are allowed if economically, environmentally and socially justified. Moreover, bioethanol imports to demand zones are permitted if either justified or even necessary to satisfy the desired demand.

Fig. 1. Main elements of the considered LBSC network.

The proposed multi-objective model considers minimization of total cost as economic objective function, maximization of reduction in GHG emissions as environmental objective and maximization of job opportunities created as social objective. The proposed model determines


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both strategic and tactical decision variables. In order to optimize economic, environmental and social performances of the model the following strategic decisions will be optimized:   

Biorefinery locations Processing capacity of biorefineries considering capacity expansions Production technology of biorefineries

Also the following tactical decisions will be optimized in each planning period:      

Amount of harvested biomass in each supply zone to be sent to each biorefinery Amount of each biomass type to be processed by each biorefinery Amount of bioethanol to be produced by each biorefinery Amount of produced bioethanol to be sent to each oil refinery Amount of bioethanol to be exported from each biorefinery Amount of bioethanol to be imported to each oil refinery

This study considers the following inherent sources of uncertainty: 

Biomass feedstock yield due to variations in rainfall and other unpredictable weather conditions,  Bioethanol demand caused by variations in gasoline production of oil refineries,  Prices of commodities and various costs arising from market fluctuations,  GHG emission coefficients due to different composition of lignocellulosic biomass feedstocks and GHG emission coefficients in different points of bioethanol supply chain such as biomass harvest, transportation, bioethanol production, etc. and  Job creation coefficients arising from lack of knowledge. Due to limited available data, fuzzy numbers and robust possibilistic approach are applied to handle the above mentioned inherent uncertainties.

3.2 Model formulation The indices, input parameters and decision variables of the mathematical model are summarized in Table 2. It should be noted that symbols with a tilde (~) on indicate the uncertain parameters. Table 2. Indices, parameters and decision variables of the mathematical model Nomenclature Indices

b c i j k m s t

lignocellulosic biomass feedstocks, b =1, …, B byproducts, c =1, …, C lignocellulosic biomass supply zones, i =1, …, I biorefinery candidate locations, j =1, …, J bioethanol demand zones, k =1, …, K transportation modes, m =1, …, M bioethanol conversion technologies, s =1, …, S planning periods, t =1, …, T

Parameters

𝐵𝐹𝑡

bioethanol blending fraction into gasoline to be satisfied in planning period t 11 ACS Paragon Plus Environment


𝐵𝑃𝑐,t 𝐶𝐻𝑀𝑏 𝐶𝑃𝑀b,s 𝐶𝑇𝐸𝑚 𝐶𝑇𝑀b,𝑚

DisRDj,k,m DisSRi,j,m

𝐸𝑥𝑃𝑡 𝐹𝐶𝑅j,s 𝐻𝐶𝑀b,i 𝐼𝑚𝑃𝑡 𝐽𝐶𝑅j,s 𝐽𝐻𝑀𝑏 𝐽𝑃𝐸j,s

Li,b 𝐿𝐶𝐸j,k,m 𝐿𝐶𝑀b,i,j,m

𝐿𝑅𝑠 MCb 𝑂𝐵𝐹𝑏,𝑖 𝑃𝐶𝐸j,s

𝑃𝐺k,t 𝑅𝐶𝐵𝑐 𝑅𝐶𝐸 𝑅𝐶𝑀𝑏 TCDm 𝑇𝐶𝐸j,k,m TCLm 𝑇𝐶𝑀b,i,j,m

𝑈𝑅𝑠 𝑉𝐶𝑅j,s

sale price of byproduct c in planning period t, $/gal or $/MWh carbon emissions of harvesting biomass type b, ton CO2-equiv/ton carbon emissions of processing biomass type b with technology s, ton CO2equiv/ton carbon emissions of transporting bioethanol by transportation mode m, ton CO2-equiv/gal.km carbon emissions of transporting biomass type b by transportation mode m, ton CO2-equiv/ton.km distance between biorefinery j and demand zone k by transportation mode m, km distance between supply zone i and biorefinery j by transportation mode m, km export price of bioethanol in planning period t, $/gal annualized fixed opening cost of biorefinery j with technology s, $ harvest or purchase cost of biomass feedstock type b in supply zone i, $/ton import cost of bioethanol in planning period t, $/gal number of jobs created per year due to the construction of biorefinery j with technology s, job/ton (of biomass) number of jobs created due to harvesting unit of biomass type b, job/ton number of jobs created due to the producing a unit of bioethanol in biorefinery j with technology s, job/gal allocated land area of supply zone i for cultivation of biomass feedstock type b, ha loading and unloading cost of bioethanol by transportation mode m from biorefinery j to demand zone k, $ loading and unloading cost of biomass type b by transportation mode m from supply zone i to biorefinery j, $ minimum biomass quantity that can be processed by refineries with technology s, ton/year moisture content of biomass type b open-field burning fraction of biomass type b in supply zone i production cost of bioethanol in biorefinery j with technology s, $/gal gasoline production quantity of bioethanol demand zone (oil biorefinery) k in planning period t, ton/year reduction in carbon emissions from byproduct c, ton CO2-equiv/gal or ton CO2-equiv/MWh reduction in carbon emissions from bioethanol, ton CO2-equiv/gal reduction in carbon emissions by avoiding open-field burning of biomass type b, ton CO2-equiv/ton capacity of transportation mode m, dry ton transportation cost of bioethanol by transportation mode m per unit of distance between biorefinery j and demand zone k, $/km liquid capacity of transportation mode m, gal transportation cost of biomass type b by transportation mode m per unit of distance between supply zone i and biorefinery j, $/km maximum biomass quantity that can be processed by refineries with technology s, ton/year variable opening cost of biorefinery j with technology s, $/ton 12 ACS Paragon Plus Environment

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Page 13 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


𝑌𝑀b,t λb,s,c ν φb,s

𝜓 ωb,i,t

yield of biomass type b in planning period t, ton/ ha.year conversion factor of biomass feedstock type b through technology s to byproduct c, gal/dry ton or MWh/dry ton maximum allowed ratio of crop residues that can be removed from supply zones conversion factor of biomass feedstock type b through technology s to bioethanol gal/dry ton minimum acceptable efficiency percentage for biorefinery capacity harvesting loss fraction of biomass type b in supply zone i in planning period t

Binary variables

yj,s,t

1 if a biorefinery with technology s is opened at location j in planning period t and 0 otherwise

Continuous variables

CMb,j,s,t CRj,s,t ExEj,s,t HMb,i,t ImEk,t PBc,j,s,t PEj,s,t TEj,s,k,m,t TMb,i,j,m,t

quantity of biomass type b consumed for the production of bioethanol in biorefinery j with technology s in planning period t, ton biomass processing capacity of biorefinery j with technology s in planning period t, ton quantity of exported bioethanol from biorefinery j with technology s in planning period t, gal quantity of biomass type b harvested from supply zone i in planning period t, ton quantity of bioethanol imported to demand zone k in planning period t, gal quantity of byproduct c produced by biorefinery j with technology s in planning period t, gal or MWh quantity of bioethanol produced by biorefinery j with technology s in planning period t, gal quantity of bioethanol produced by biorefinery j with technology s and transported to demand zone k by transportation mode m in period t, gal quantity of biomass type b transported from supply zone i to biorefinery j by transportation mode m in planning period t, ton

3.2.1 Objective functions Economic objective function: The economic objective function (1) is to minimize total cost, or to be more precise, total cost minus revenues from byproducts sale and bioethanol export. Since, in fact, revenues from byproducts sale and bioethanol export reduce total cost of the considered LBSC, they are subtracted from total cost. Therefore, economic objective function can be stated as: min z1 = biomass harvesting and purchase cost + fixed opening cost of biorefineries + variable opening cost of biorefineries + bioethanol production cost + biomass transportation cost from the supply zones to the biorefineries + bioethanol transportation cost from the biorefineries to the demand zones + import cost of bioethanol − revenue from byproducts sale – revenue from bioethanol export. Costs and revenues are considered on an annual basis. The method used by Osmani and Zhang54 is applied to provide economy of scale in capacity by breaking down the investment cost into fixed opening cost and variable (capacity) opening cost (the second and third terms). This is because investment cost of biorefineries includes a fixed part which does not depend on biorefineries capacity and a variable part based on their capacity which is calculated through multiplying capacity of biorefineries by unit variable opening cost. Biomass transportation cost, 13 ACS Paragon Plus Environment


Page 14 of 37

the fifth term, is obtained through multiplying the amount of transported biomass by unit transportation cost between two nodes. Unit transportation cost is calculated through dividing total transportation cost (the numerator) by capacity (the denominator). The numerator itself is sum of transportation cost and loading and unloading cost. Since biomass is assumed to be transported wet, moisture content is applied to account for wetness of the biomass transported. Bioethanol transportation cost, the sixth term, is calculated in a similar way. Biomass harvesting and purchase cost, bioethanol production and bioethanol import cost (the first, fourth and seventh terms) are easily obtained through multiplying the harvested amount of biomass, produced amount of bioethanol and imported amount of bioethanol by their related unit costs. Also the last two terms, i.e. revenues from byproducts sales and bioethanol export, are acquired by multiplying the amounts of byproducts sale and bioethanol export by sale and export prices, respectively. min z1 =

∑∑∑𝐻𝐶𝑀

b,iHMb,i,t

i

+

b

∑∑∑𝐹𝐶𝑅

j,syj,s,t

𝑗

∑∑∑𝑃𝐶𝐸

j,sPEj,s,t

j

+

t

s

+

𝑠

+

j

∑∑∑∑∑TM

t

b

∑∑∑𝑉𝐶𝑅

𝑡

i

j

m

s

b,i,j,m,t

t

(

1

TCDm

(1 - MCb)

)

DisRDj,k,m𝑇𝐶𝐸j,k,m + 𝐿𝐶𝐸j,k,m

j,s,k,m,t

𝑗

s

k

m

𝑐

𝑗

𝑠

𝑡

m

t

c,j,s,t

)(

DisSRi,j,m𝑇𝐶𝑀b,i,j,m + 𝐿𝐶𝑀b,i,j,m

∑∑∑∑∑TE ( TCL ― ∑∑∑∑PB 𝐵𝑃 ― ∑∑∑ExE +

j,sCRj,s,t

t

+

∑∑ImE k

)

k,t 𝐼𝑚𝑃𝑡

t

j,s,t 𝐸𝑥𝑃𝑡

𝑐,t

𝑗

s

t

(1) Environmental objective function: The environmental objective (2) is to maximize the reduction in GHG emissions i.e., decrease in GHG emissions minus increase in GHG emissions. It can be formulated as: max z2 = reduction in emissions due to gasoline being substituted with bioethanol + reduction in emissions due to substitution of conventional electricity with bioelectricity or heating oil with mixed alcohols + reduction in emissions due to avoiding open-field burning of lignocellulosic biomass − increase in emissions from biomass harvesting − increase in emissions from converting biomass into bioethanol − increase in emissions due to biomass transportation from supply zones to biorefineries − increase in emissions due to bioethanol transportation from biorefineries to demand zones. max z2 =

∑∑BF 𝑃𝐺 𝑅𝐶𝐸 + ∑∑∑∑PB t

𝑘

―

𝑐

∑∑∑𝐶𝐻𝑀 HM b

i

―

𝑘

𝑡

b

b,i,t

t

𝑗

―

𝑠

i

j

m

∑∑∑∑∑TM 𝑏

i

j

m

b,i,j,m,t 𝑅𝐶𝑀𝑏𝑂𝐵𝐹𝑏,𝑖

t

b,sCMb,j,s,t

𝑗

𝑠

𝑡

b,𝑚TMb,i,j,m,t DisSRi,j,m

𝑏

+

∑∑∑∑𝐶𝑃𝑀 𝑏

∑∑∑∑∑𝐶𝑇𝑀

c,j,s,t 𝑅𝐶𝐵𝑐

𝑡

―

t

∑∑∑∑∑𝐶𝑇𝐸

m TEj,s,k,m,t DisRDj,k,m

𝑗

s

k

m

t

(2) Social objective function: Due to structure of the considered bioethanol supply chain network, three terms like as Osmani and Zhang1 are considered in the social objective function to maximize local job opportunities created along the supply chain as follows: max z3 = number of jobs created due to harvesting biomass + number of jobs created due to bioethanol production + number of jobs created due to construction of biorefineries. 14 ACS Paragon Plus Environment

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max z3 =

∑∑∑HM

b,i,t 𝐽𝐻𝑀𝑏

i

b

+

t

∑∑∑PE j

s

j,s,t𝐽𝑃𝐸j,s

t

+

∑∑∑PCRE j

s

j,s,t𝐽𝐶𝑅j,s

(3)

t

Note that the average number of created jobs is considered to calculate the coefficients of the social objective function. In harvesting phase, the jobs are created due to biomass cultivation, collection and baling, in bioethanol production phase, they are created in relation with pretreatment, conversion process and biomass and bioethanol storage, and finally jobs are created in biorefinery construction stage due to building biorefinery plant and construction and installation of the equipment.

3.2.2 Constraints Biomass availability constraint (4) HMb,i,t ≤ ν𝑌𝑀b,tLi,b ∀i,b,t Eq. (4) shows that each type of biomass feedstock harvested from each supply zone in each planning period cannot be greater than biomass yield of that supply zone considering maximum fraction of residues that could be removed from supply zones. Material balance constraints ∑ ∑ TMb,i,j,m,t = HMb,i,t (1 - ωb,i,t) ∀i,b,t (5) j m Eq. (5) illustrates that the quantity of each type of biomass feedstock transported from each supply zone in each planning period equals the harvested biomass considering harvesting loss fraction of biomass feedstock. (6) (7) Eqs. (6) and (7) for each biorefinery show mass balances of biomass feedstock and bioethanol, respectively. Eq. (6) states that the quantity of each type of biomass transported to each biorefinery in each planning period equals the quantity of consumed biomass feedstock in production of bioethanol. Eq. (7) states that for each biorefinery the quantity of produced bioethanol in each planning period equals summation of the quantity of transported bioethanol to the demand zones and the quantity of exported bioethanol. ∑i∑mTMb,i,j,m,t = ∑sCMb,j,s,t ∀b,j,t PEj,s,t = ∑k∑mTEj,s,k,m,t + ExEj,s,t ∀j,s,t

Conversion constraints PEj,s,t = ∑bφb,s CMb,j,s,t ∀j,s,t PBc,j,s,t = ∑bλb,s,c CMb,j,s,t ∀j,s,c,t

(8) (9) Eqs. (8) and (9) show the quantity of bioethanol and byproducts produced in each biorefinery through each technology in each planning period, respectively. Capacity constraints (10) 𝐿𝑅𝑠 yj,s,t ≤ CRj,s,t ≤ 𝑈𝑅𝑠 yj,s,t ∀j,s,t Eq. (10) illustrates that the processing capacity of a biorefinery (if established) in each planning period must not be less than the minimum acceptable capacity and cannot be greater than the maximum acceptable capacity.

(11) 𝜓CRj,s,t ≤ ∑bCMb,j,s,t ≤ CRj,s,t ∀j,s,t Eq. (11) states that for each biorefinery the consumed biomass in each planning period should be less than the processing capacity and greater than the minimum efficiency percentage of biorefinery capacity. 15 ACS Paragon Plus Environment


Page 16 of 37

∑s yj,s,t ≤ 1 ∀j,t Eq. (12) assigns at most one biorefinery to each candidate location.

(12)

yj,s,t ― 1 ≤ yj,s,t ∀j,s,t Eq. (13) ensures once a biorefinery opens it will not shut down.

(13)

(14) CRj,s,t ― 1 ≤ CRj,s,t ∀j,s,t Eq. (14) indicates that the processing capacity of a biorefinery can increase but not decrease in subsequent planning periods. Demand satisfaction constraint ∑j∑𝑠∑mTEj,s,k,m,t +I𝑚𝐸k,t ≥ 𝐵𝐹𝑡𝑃𝐺k,t ∀k,t

(15) Eq. (15) shows that in each planning period the bioethanol transported from biorefineries plus imported bioethanol to each demand zone satisfies bioethanol demand of each demand zone considering the planned blending fraction with gasoline.

4 Proposed robust possibilistic programming approach In this section, first fuzzy mathematical programming (especially Me measure) is briefly explained and then the approach based on fuzzy programming and the robust possibilistic approach proposed by Mousazadeh et al.58 is applied to cope with the inherent uncertainties of the LBSC model.

4.1 Fuzzy mathematical programming In possibilistic chance-constrained programming (PCCP), the DM determines a minimum confidence level (𝛼) for each possibilistic chance constraint that should be satisfied.59 Possibility (Pos) and necessity (Nec) measures, defined by Dubois and Prade60 are two basic fuzzy measures widely used to enable the DM to include such confidence in the PCCP models. While Pos measure has an extreme optimistic attitude towards chance constraints, Nec measure has an extreme pessimistic attitude. Next fuzzy measure in the literature, introduced by Liu and Liu,61 is credibility (Cr) measure which is actually the average of Pos and Nec measures. The most recent fuzzy measure introduced by Xu and Zhou62 is Me measure which is actually a generalized form of Cr measure. Me measure provides more flexibility by applying a parameter known as optimistic– pessimistic parameter. Me measure can be defined as a convex combination of Pos and Nec measures shown in eq. (16). (16) 𝑀𝑒{𝐴} = 𝛾 . 𝑃𝑜𝑠 {𝐴} + (1 ― 𝛾) . Nec {𝐴} = Nec {𝐴} + 𝛾 (𝑃𝑜𝑠 {𝐴} ― Nec {𝐴}) In which 𝛾 (0 ≤ 𝛾 ≤ 1) is the optimistic–pessimistic parameter. It is worth noting that when 𝛾 takes values 0, 1 and 0.5, Me measure transforms into Nec, Pos and Cr measures, respectively. For a given trapezoidal fuzzy variable 𝜉 = (r1, r2, r3, r4 ), 𝑟1 ≤ 𝑟2 ≤ 𝑟3 ≤ 𝑟4 with a membership function as eq. (17),


Page 17 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


𝜇(𝑥) =

{

𝑥 ― 𝑟1

if 𝑟1 ≤ 𝑥 ≤ 𝑟2 if 𝑟2 ≤ 𝑥 ≤ 𝑟3

𝑟2 ― 𝑟1

1

𝑟4 ― 𝑥

(17)

if 𝑟3 ≤ 𝑥 ≤ 𝑟4 otherwise

𝑟4 ― 𝑟3

0

it can be written that:58

{ {

0

𝛾𝑟2 ― 𝑟1 𝛾 𝑀𝑒{𝜉 ≤ 𝑥} =

𝑀𝑒{𝜉 ≥ 𝑥} =

if 𝑥 ≤ 𝑟1

𝑥 ― 𝑟1

if 𝑟1 ≤ 𝑥 ≤ 𝑟2 if 𝑟2 ≤ 𝑥 ≤ 𝑟3 𝑥 ― 𝑟3

𝛾 + (1 ― 𝛾)𝑟4 ― 𝑟3 1

1

(18)

if 𝑟3 ≤ 𝑥 ≤ 𝑟4 if 𝑥 ≥ 𝑟4

if 𝑥 ≤ 𝑟1 𝑟2 ― 𝑥

𝛾 + (1 ― 𝛾)𝑟2 ― 𝑟1 𝛾 𝑟4 ― 𝑥

𝛾𝑟4 ― 𝑟3 0

if 𝑟1 ≤ 𝑥 ≤ 𝑟2 if 𝑟2 ≤ 𝑥 ≤ 𝑟3

(19)

if 𝑟3 ≤ 𝑥 ≤ 𝑟4 if 𝑥 ≥ 𝑟4

and for 𝑟1 ≥ 0, according to Xu and Zhou62, the expected value of fuzzy variable 𝜉 applying Me measure is: +∞

0

𝐸𝑀𝑒[𝜉] = ∫0 𝑀𝑒{𝜉 ≥ 𝑥}𝑑𝑥 ― ∫ ―∞𝑀𝑒{𝜉 ≤ 𝑥}𝑑𝑥 =

1―𝛾 2

𝛾

(𝑟1 + 𝑟2) + 2(𝑟3 + 𝑟4)

(20)

For 0 ≤ 𝛾 ≤ 0.5, the following equations hold:58 𝑥 ― 𝑟3

𝑀𝑒{𝜉 ≤ 𝑥} ≥ 𝛼⇔𝛾 + (1 ― 𝛾)𝑟4 ― 𝑟3 ≥ 𝛼⇔𝑥 ≥ 𝑟2 ― 𝑥

𝑀𝑒{𝜉 ≥ 𝑥} ≥ 𝛼⇔𝛾 + (1 ― 𝛾)𝑟2 ― 𝑟1 ≥ 𝛼⇔𝑥 ≤

(𝛼 ― 𝛾)𝑟4 + (1 ― 𝛼)𝑟3 (1 ― 𝛾) (𝛼 ― 𝛾)𝑟1 + (1 ― 𝛼)𝑟2 (1 ― 𝛾)

(21) (22)

For 0.5 ≤ 𝛾 ≤ 1, one can refer to Mousazadeh et al.58

4.2 The basic possibilistic chance-constrained programming (BPCCP) model In order to avoid prolongation, the LBSC model can be rewritten in a compact form (23) as: min 𝑧1 = 𝑓 ∙ 𝑌 + 𝑔 ∙ 𝑋 ― ℎ ∙ 𝑋 max 𝑧2 = 𝑘 ∙ 𝑋



Page 18 of 37

max 𝑧3 = 𝑙 ∙ 𝑋 s.t. (23)

𝑋 ≤ 𝐴 ∙ 𝑌𝑀 𝐵∙𝑋=0 𝐶∙𝑌≤𝑋≤𝐷∙𝑌 𝐸∙𝑌≥0 𝐹∙𝑌≤1 𝑋 ≥ 𝐺 ∙ 𝑃𝐺 𝑌 ∈ {0,1}, X ≥ 0

Where vector f indicates fixed opening costs of biorefineries, vector g corresponds to other costs including variable opening costs of biorefineries, biomass harvest cost, bioethanol production cost and biomass and bioethanol transportation costs and vector h represents bioethanol export price and byproducts sale price. Also, vectors k and l denote GHG emissions and job creation coefficients, respectively. Matrices A, B, C, D, E, F and G are coefficient matrices of the constraints, in which parameters YM and PG are biomass yields and gasoline production of oil refineries. It should be notified that tilde (~) shows imprecise parameters that are presented as fuzzy numbers. Vector X displays positive continuous variables and vector Y shows binary variables. Note that, without loss of generality, the second and third objective functions will be omitted from now on, since they could be simply treated as the first one. In this paper imprecise parameters are considered to have trapezoidal possibility distributions characterized by their four prominent points (for example, 𝜉 = (r1, r2, r3, r4 )), as shown in Fig. 2.

Fig. 2. The trapezoidal possibility distribution of fuzzy parameter 𝜉.

According to Pishvaee et al.63 and Me measure introduced by Xu and Zhou,62 the BPCCP model (24) could be formulated as follows: min 𝐸[𝑧1] = 𝐸[𝑓] ∙ 𝑌 + 𝐸[𝑔] ∙ 𝑋 ― 𝐸[ℎ] ∙ 𝑋 s.t. 𝑀𝑒{𝑋 ≤ 𝐴 ∙ 𝑌𝑀} ≥ 𝛼 18 ACS Paragon Plus Environment

Page 19 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


𝐵∙𝑋=0 (24)

𝐶∙𝑌≤𝑋≤𝐷∙𝑌 𝐸∙𝑌≥0 𝐹∙𝑌≤1 𝑀𝑒{𝑋 ≥ 𝐺 ∙ 𝑃𝐺} ≥ 𝛽 𝑌 ∈ {0,1}, X ≥ 0

The crisp counterpart (25) of the BPCCP model based on the expected value operator and Me measure can be written as:

[1 ―2 𝛾(𝑓 1―γ ― [ (h 2

min 𝐸[𝑧1] =

(1)

(1)

] [ )] ∙ X

]

𝛾 1―𝛾 𝛾 (𝑔(1) + 𝑔(2)) + (𝑔(3) + 𝑔(4)) ∙ 𝑋 + 𝑓(2)) + (𝑓(3) + 𝑓(4)) ∙ Y + 2 2 2 γ + h(2)) + (h(3) + h(4) 2

s.t. 𝑋≤𝐴∙

[

(𝛼 ― 𝛾)𝑌𝑀(1) + (1 ― 𝛼)𝑌𝑀(2) 1―𝛾

] (25)

𝐵∙𝑋=0 𝐶∙𝑌≤𝑋≤𝐷∙𝑌 𝐸∙𝑌≥0 𝐹∙𝑌≤1 𝑋≥𝐺∙

[

(𝛽 ― 𝛾)𝑃𝐺(4) + (1 ― 𝛽)𝑃𝐺(3) 1―𝛾

]

𝑌 ∈ {0,1}, X ≥ 0

4.3 Hybrid robust possibilistic programming approach Although the BPCCP model takes into account feasibility robustness, it is not sensitive to deviation of objective function from its expected value and does not consider optimality robustness. According to Pishvaee et al.63 a solution of an optimization problem is robust if it has both feasibility robustness and optimality robustness. Feasibility robustness denotes that the solution should keep its feasibility for (almost) all possible values of uncertain parameters and optimality robustness denotes that the value of objective function should nearly keep its optimality or have the least undesirable deviation from the optimal value for (almost) all possible values of uncertain parameters. In order to include optimality robustness in addition to feasibility robustness, four versions of HRPP models introduced by Mousazadeh et al.58 are used in this paper. These models applying robust and fuzzy approaches, involve three realistic models including 19 ACS Paragon Plus Environment


Page 20 of 37

HRPP-I, HRPP-II, HRPP-III, and the hard worst-case robust possibilistic programming (HWRPP) model. Considering the Me measure, the HRPP-I model (26) can be defined as: min 𝐸[𝑧1] + 𝜙(𝑧1𝑚𝑎𝑥 ― 𝑧1𝑚𝑖𝑛) + 𝛿1𝐴 ∙

[

+ 𝛿2𝐺 ∙ 𝑃𝐺(4) ―

[

(𝛼 ― 𝛾)𝑌𝑀(1) + (1 ― 𝛼)𝑌𝑀(2) 1―𝛾

(𝛽 ― 𝛾)𝑃𝐺(4) + (1 ― 𝛽)𝑃𝐺(3) 1―𝛾

― 𝑌𝑀(1)

]

]

s.t. 𝑋≤𝐴∙

[

(𝛼 ― 𝛾)𝑌𝑀(1) + (1 ― 𝛼)𝑌𝑀(2) 1―𝛾

]

𝐵∙𝑋=0 (26)

𝐶∙𝑌≤𝑋≤𝐷∙𝑌 𝐸∙𝑌≥0 𝐹∙𝑌≤1 𝑋≥𝐺∙

[

(𝛽 ― 𝛾)𝑃𝐺(4) + (1 ― 𝛽)𝑃𝐺(3) 1―𝛾

]

𝑌 ∈ {0,1}, X ≥ 0

The objective function has three more terms in addition to the expected value of z1. While the first term in the objective function tends to minimize the expected value of z1, the second term minimizes the maximum deviation over and under expected value of z1 and therefore tries to maintain the optimality robustness of the solution. It is worth mentioning that z1max and z1min are the upper and lower extreme values of z1, and can be calculated as: 𝑧1𝑚𝑎𝑥 = 𝑓(4) ∙ 𝑌 + 𝑔(4) ∙ 𝑋 ― ℎ(1) ∙ 𝑋 (27)

𝑧1𝑚𝑖𝑛 = 𝑓(1) ∙ 𝑌 + 𝑔(1) ∙ 𝑋 ― ℎ(4) ∙ 𝑋

The last two terms in the objective function try to keep the feasibility robustness of the solution through minimizing the difference between RHS of chance constraints and their worst-case values, 𝑌𝑀(1) and 𝑃𝐺(4). It should be noted that parameters 𝛿1 and 𝛿2 are unit penalty cost of such possible violations. Also parameter 𝜙 indicates the importance weight of optimality robustness against feasibility robustness. For the cases that the DM is sensitive to the deviation of objective function value over the expected optimal value (in minimization objectives) or under the expected optimal value (in maximization objectives), HRPP-II model is introduced by Mousazadeh et al.58 with the objective function as follows and constraints the same as HRPP-I: min 𝐸[𝑧1] + 𝜙(𝑧𝑚𝑎𝑥 ― 𝐸[𝑧1]) + 𝛿1𝐴 ∙

[

(𝛼 ― 𝛾)𝑌𝑀(1) + (1 ― 𝛼)𝑌𝑀(2) 1―𝛾 20

ACS Paragon Plus Environment

― 𝑌𝑀(1)

] (28)

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[

+ 𝛿2𝐺 ∙ 𝑃𝐺(4) ―

(𝛽 ― 𝛾)𝑃𝐺(4) + (1 ― 𝛽)𝑃𝐺(3) 1―𝛾

]

Furthermore, HRPP-III model is introduced for a less compensator DM with objective function as follows and constraints the same as HRPP-I: min 𝐸[𝑧1] + 𝜙𝑧𝑚𝑎𝑥 + 𝛿1𝐴 ∙

[

+ 𝛿2𝐺 ∙ 𝑃𝐺(4) ―

[

(𝛼 ― 𝛾)𝑌𝑀(1) + (1 ― 𝛼)𝑌𝑀(2) 1―𝛾

(𝛽 ― 𝛾)𝑃𝐺(4) + (1 ― 𝛽)𝑃𝐺(3) 1―𝛾

― 𝑌𝑀(1)

]

] (29)

Also the most conservative and risk-averse version of robust programming, i.e. the worstcase robust programming approach considers the worst-case value of uncertain parameters both in the objective function and constraints. HWRPP model (30) is formulated as: min 𝑧𝑚𝑎𝑥 s.t. 𝑋 ≤ 𝐴 ∙ 𝑌𝑀(1) 𝐵∙𝑋=0 (30)

𝐶∙𝑌≤𝑋≤𝐷∙𝑌 𝐸∙𝑌≥0 𝐹∙𝑌≤1 𝑋 ≥ 𝐺 ∙ 𝑃𝐺(4) 𝑌 ∈ {0,1}, X ≥ 0

5 Implementation and evaluation A case study located in Iran is applied in order to evaluate the performance and desirability of the proposed BPCCP, HRPP-I, HRPP-II, HRPP-III, and HWRPP models. The developed models are coded in GAMS 24.8.5 and solved by CPLEX solver using an Intel core i7 2.60 GHz laptop with 8 GB of RAM.

5.1 Case study Iran has a large area and a great variety of climate, which makes it possible to cultivate a wide range of biomass needed to produce biofuels. Corn, wheat, barley and rice are among the main cereal crops cultivated and consumed in Iran. Considerable part of residues of these crops is left unused that can be harvested and used in producing lignocellulosic bioethanol. Therefore, corn stover, wheat straw, barley straw and rice straw are considered as biomass feedstocks in this study. 23 provinces out of 31 provinces of Iran which produce more than 90% of biomass feedstock are potential biomass supply zones. Since it is assumed that the produced bioethanol will be blended into gasoline in oil refineries, all 9 oil refineries of Iran are considered as bioethanol demand zones. 21 ACS Paragon Plus Environment


Page 22 of 37

And 14 provinces of Iran, selected based on some geographical, social and underlying structural considerations are potential biorefinery locations. Demand of bioethanol in each demand zone (i.e. oil refinery) is determined through multiplying the volume of gasoline produced in each oil refinery and the desired blending percentage of bioethanol with gasoline. Desired blending percentage is assumed to be 5% in beginning of the planning horizon which increases to 10% after 5 years. The planning horizon is 10 years, broken into 10 one-year planning periods. It should be noted that the most possible values of the fuzzy parameters are determined based on the related literature and available historical data, and the range of variation of fuzzy parameters are estimated based on experts’ opinion. Due to space limitation, the input data and their sources are provided through tables I1-I8 in the supporting information document.

5.2 Implementation results The steps taken in order to assess the desirability and robustness of the proposed models can be summarized as: Step 1: Determine the positive ideal solution (PIS) and negative ideal solution (NIS) of each objective function for each of the proposed models as follows: 𝑧𝑃𝐼𝑆 𝑖 = 1,2,3

𝑧𝑁𝐼𝑆 𝑖 = 1,2,3

{

min {𝑧𝑖(𝑥𝑖∗ )} max {𝑧𝑖(𝑥𝑖∗ )}

𝑖=1 𝑖 = 2,3

{

max {𝑧𝑖(𝑥𝑖∗ )} min {𝑧𝑖(𝑥𝑖∗ )}

𝑖=1 𝑖 = 2,3

(31)

Step 2: Calculate a linear membership function for the first objective function (minimization) as follows: 𝜇1(𝑥) =

{

if 𝑧1 < 𝑧𝑃𝐼𝑆 1

1 𝑧𝑁𝐼𝑆 1 ― 𝑧1 𝑧𝑁𝐼𝑆 1

―

𝑁𝐼𝑆 if 𝑧𝑃𝐼𝑆 1 ≤ 𝑧1 ≤ 𝑧1

𝑧𝑃𝐼𝑆 1

(32)

if 𝑧1 > 𝑧𝑁𝐼𝑆 1

0

and linear membership functions for the second and third objective functions (maximization) as follows (i=2, 3):

𝜇𝑖(𝑥) =

{

if 𝑧𝑖 > 𝑧𝑃𝐼𝑆 𝑖

1 𝑧𝑖 ― 𝑧𝑁𝐼𝑆 𝑖

if 𝑧𝑁𝐼𝑆 ≤ 𝑧𝑖 ≤ 𝑧𝑃𝐼𝑆 𝑖 𝑖

𝑧𝑃𝐼𝑆 ― 𝑧𝑁𝐼𝑆 𝑖 𝑖 0

(33)

if 𝑧𝑖 < 𝑧𝑁𝐼𝑆 𝑖

Step 3: Applying the TH aggregation function (introduced by Torabi and Hassini64) convert the multi-objective model into a single-objective model as follows:

∑𝜎 𝜇 (𝑥)

max 𝜏(𝑥) = 𝜌𝜏0 + (1 ― 𝜌)

𝑖 𝑖

𝑖

s.t. 22 ACS Paragon Plus Environment

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(34)

𝜏0 ≤ 𝜇𝑖(𝑥) 𝑥 ∈ 𝑆(𝑥)

In which parameter 𝜎𝑖 indicates the relative weight of the ith objective function that must be greater than 0 and summation on all 𝜎𝑖 must be equal to 1. As can be seen, decision variable 𝜏0 is the minimum satisfaction degree of all objectives and therefore it will have a value between 0 and 1 inclusive. Parameter 𝜌 denotes the relative importance of the minimum satisfaction degree to aggregated satisfaction degree of all objectives. The more is the value of 𝜌, the more the DM tends to maximize minimum satisfaction degree of all objective functions. Parameter 𝜌 should also have a value between 0 and 1 inclusive. Torabi and Hassini64 proved that the optimal solution of the model (34) is an efficient solution to the original multi-objective model and cannot be dominated by any other solution. Additionally, the Pareto efficient front can be achieved by changing the values of 𝜎𝑖 and 𝜌. Step 4: Compare the results of the different variations of the model and choose the one that most satisfies DMs' preferences. It should be noted that none of the variants of the model is the best and the most appropriate one can be selected according to the nature of the problem and preferences of DMs. The results of the variants of the model are summarized in Table 3. In this study, DMs prefer HRPP-I(c) due to their priorities in objective functions (𝜎1 = 0.7, 𝜎2 = 0.2 and 𝜎3 = 0.1) and values of 𝜏. Location of thermochemical and biochemical biorefineries as well as existing oil refineries of HRPP-I(c) version are illustrated in Fig. 3. Size of the biorefinery icons (i.e. circle or triangle) is correlated to its processing capacity. As can be seen in the figure, a biochemical biorefinery is to be located in the province of Tehran and four thermochemical biorefineries are to be located in the provinces of East Azerbaijan, Kermanshah, Khuzestan and Fars with the capacity levels of values reported in Table 3. Table 4 represents transportation of biomass feedstock from supply zones to each biorefinery. Because of space limitation all four kinds of biomass have been aggregated together. And transportation of bioethanol from each biorefinery to oil refineries is represented in Table 5. Required biomass feedstock of East Azerbaijan biorefinery is supplied from the provinces of Ardabil, East Azerbaijan, West Azerbaijan and Zanjan. Fars biorefinery obtains its biomass feedstock from provinces of Fars, Isfahan, Kerman and Kurdistan. Biomass feedstock for Kermanshah biorefinery is supplied from provinces of Hamadan, Ilam and Kermanshah. Provinces of Khuzestan, Lorestan and Markazi are responsible to provide the necessary biomass feedstock of Khuzestan biorefinery. Unlike other biorefineries which attain their required biomass feedstock from adjacent or close provinces, Tehran biorefinery acquires its biomass feedstock from 16 provinces out of 23 biomass supplier provinces. This result could be justified due to higher amount of bioethanol demand in Tehran. Table 5 shows that the bioethanol produced in East Azerbaijan and Tehran biorefineries is sent to Tabriz, Bandar Abbas, Isfahan and Arak oil refineries. Tehran biorefinery also provides the bioethanol demand of Tehran oil refinery. Fars biorefinery sends its production to Shiraz, Bandar Abbas, Isfahan and Lavan oil refineries. The bioethanol produced in Kermanshah and Khuzestan biorefineries provide the required bioethanol of Kermanshah and Abadan oil refineries. They also provide part of bioethanol demand of Arak oil refinery. The results reported in Tables 4 and 5 also reveal that biomass and bioethanol are mainly shipped by railroad transportation system and in most cases where railroad transportation is not selected, lack of access to rail network has been the cause which emphasizes the cost-effectiveness of railroad transportation.




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Table 3. Performance of the proposed models Models

Parameters

τ

𝜇1

𝜇2

𝜇3

BPCCP(a)

λ=0.00, α,β=1.00

0.80

0.80

0.80

0.80

1 (1, 1.51E+06), 2 (1, 1.57E+06), 7 (2, 1.45E+06), 9 (2, 1.29E+06), 13 (2, 2.97

BPCCP(b)

λ=0.25, α,β=0.75

0.81

0.81

0.81

0.81

1 (1, 1.99E+06), 2 (1, 1.67E+06), 7 (2, 1.48E+06), 9 (2, 1.69E+06), 11 (2, 2.14

BPCCP(c)

λ=0.50, α,β=0.50

0.80

0.80

0.80

0.80

1 (1, 1.83E+06), 2 (1, 1.66E+06), 7 (2, 1.54E+06), 9 (2, 1.37E+06), 13 (2, 2.93

HRPP-I(a)

λ=0.00

0.81

0.99

0.59

0.59

2 (1, 1.32E+06), 7 (1, 1.00E+06), 9 (1, 1.35E+06), 12 (1, 3.00E+06)

HRPP-I(b)

λ=0.25

0.82

0.99

0.61

0.61

2 (1, 1.23E+06), 7 (1, 1.00E+06), 9 (1, 1.30E+06), 12 (1, 2.92E+06)

HRPP-I(c)

λ=0.50

0.83

0.97

0.66

0.66

1 (1, 1.52E+06), 2 (1, 1.33E+06), 7 (1, 1.22E+06), 9 (1, 1.28E+06), 13 (2, 1.79

HRPP-II(a)

λ=0.00

0.81

0.81

0.81

0.81

1 (1, 2.26E+06), 2 (1, 1.84E+06), 7 (2, 1.49E+06), 9 (2,1.61E+06), 11 (2, 1.85E

HRPP-II(b)

λ=0.25

0.80

0.80

0.80

0.80

1 (1, 2.31E+06), 2 (1, 1.86E+06), 7 (2, 1.51E+06), 9 (2, 1.62E+06), 11 (2, 1.85

HRPP-II(c)

λ=0.50

0.81

0.81

0.81

0.81

1 (1, 2.37E+06), 2 (1, 1.89E+06), 7 (2, 1.54E+06), 9 (2, 1.66E+06), 11 (2, 1.87

HRPP-III(a)

λ=0.00

0.80

0.80

0.82

0.80

1 (1, 1.84E+06), 2 (1, 1.62E+06), 7 (2, 1.49E+06), 9 (2, 1.33E+06), 13 (2, 2.78

HRPP-III(b)

λ=0.25

0.81

0.80

0.82

0.80

1 (1, 186 E+06), 2 (1, 1.63E+06), 7 (2, 1.51E+06), 9 (2, 1.34 E+06), 13 (2, 2.81

HRPP-III(c)

λ=0.50

0.81

0.80

0.81

0.80

1 (1, 1.89E+06), 2 (1, 1.66E+06), 7 (2, 1.54E+06), 9 (2, 1.37E+06), 13 (2, 2.87

0.88

0.88

0.88

0.88

1 (1, 1.96E+06), 2 (2, 1.78E+06), 7 (2, 1.45E+06), 9 (2, 1.56E+06), 11 (2, 2.03

HWRPP


Biorefinery location (conversion technology, final capacity in tons of bioma


Fig 3. Location of existing oil refineries and biorefineries of the preferred RPP model.

Table 4. Biomass feedstock logistics for the model biorefineries Biorefinery Location j Azerbaijan, East

Supply zone i (average transported biomass in tons for years 1-5, average transported biomass in tons for years 6-10, transportation mode*) 1 (0, 4.22E+05, 1), 2 (0, 4.25E+05, 1), 3 (0, 3.74E+05, 1), 23 (0, 3.02E+05, 1)

Fars

4 (5.62E+05, 5.62E+05, 2), 10 (8.29E+04, 1.24E+05, 2), 11 (0, 8.08E+04, 2), 16 (5.45E+05, 5.65E+05, 1)

Kermanshah

7 (0, 4.71E+05, 1), 9 (0, 1.83E+05, 1), 12 (0, 5.69E+05, 1)

Khuzestan

15 (6.61E+05, 7.59E+05, 2), 17 (3.23E+05, 3.23E+05, 2), 18 (1.98E+05, 2.02E+05, 2)

Tehran

2 (2.93E+03, 2.93E+03, 2), 3 (4.02E+01, 4.02E+01, 2), 5 (2.04E+05, 2.16E+05, 1), 6 (4.62E+05, 4.62E+05, 2), 7 (0, 6.96E+03, 1), 10 (4.95E+04, 8.05E+03, 2), 11 (0, 5.37E+04, 2), 14 (2.63E+03, 3.84E+05, 2), 15 (9.79E+04, 0, 2), 17 (7.49E+03, 7.49E+03, 2), 18 (3.81E+04, 3.39E+04, 2), 19 (3.37E+05, 3.37E+05, 2), 20 (1.84E+05, 1.84E+05, 2), 21 (0, 3.69E+03, 2), 22 (6.57E+04, 6.57E+04, 2), 23 (3.26E+05, 2.35E+04, 2)

*1 refers to road and 2 refers to rail transportation.


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Table 5. Bioethanol Logistics for oil refineries Biorefinery Location j Azerbaijan, East

Demand zone k (average transported bioethanol in gallons for years 1-5, average transported bioethanol in gallons for years 6-10, transportation mode*) 1 (0, 3.17E+07, 2), 3 (0, 1.44E+07, 2), 4 (0, 2.89E+07, 2), 7 (0, 3.65E+07, 2)

Fars

2 (8.92E+06, 1.78E+07, 2), 3 (1.06E+07, 0, 2), 4 (5.60E+07, 7.94E+07, 2), 9 (1.09E+07, 0 ,1)

Kermanshah

5 (0, 5.94E+06, 1), 6 (0, 5.41E+06, 1), 7 (0, 7.90E+07, 1),

Khuzestan

5 (2.97E+06, 0, 1), 6 (4.95E+07, 9.37E+07, 1), 7 (3.43E+07, 0, 2)

Tehran

1 (1.59E+07, 0, 2), 3 (3.15E+07, 2.17E+07, 2), 4 (0, 3.68E+06, 2), 7 (3.80E+07, 2.91E+07, 2), 8 (3.27E+07, 6.54E+07, 2)

*1 refers to road and 2 refers to rail transportation.

5.3 Sensitivity analysis Sensitivity analysis is performed on parameters 𝜌 and 𝜎𝑖 of the most suitable variant of the HRPP model, HRPP-I (c), to reveal the effect of changes of these parameters on the optimal solution. As mentioned before, changing the values of the parameters 𝜌 and 𝜎𝑖 of TH approach can provide Pareto efficient front. It is obvious that changes in these parameters can shift the optimal solution considerably. The results of sensitivity analysis on these parameters are demonstrated in Fig. 4 a-e. Since summation on parameters 𝜎1, 𝜎2 and 𝜎3 is equal to 1, the values of 𝜎1 and 𝜎2 are displayed on the figure and the value of 𝜎3 is 1 ― 𝜎1 ― 𝜎2. It can be seen that Figs. 4 a and 4 e have the most and least dispersion in value of THaggregated objective function and satisfaction degree of objective functions. And as the value of 𝜌 increases from Fig. 4 a to Fig. 4 e, dispersion in value of TH-aggregated objective function decreases so much that all values of 𝜏 are the same in Fig. 4 e. Since, for higher values of 𝜌 in THaggregated objective function it becomes more important to maximize minimum satisfaction degree of all objectives. Also satisfaction degrees of three objective functions have the highest difference with each other in Fig. 4 a and the difference decreases from Fig. 4 a to Fig. 4 e so that there is no difference among 𝜇1, 𝜇2 and 𝜇3 in Fig. 4 e. In addition, it can be seen that in each chart for the same value of 𝜌, as the value of 𝜎1, 𝜎2 or 𝜎3 increases, satisfaction degree of corresponding objective function rises.



a.

Sensitivity analysis on parameters 𝜎1, 𝜎2, 𝜎3 and 𝜌 for 𝜌 = 0.

b.

Sensitivity analysis on parameters 𝜎1, 𝜎2, 𝜎3 and 𝜌 for 𝜌 = 0.25.

c. Sensitivity analysis on parameters 𝜎1, 𝜎2, 𝜎3 and 𝜌 for 𝜌 = 0.5.

d. Sensitivity analysis on parameters 𝜎1, 𝜎2, 𝜎3 and 𝜌 for 𝜌 = 0.75.


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e. Sensitivity analysis on parameters 𝜎1, 𝜎2, 𝜎3 and 𝜌 for 𝜌 = 1. Fig. 4. Sensitivity analysis on parameters 𝜎1, 𝜎2, 𝜎3 and 𝜌.

5.4 Comparative analysis The proposed HRPP model includes different variants (10 versions) of RPP method based on Me measure. It provides greater flexibility for DMs in two ways. First, this model is more flexible than other models based on necessity, possibility and credibility measures by applying an optimistic-pessimistic parameter (λ) and forming a convex combination of extreme attitudes. Actually Cr, Nec and Pos measures are special cases of Me measure. Second, the proposed HRPP model incorporates three realistic models (with different objective functions) and the HWRPP model which DMs can choose among them according to their preferences and priorities. In the similar RPP models the DMs are provided with less flexibility in their choice. For example Pishvaee et al.63 only consider Nec measure with λ=0 (versions HRPP-I(a), HRPP-II(a) and HRPP-III(a) of the hybrid model presented in Table 3). And Pishvaee et al.59 only consider Cr measure with λ=0.5, (versions HRPP-I(c), HRPP-II(c) and HRPP-III(c) of Table 3). Also, compared with the model proposed by Xu and Zhu 62, the proposed HRPP model provides more flexibility. Xu and Zhu 62 find the upper bound (UAM) and lower bound (LAM ) of the model based on Pos and Nec measures, and give interval values as the model's solutions. Actually λ exists in their method but the point is that it only exists in the objective function. Therefore, DMs' optimistic or pessimistic attitude only affects the optimality of the model and not its feasibility.

5.5 Policy scenarios and managerial implications There exist some crucial questions in DMs minds such as: Does the blending percentage of bioethanol affect the unit production cost of bioethanol and subsequently the unit price of gasoline blended with bioethanol? Does increase in the blending percentage result in more job creation? Or does it have any effect on import and export volumes? In order to better reply these questions and evaluate the impact of blending percentage on some critical variables three more scenarios are defined in addition to the base scenario. Scenario 0: The blending percentage of bioethanol is 5% for the first 5 years of the planning horizon and 10% for the second 5 years. This scenario is the base scenario of the paper. Scenario 1: The blending percentage of bioethanol is 5% for the whole 10 years of the planning horizon. Scenario 2: The blending percentage of bioethanol is 7% for the whole 10 years of the planning horizon. Scenario 3: The blending percentage of bioethanol is 10% for the whole 10 years of the planning horizon. The results of some important variables are summarized in Table 6. Total bioethanol supply (column 2) is the amount of bioethanol supply considering both bioethanol domestic production and its import in the planning horizon (10 years) and total bioethanol supply cost (column 3) is its 29 ACS Paragon Plus Environment


supply cost. Column 4 calculates average bioethanol supply cost through dividing total bioethanol supply cost (column 3) by total bioethanol supply (column 2). Column 5 shows average cost of a gallon of gasoline blended with bioethanol assuming average cost of 1.7 $ per gallon for pure gasoline and according to bioethanol blending percentage of each scenario. And Column 6 shows average percentage increase in cost of blended gasoline compared to 1.7 $ per gallon for pure gasoline. Columns 7 and 8 indicate average amount of annual bioethanol export and import, respectively. And column 9 shows average percentage of bioethanol imported. Average annual biomass available for production of bioethanol and average annual amount of biomass consumed in production of bioethanol are presented in columns 10 and 11. Column 12 illustrates average percentage of available biomass consumed to produce bioethanol through dividing column 11 by column 10. Columns 13 and 14 show total reduction in GHG emissions and total number of jobs created. Finally, column 15 represents the value of TH-aggregated objective function. Considering the results represented, some managerial implications are drawn as follows:


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Table 6. Results comparison of defined scenarios Total bioethanol supply cost ($)

Average bioethanol supply cost ($/gal)

Average blended gasoline cost ($/gal)

Average increase in blended gasoline cost

Average annual bioethanol export (gal/year)

Average annual bioethanol import (gal/ year)

Average bioethanol import percentage

Average annual biomass available (ton/year)

Average annual biomass consumption (ton/year)

Average biomass consumption percentage

Total reduction in GHG emissions (ton CO2equ.)

Total job creation (job)

4.37E+09

1.29E+10

2.96

1.79

5.56%

0.00

(0.00, 6.99E+07)*

8.00%

7.47E+06

(4.15E+06, 7.15E+06)*

(55.55%, 95.76%)*

1.48E+07

3.13E+05

0

2.91E+09

9.43E+09

3.24

1.78

4.53%

7.67E+07

0.00

0.00%

7.47E+06

5.04E+06

67.44%

8.40E+06

3.12E+05

0

4.06E+09

1.18E+10

2.91

1.78

4.98%

0.00

8.60E+06

2.12%

7.47E+06

5.54E+06

74.18%

1.35E+07

3.09E+05

0

5.83E+09

1.76E+10

3.02

1.83

7.76%

0.00

1.80E+08

30.82%

7.47E+06

5.58E+06

74.69%

2.12E+07

3.12E+05

0

Total bioethanol Scenario supply (ton) Scenario 0 Scenario 1 Scenario 2 Scenario 3

*First and second numbers in parentheses correspond to years 1-5 and 6-10, respectively.

Table 7. Results comparison of defined scenarios with domestic production priority

Scenario

Scenario 0 Scenario 1 scenario 2 Scenario 3

Total bioethanol supply (ton)

Total bioethanol supply cost ($)

Average bioethanol supply cost ($/gal)

Average increase in bioethanol supply cost

Average annual bioethanol export (gal/year)

Average annual bioethanol import (gal/ year)

Average bioethanol import percentage

Average annual biomass available (ton/year)

Average annual biomass consumption (ton/year)

Average biomass consumption percentage

Toral reduction in GHG emissions (ton CO2equ.)

Total job creation (job)

4.33E+09

1.42E+10

3.29

11.09%

(1.87E+8, 0.00)*

(0.00, 2.68E+7)*

3.10%

7.47E+06

(6.52E+06, 7.47E+06)*

(87.18%, 100%)*

1.27E+07

4.21E+05

0

2.91E+09

9.43E+09

3.24

0.00%

7.67E+07

0.00

0.00%

7.47E+06

5.04E+06

67.44%

8.40E+06

3.12E+05

0

4.08E+09

1.31E+10

3.22

10.78%

8.53E+07

0.00

0.00%

7.47E+06

7.47E+06

100.00%

1.19E+07

4.24E+05

0

5.77E+09

1.76E+10

3.06

1.33%

0.00

2.68E+07

4.65%

7.47E+06

7.47E+06

100.00%

1.86E+07

4.41E+05

0

*First and second numbers in parentheses correspond to years 1-5 and 6-10, respectively.



 



 

 

Average bioethanol supply cost (column 4) varies between 2.96 and 3.24 $/gal. Scenarios 2 and 1 show the least and the most bioethanol supply costs. Blending bioethanol with gasoline increases cost of gasoline, since currently average cost of bioethanol is more than average cost of gasoline. Assuming average cost of 1.7 $ per gallon for gasoline and considering average bioethanol supply cost (column 4) will lead to an increase in gasoline cost between 4.53% and 7.76% in different scenarios (column 6). Despite the fact that there is no limitation to bioethanol export in the constraints of the proposed model, its value is calculated as zero in all scenarios except for scenario 1 (column 7), indicating that bioethanol export is not economical. This can also be implied by comparing bioethanol export price in the model (2 $/gal) and the calculated bioethanol supply cost (column 4) in each scenario. Even in scenario 1 the amount of export is very low compared to total bioethanol supply. Average bioethanol import percentage (column 9) has the least values in scenarios 1 and 2, 0 and 2.12%, respectively. Considering average bioethanol import percentage (column 9) of each scenario and average biomass consumption percentage (column 12) reveals that in most scenarios import is done although a great percentage of the biomass is left unused. As the blending percentage of bioethanol increases, GHG emissions reduction (column 13) increases by roughly the same proportion. Increase in bioethanol blending percentage does not create a considerable amount of job opportunities (column 14), since a great percentage of bioethanol is provided by importation.

Here another question arises; how much subsidy for a gallon of bioethanol undertaken by government can tip the scale in favor of domestic production against importation while maintaining current price of bioethanol. In order to answer this question, the above mentioned scenarios are considered once more, this time, assuming that bioethanol is provided as much as possible from the internal resources of biomass feedstock and bioethanol imports will only be carried out if the internal resources of biomass feedstock are insufficient. Table 7 shows the results.  



Obviously scenario 1 shows no difference compared to Table 6, since in Table 6 no imports were made for scenario 1. Internal biomass feedstock is not sufficient to satisfy the desired level of bioethanol blending percentage in scenarios 0 and 3. Therefore, 3.10% of bioethanol demand in scenario 0 and 4.65% of bioethanol demand in scenario 3 are met by bioethanol import (column 8). Comparing column 4 of Tables 6 and 7, government should pay up to 0.33 $/gal as subsidies to maintain the previous price of bioethanol and blended gasoline consequently, assuming that biomass cost is the same as Table 6. It should be noted that biomass cost is likely to increase as biomass consumption increases. Therefore, even more subsidies should be paid.


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



GHG emissions reduction (column 12) has worse (smaller) values compared to relevant scenarios in Table 6. But, this does not necessarily mean that more domestic production leads to less reduction in GHG emissions. It just occurs because GHG emissions due to bioethanol production at biorefineries and biomass and bioethanol transportation across the supply chain are calculated for domestic production but not for bioethanol import. Job creation (column 13) increases significantly in most scenarios, except for scenario 1. Therefore, government may be able to cover some part of subsidy cost from the special budget allocated for employment.

6 Conclusions and future research This paper has developed a multi-objective MILP model for design and planning of a lignocellulosic biofuel supply chain. The model determines strategic decisions, such as facilities location, initial capacity, capacity expansion and technology type, in addition to tactical decisions, such as biomass allocation, production amounts, and transportations through the supply chain. To cope with inherent epistemic uncertainties in the input data involving market prices, biofuel demands, biomass supply, GHG emissions and job creation coefficients, a robust possibilistic programming (RPP) approach is applied. Several variants of RPP models, including the hard worst-case and the realistic RPP approaches are developed based on Me fuzzy measure. The proposed hybrid RPP model provides DMs with greater flexibility compared with other approaches in the literature. To the best of our knowledge, there is no research work applying Me measure and a hybrid RPP approach in the design of a BSCN, so far. The proposed hybrid RPP model is applied to perform a real case study of bioethanol supply chain located in Iran. The HRPP-I(c) variant of the HRPP model is recognized as the most suitable one based on the DMs' priorities. According to this variant of the HRPP model, a biochemical biorefinery is to be located in the province of Tehran and four thermochemical biorefineries are to be located in the provinces of East Azerbaijan, Fars, Kermanshah and Khuzestan. In addition, four scenarios defined on blending percentage of bioethanol are compared and a number of beneficial managerial implications are drawn, some of which are: Average cost of gasoline blended with bioethanol does not vary much (1.78 to 1.83 $/gal) in different scenarios. GHG emissions reduction is proportional to bioethanol blending percentage while job creation does not differ much (3.09E+05 to 3.13E+05 jobs) in different scenarios. In order to create more job opportunities, it is necessary to put limitations on amount of bioethanol import which also leads to more use of available internal biomass feedstock. But this increases bioethanol supply cost up to 11.09% and results in a less reduction in GHG emissions. Considering multiple types of uncertainty including randomness, epistemic and deep uncertainties can be a direction for future research. Also incorporating disruptional uncertainties in addition to inherent epistemic uncertainties could be another interesting extension to make the model more realistic. Mentioned expansions result in more complicated models and one may need to develop customized heuristics or metaheuristics in order to solve the model in a reasonable processing time. Supporting Information Values of input parameters used in the case study are presented in Tables S1-S8; key deterministic parameters and nominal values of uncertain parameters (Tables S1 and S2), allocated



land area of supply zones for cultivation of different biomass feedstocks (Table S3), nominal gasoline production of bioethanol demand zones (Table S4), road and rail distance between supply zones and potential biorefinery locations (Tables S5 and S6), road and rail distance between potential biorefinery locations and demand zones (Table S7 and S8). This information is available free of charge via the Internet at http://pubs.acs.org/. References 1. Osmani, A.; Zhang, J., Multi-period stochastic optimization of a sustainable multi-feedstock second generation bioethanol supply chain− A logistic case study in Midwestern United States. Land Use Policy 2017, 61, 420-450. 2. Babazadeh, R., Optimal design and planning of biodiesel supply chain considering non-edible feedstock. Renewable and Sustainable Energy Reviews 2017, 75, 1089-1100. 3. Dufey, A., Biofuels production, trade and sustainable development: emerging issues. Iied: 2006. 4. Muktham, R.; Bhargava, S. K.; Bankupalli, S.; Ball, A. S., A review on 1st and 2nd generation bioethanol production-recent progress. Journal of Sustainable Bioenergy Systems 2016, 6 (03), 72. 5. Ghaderi, H.; Pishvaee, M. S.; Moini, A., Biomass supply chain network design: an optimizationoriented review and analysis. Industrial crops and products 2016, 94, 972-1000. 6. Balaman, Ş. Y.; Selim, H., A decision model for cost effective design of biomass based green energy supply chains. Bioresource technology 2015, 191, 97-109. 7. Pishvaee, M. S.; Torabi, S. A., A possibilistic programming approach for closed-loop supply chain network design under uncertainty. Fuzzy sets and systems 2010, 161 (20), 2668-2683. 8. Bairamzadeh, S.; Pishvaee, M. S.; Saidi-Mehrabad, M., Multiobjective robust possibilistic programming approach to sustainable bioethanol supply chain design under multiple uncertainties. Industrial & Engineering Chemistry Research 2015, 55 (1), 237-256. 9. Babazadeh, R., A robust optimization method to green biomass-to-bioenergy systems under deep uncertainty. Industrial & Engineering Chemistry Research 2018, 57(23), 7975–7986. 10. Ghaderi, H.; Moini, A.; Pishvaee, M. S., A multi-objective robust possibilistic programming approach to sustainable switchgrass-based bioethanol supply chain network design. Journal of Cleaner Production 2018, 179, 368-406. 11. Zandi Atashbar, N.; Labadie, N.; Prins, C., Modelling and optimisation of biomass supply chains: a review. International Journal of Production Research 2017, 1-25. 12. Sharma, B.; Ingalls, R. G.; Jones, C. L.; Khanchi, A., Biomass supply chain design and analysis: basis, overview, modeling, challenges, and future. Renewable and Sustainable Energy Reviews 2013, 24, 608-627. 13. Yue, D.; You, F.; Snyder, S. W., Biomass-to-bioenergy and biofuel supply chain optimization: overview, key issues and challenges. Computers & Chemical Engineering 2014, 66, 36-56. 14. Awudu, I.; Zhang, J., Uncertainties and sustainability concepts in biofuel supply chain management: A review. Renewable and Sustainable Energy Reviews 2012, 16 (2), 1359-1368. 15. Lee, M.; Cho, S.; Kim, J., A comprehensive model for design and analysis of bioethanol production and supply strategies from lignocellulosic biomass. Renewable Energy 2017, 112, 247-259. 16. Mutenure, M.; Čuček, L.; Egieya, J.; Isafiade, A. J.; Kravanja, Z., Optimization of bioethanol and sugar supply chain network: a South African case study. Clean Technologies and Environmental Policy 2018, 1-24. 17. Giarola, S.; Bezzo, F.; Shah, N., A risk management approach to the economic and environmental strategic design of ethanol supply chains. biomass and bioenergy 2013, 58, 31-51.


Page 34 of 37

Page 35 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


18. Marufuzzaman, M.; Ekşioğlu, S. D.; Hernandez, R., Environmentally friendly supply chain planning and design for biodiesel production via wastewater sludge. Transportation Science 2014, 48 (4), 555-574. 19. Paolucci, N.; Bezzo, F.; Tugnoli, A., A two-tier approach to the optimization of a biomass supply chain for pyrolysis processes. Biomass and Bioenergy 2016, 84, 87-97. 20. Cambero, C.; Sowlati, T.; Pavel, M., Economic and life cycle environmental optimization of forest-based biorefinery supply chains for bioenergy and biofuel production. Chemical Engineering Research and Design 2016, 107, 218-235. 21. Santibañez-Aguilar, J. E.; Morales-Rodriguez, R.; González-Campos, J. B.; Ponce-Ortega, J. M., Stochastic design of biorefinery supply chains considering economic and environmental objectives. Journal of cleaner production 2016, 136, 224-245. 22. d’Amore, F.; Bezzo, F., Strategic optimisation of biomass-based energy supply chains for sustainable mobility. Computers & Chemical Engineering 2016, 87, 68-81. 23. Ng, R. T.; Maravelias, C. T., Design of cellulosic ethanol supply chains with regional depots. Industrial & Engineering Chemistry Research 2015, 55 (12), 3420-3432. 24. Duarte, A.; Sarache, W.; Costa, Y., Biofuel supply chain design from Coffee Cut Stem under environmental analysis. Energy 2016, 100, 321-331. 25. Wheeler, J.; Caballero, J. A.; Ruiz-Femenia, R.; Guillén-Gosálbez, G.; Mele, F. D., MINLP-based Analytic Hierarchy Process to simplify multi-objective problems: Application to the design of biofuels supply chains using on field surveys. Computers & Chemical Engineering 2017, 102, 64-80. 26. Wheeler, J.; Páez, M.; Guillén-Gosálbez, G.; Mele, F., Combining multi-attribute decision-making methods with multi-objective optimization in the design of biomass supply chains. Computers & Chemical Engineering 2018, 113, 11-31. 27. Ghasemi Nodooshan, K.; Moraga, R. J.; Chen, S.-J.; Nguyen, C.; Wang, Z.; Mohseni, S., An environmental and economic optimization of Algal Biofuel Supply Chain with multiple technological pathways. Industrial & Engineering Chemistry Research 2018, 57(20), 6910–6925. 28. Babazadeh, R.; Razmi, J.; Pishvaee, M. S.; Rabbani, M., A sustainable second-generation biodiesel supply chain network design problem under risk. Omega 2017, 66, 258-277. 29. Gonela, V.; Zhang, J.; Osmani, A., Stochastic optimization of sustainable industrial symbiosis based hybrid generation bioethanol supply chains. Computers & Industrial Engineering 2015, 87, 40-65. 30. Yue, D.; Slivinsky, M.; Sumpter, J.; You, F., Sustainable design and operation of cellulosic bioelectricity supply chain networks with life cycle economic, environmental, and social optimization. Industrial & Engineering Chemistry Research 2014, 53 (10), 4008-4029. 31. Roni, M. S.; Eksioglu, S. D.; Cafferty, K. G.; Jacobson, J. J., A multi-objective, hub-and-spoke model to design and manage biofuel supply chains. Annals of Operations Research 2017, 249 (1-2), 351380. 32. Miret, C.; Chazara, P.; Montastruc, L.; Negny, S.; Domenech, S., Design of bioethanol green supply chain: Comparison between first and second generation biomass concerning economic, environmental and social criteria. Computers & Chemical Engineering 2016, 85, 16-35. 33. Cambero, C.; Sowlati, T., Incorporating social benefits in multi-objective optimization of forestbased bioenergy and biofuel supply chains. Applied Energy 2016, 178, 721-735. 34. Gonela, V.; Zhang, J.; Osmani, A.; Onyeaghala, R., Stochastic optimization of sustainable hybrid generation bioethanol supply chains. Transportation Research Part E: Logistics and Transportation Review 2015, 77, 1-28. 35. Osmani, A.; Zhang, J., Stochastic optimization of a multi-feedstock lignocellulosic-based bioethanol supply chain under multiple uncertainties. Energy 2013, 59, 157-172.



36. Tong, K.; You, F.; Rong, G., Robust design and operations of hydrocarbon biofuel supply chain integrating with existing petroleum refineries considering unit cost objective. Computers & Chemical Engineering 2014, 68, 128-139. 37. Azadeh, A.; Arani, H. V.; Dashti, H., A stochastic programming approach towards optimization of biofuel supply chain. Energy 2014, 76, 513-525. 38. Shabani, N.; Sowlati, T., A hybrid multi-stage stochastic programming-robust optimization model for maximizing the supply chain of a forest-based biomass power plant considering uncertainties. Journal of Cleaner Production 2016, 112, 3285-3293. 39. Sharifzadeh, M.; Garcia, M. C.; Shah, N., Supply chain network design and operation: Systematic decision-making for centralized, distributed, and mobile biofuel production using mixed integer linear programming (MILP) under uncertainty. Biomass and Bioenergy 2015, 81, 401-414. 40. Li, Q.; Hu, G., Supply chain design under uncertainty for advanced biofuel production based on bio-oil gasification. Energy 2014, 74, 576-584. 41. Tong, K.; Gleeson, M. J.; Rong, G.; You, F., Optimal design of advanced drop-in hydrocarbon biofuel supply chain integrating with existing petroleum refineries under uncertainty. biomass and bioenergy 2014, 60, 108-120. 42. Azadeh, A.; Arani, H. V., Biodiesel supply chain optimization via a hybrid system dynamicsmathematical programming approach. Renewable Energy 2016, 93, 383-403. 43. Mohseni, S.; Pishvaee, M. S.; Sahebi, H., Robust design and planning of microalgae biomass-tobiodiesel supply chain: A case study in Iran. Energy 2016, 111, 736-755. 44. Bairamzadeh, S.; Saidi-Mehrabad, M.; Pishvaee, M. S., Modelling different types of uncertainty in biofuel supply network design and planning: A robust optimization approach. Renewable Energy 2018, 116, 500-517. 45. Marufuzzaman, M.; Eksioglu, S. D.; Huang, Y. E., Two-stage stochastic programming supply chain model for biodiesel production via wastewater treatment. Computers & Operations Research 2014, 49, 1-17. 46. Balaman, Ş. Y.; Selim, H., Sustainable design of renewable energy supply chains integrated with district heating systems: A fuzzy optimization approach. Journal of cleaner production 2016, 133, 863885. 47. Zhang, Y.; Jiang, Y., Robust optimization on sustainable biodiesel supply chain produced from waste cooking oil under price uncertainty. Waste Management 2017, 60, 329-339. 48. Gao, J.; You, F., Modeling framework and computational algorithm for hedging against uncertainty in sustainable supply chain design using functional-unit-based life cycle optimization. Computers & Chemical Engineering 2017, 107, 221-236. 49. Xie, F.; Huang, Y., A multistage stochastic programming model for a multi-period strategic expansion of biofuel supply chain under evolving uncertainties. Transportation Research Part E: Logistics and Transportation Review 2018, 111, 130-148. 50. Ghelichi, Z.; Saidi-Mehrabad, M.; Pishvaee, M. S., A stochastic programming approach toward optimal design and planning of an integrated green biodiesel supply chain network under uncertainty: A case study. Energy 2018, 156, 661-687. 51. Ren, J.; Dong, L.; Sun, L.; Goodsite, M. E.; Tan, S.; Dong, L., Life cycle cost optimization of biofuel supply chains under uncertainties based on interval linear programming. Bioresource technology 2015, 187, 6-13. 52. Giarola, S.; Shah, N.; Bezzo, F., A comprehensive approach to the design of ethanol supply chains including carbon trading effects. Bioresource technology 2012, 107, 175-185. 53. Castillo-Villar, K. K.; Eksioglu, S.; Taherkhorsandi, M., Integrating biomass quality variability in stochastic supply chain modeling and optimization for large-scale biofuel production. Journal of cleaner production 2017, 149, 904-918.


Page 36 of 37

Page 37 of 37 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


54. Osmani, A.; Zhang, J., Economic and environmental optimization of a large scale sustainable dual feedstock lignocellulosic-based bioethanol supply chain in a stochastic environment. Applied Energy 2014, 114, 572-587. 55. Tong, K.; Gong, J.; Yue, D.; You, F., Stochastic programming approach to optimal design and operations of integrated hydrocarbon biofuel and petroleum supply chains. ACS Sustainable Chemistry & Engineering 2013, 2 (1), 49-61. 56. Ben-Tal, A.; El Ghaoui, L.; Nemirovski, A., Robust optimization. Princeton University Press: 2009; Vol. 28. 57. Bertsimas, D.; Sim, M., The price of robustness. Operations research 2004, 52 (1), 35-53. 58. Mousazadeh, M.; Torabi, S.; Pishvaee, M.; Abolhassani, F., Health service network design: a robust possibilistic approach. International Transactions in Operational Research 2018, 25 (1), 337-373. 59. Pishvaee, M. S.; Torabi, S. A.; Razmi, J., Credibility-based fuzzy mathematical programming model for green logistics design under uncertainty. Computers & Industrial Engineering 2012, 62 (2), 624-632. 60. PRADE, D. D.-H.; Dubois, D., Possibility theory. Plenum Press, New York: 1988. 61. Liu, B.; Liu, Y.-K., Expected value of fuzzy variable and fuzzy expected value models. IEEE transactions on Fuzzy Systems 2002, 10 (4), 445-450. 62. Xu, J.; Zhou, X., Approximation based fuzzy multi-objective models with expected objectives and chance constraints: Application to earth-rock work allocation. Information Sciences 2013, 238, 75-95. 63. Pishvaee, M. S.; Razmi, J.; Torabi, S. A., Robust possibilistic programming for socially responsible supply chain network design: A new approach. Fuzzy sets and systems 2012, 206, 1-20. 64. Torabi, S. A.; Hassini, E., An interactive possibilistic programming approach for multiple objective supply chain master planning. Fuzzy sets and systems 2008, 159 (2), 193-214.

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