Multiobjective Robust Possibilistic Programming Approach to

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A multi-objective robust possibilistic programming approach to sustainable bioethanol supply chain design under multiple uncertainties Samira Bairamzadeh, Mir Saman Pishvaee, and Mohammad Saidi-Mehrabad Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b02875 • Publication Date (Web): 09 Dec 2015 Downloaded from http://pubs.acs.org on December 15, 2015

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Industrial & Engineering Chemistry Research

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A multi-objective robust possibilistic programming approach to sustainable

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bioethanol supply chain design under multiple uncertainties

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Samira Bairamzadeh, Mir Saman Pishvaee*, Mohammad saidi-Mehrabad

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School of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

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Abstract: In this paper, a multi-objective mixed-integer programming (MILP) model is proposed to

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address the optimal design and planning of lignocellulosic biofuel supply chain (LBSC) considering a

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sustainable supply chain optimization framework including economic, environmental and social

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objectives. The proposed model is capable of determining strategic decisions, including biomass sourcing

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and allocation, locations, capacity levels and technology type selection of biorefinery facilities as well as

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the tactical decisions including inventory levels, production amounts, and shipments among the network.

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Eco-indicator 99 which is a well-known LCA-based environmental impact assessment method is

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incorporated in the model to estimate the relevant environmental impacts. In order to handle the inherent

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uncertainty of input data in the concerned problem, a novel multi-objective robust possibilistic

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programming (MORPP) approach is developed. The performance of the model is demonstrated through a

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case study developed for biofuel supply chain in Iran. Diverse solutions achieved by the proposed

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MORPP approach outperform deterministic solutions in terms of given performance measures.

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Keywords: Lignocellulosic biofuel supply chain, Biorefinery, Robust optimization, Sustainability, Life cycle assessment, Robust possibilistic programming

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1. Introduction

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Due to increasing energy demand and significant social, economic and environmental problems caused by

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fossil fuels, researchers have been attracted to develop renewable energy sources (RES) to secure the

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energy consumption, protect the environment, and promote regional development.

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Biofuels as one of the renewable energy sources include liquid, gas and solid fuels which are in some way

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derived from biomass. Liquid biofuels and various biogases are types of biofuels. The liquid fuels and

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especially bioethanol, which is produced from lignocellulosic raw materials are used as substitutes as well

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as additives for transportation fuel. Biofuels can help reduce greenhouse gas (GHG) emissions and lead to

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new jobs and greater vitality in rural areas 1-3.

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Lignocellulosic biomass feedstocks as one of the most promising resources for biofuels include

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agricultural residues (e.g., corn stover), energy crops (e.g., switchgrass), and wood residues (e.g., forest

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thinning) 3. As of 2012, Cellulosic ethanol production has not yet been produced on a commercial scale

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and has been limited to pilot-scale projects 4. Lignocellulosic biomass can be converted into ethanol

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through either biochemical (involving hydrolysis and fermentation) or thermochemical (involving

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gasification and catalytic synthesis) conversion processes 5.

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Agricultural residues such as wheat straw (by-product of wheat production) and corn stover (the above

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ground remainder of the corn plant after grain harvest) appears to be attractive feedstocks for bioethanol

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production since their utilization does not directly compete with food for humans and feed for animals. In

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this study, we consider corn stover and wheat straw as sources of linocellulosic biomass for bioethanol

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production.

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Asia is the largest potential producer of bioethanol from crop residues and wasted crop in which Rice

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straw, wheat straw and corn stover are the most favorable bioethanol feedstocks. The main feedstocks in

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Europe and North America are wheat straw and corn stover, respectively 6. Iran’s diversity of terrain and

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climate enables cultivation of various types of biomass in order to produce biofuels 7.

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One of the most important barriers of a strong bioenergy sector development is the cost of the biomass

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supply chain because of economics, energetic and environmental implications caused by handling and

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transport of biomass from the source location to the conversion facility. Besides, not enough attention is

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paid to incorporate uncertainties related to the biomass supply, transportation, production, operation,

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demand and price in the biofuel supply chain optimal design. Uncertainties will result in either an

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infeasible supply chain design or suboptimal performance

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sustainability as a holistic perspective of supply chain processes has become a key topic in the

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sustainability literature in recent years due to increasing concerns about the social and environmental

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impacts of business processes. Stakeholders and governments are pressuring companies to incorporate all

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three aspects of sustainability (i.e., economic, environmental and social aspects) in their business

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strategies. Therefore, it is of great importance to consider uncertainties and sustainability concepts in

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biofuel supply chain planning and network design.

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The major uncertainties in the biofuel supply chain are related to raw material supply, biofuel demand and

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commodity prices. A number of works have been done to incorporate uncertainties in biofuel supply

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. On the other hand, supply chain


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chain optimal design. The most widely used approaches to deal with uncertain parameters in optimization

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models include stochastic programming, robust optimization and fuzzy programming 10.

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Reviewed literature shows that scenario based and especially two-stage stochastic programming is the

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most common approach to deal with uncertainties in the biofuel supply chain optimization models. On the

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other hand, according to De Meyer et al.

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overall costs, overall profit, transportation costs, net present value, risk on assessment), energetic (e.g.

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energy return, energy use), environmental (e.g. CO2 emissions, greenhouse gas emissions, carbon

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footprint, global warming potential) and social (e.g. number of job opportunities). For example, Kim et al.

9

11

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considered objectives can be classified to economic (e.g.

presented a two-stage mixed integer stochastic model for the optimal design of biofuel supply chain

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networks under multiple uncertainties with the objective of maximizing the expected profit over the

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different scenarios. First, the single nominal scenario was optimized and then a multi-scenario approach

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was done based on some dominant parameters such as biomass availability, demand, products sale price

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and yields. They performed the robustness analysis and Monte Carlo global sensitivity analysis for the

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comparison of nominal design vs. scenario design. An et al.

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maximizing total system profit of a lignocellulosic biomass to biofuel supply chain that has multiple

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commodity flows which range from biomass suppliers to biofuel customers. Through a case study in

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Central Texas they applied the proposed model in order to design the most profitable biofuel supply chain

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under existing scenarios. Dal Mas et al.

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model for the optimal design and planning of biofuel supply chain considering uncertainties associated

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with product price and raw material costs. In order to optimize economic performances and minimize

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financial risk on investment, two objective functions of expected Net Present Value (eNPV) and the

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conditional Value at Risk (cVaR) were considered.

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In Awudu and Zhang 1, a stochastic linear programming model for the production planning of a multi-

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product biofuel supply chain subjected to demand and price uncertainties is developed. In order to solve

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the proposed model a bender’s decomposition with Monte Carlo simulation algorithm was applied.

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Kostin et al.

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strategic planning of integrated bioethanol–sugar supply chains under product demand uncertainty. A

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MILP model was presented for optimizing the expected performance of the concerned supply chain under

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several financial risk mitigation options. To solve the problem, they applied the Sample Average

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Approximation (SAA) algorithm, which provides as output a set of supply chain configurations that

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behave in different ways in the face of uncertainty. A mixed integer stochastic programming model was

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developed in Chen and fan 15 to address strategic planning of bioethanol supply chain as well as feedstock

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resource allocation under supply and demand uncertainties. The authors adopted two-stage stochastic

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13

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proposed a model with the objective of

established a multi-echelon, multi-period and stochastic MILP

proposed a two-stage stochastic mixed integer linear programming approach for the



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programming model, along with a Lagrange relaxation based decomposition algorithm to solve the

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proposed model in a case study. Gebreslassie et al.

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programming model to deal with the optimal design of hydrocarbon supply chains under uncertainties

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related to demand and supply accounting for the minimization of the expected annualized cost and

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CVaR/downside risk.

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Sharma et al. 17 presented an LP model with the objective function of minimizing cost of biomass supply

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to a biorefinery considering harvest, transportation, and storage costs. A scenario optimization model was

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developed to take into account the uncertainty of weather conditions in the biomass supply chain over a

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one-year planning period. Giarola et al.

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proposed a stochastic mixed-integer linear

discussed a risk management approach where multicriteria

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decision making tool was proposed to support strategic design and planning of ethanol supply chain under

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market uncertainty. Multi scenario two-stage stochastic model was used to deal with uncertainty arising

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from feedstock cost and carbon cost within an emission allowances trading scheme.

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A stochastic linear programming model was proposed by Azadeh et al.

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maximizing the expected profit of a biofuel supply chain which includes several capacitated biomass

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resources, biorefineries and demand points by considering both demand-side and supply-side

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uncertainties. They also developed a robust model for related biofuel supply chain. Osmani and Zhang 20

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proposed a two-stage stochastic MILP model for maximizing the expected profit as well as the net

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reduction in carbon emissions of a lignocellulosic bioethanol supply chain under supply, demand and

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price uncertainties. Tong et al.

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deal with the optimal design and operation of advanced hydrocarbon biofuel supply chain under various

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types of uncertainties. In order to consider data uncertainty, the conversion rate, operational cost

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associated with insertion point in petroleum refineries, biomass availability and product demand were

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modeled as fuzzy numbers and dealt with using a fuzzy possibilistic programming approach. In another

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paper, Tong et al.

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designing advanced hydrocarbon biofuel supply chain network with the objective function of the unit cost

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which was a modification and simplification of the previous work. In comparison with model proposed in

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Tong et al.

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and the multiperiod model was replaced by the single period. Bertsimas and Sim’s robust counterpart

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optimization was adopted as the robust optimization approach to handle the demand and supply

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uncertainty. Two tailored algorithms were adopted in solving the resulting MILFP problems.

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Recently, Balaman and Selim

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model for the planning of anaerobic digestion based biomass for bioenergy supply chain under inherent

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uncertainties. The proposed model was solved by using different fuzzy goal programming (FGP)

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21

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with the objective of

proposed a multiperiod mixed-integer linear programming model to

presented a mixed-integer linear fractional programming (MILFP) model for

overall cost minimization objective was replaced by the unit cost minimization objective

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developed a multi-objective mixed integer linear programming (MILP)


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approaches and the results were compared in terms of economic and environmental perspectives. In

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Balaman and Selim 24 a fuzzy multi objective mathematical model was proposed for designing bioenergy

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supply chain networks where simultaneously optimize multiple economic objectives and deal with

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uncertainties and decision makers’ aspiration levels for the objectives.

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Careful scanning of the resulting literature implies that although uncertainties in optimal design and

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planning of biofuel supply chain have already been studied in a substantial number of articles, but most of

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authors have proposed stochastic programming models to deal with inherent uncertainties in the

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concerned problem. However, due to a wide range of uncertainties in biofuel supply chain it seems that

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stochastic programming approaches have several major drawbacks

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, especially for strategic level

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decisions, such as high complexity and lack of uncertainty information. To avoid this, there are only few

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studies which have employed fuzzy possibilistic programming (e.g. Tong et al. 21) and robust optimization

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(e.g. Tong et al. 22) models for biofuel supply chain optimal design problems under epistemic uncertainty

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(i.e., lack of knowledge about the precise values of input data).

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In this study a multi-objective MILP model is proposed to address the optimal design and planning of

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lignocellulosic biofuel supply chain subjected to 3 uncertain parameters including: (1) uncertainty in the

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bioethanol demand, 2) uncertainty in the bioethanol and biomass main crop selling price and (3)

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uncertainty in the unit environmental impact coefficients in the Environmental objective function. The

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proposed mathematical model aims at simultaneous optimization of economic, environmental and social

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objective functions as three aspects of sustainability under various types of uncertainties. In order to

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handle the inherent uncertainty of input data in our problem, market prices, biofuel demand and

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environmental impact coefficients are treated as fuzzy numbers. A multi-objective robust possibilistic

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approach is developed to deal with multiple uncertainties associated with the biofuel supply chain design.

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Our major contribution is to develop a multi-objective robust possibilistic programming (MORPP)

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approach which extends robust possibilistic approach concepts to deal with multi-objective nature of the

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problem in the case that objective functions have uncertain parameters. To the best of our knowledge, it is

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the first time that robust possibilistic programming approach is developed for multi-objective problem in

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the presence of uncertain parameters in objective functions. The optimization model determines the

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strategic decisions, including biomass sourcing and allocation, selection of locations, technology type and

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capacity levels of facilities as well as the tactical decisions including inventory levels, production

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amounts, and shipments among the network. We also take into account typical features of the biofuel

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supply chain such as harvesting losses, biomass seasonality, deterioration of biomass during the storage,

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moisture content, diverse conversion pathway selection and product distribution. Additionally, Effective

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social and environmental life cycle assessment-based methods are adopted in the model to evaluate the 5 ACS Paragon Plus Environment


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relevant environmental and social impacts. The proposed model is applied to a case study of

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lignocellulosic supply chain established in Iran. The remainder of this paper has been organized as

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follows.

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The problem description is presented in the next section. Section 3 describes the development of the

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multi-objective MILP model. In Section 4, multi-objective robust possibilistic approach is introduced and

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utilized to solve the model. Section 5 describes the implementation and evaluation of the proposed

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approach for the applied case study and presents the computational results. Finally, Section 6 concludes

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the paper and offers some suggestions for future research.

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2. Problem definition

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The structure of the lignocellulosic biofuel supply chain network taken as a reference in this study is

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illustrated in Figure 1, in which network nodes represent biomass feedstock supply zones, potential

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locations for biorefineries and biofuel demand zones. Biomass-for-biofuels supply chain consists of

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biomass production in supply zones, biomass harvesting and transportation, biofuel production and

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distribution to customers. The biomass feedstocks are cultivated in the available supply zones and after

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harvesting, sent to the biorefinery facilities.

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In the biorefineries, lignocellulosic biomass is converted to bioethanol through biochemical or

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thermochemical technologies 26. Finally the produced bioethanol is shipped from the biorefineries to the

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customer demand zones.

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Lignocellulosic feedstocks go through hydrolysis and then fermentation and distillation in the

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biochemical conversion. Two major steps of thermochemical conversion are gasification and ethanol

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synthesis. There are several different technical approaches for performing aforementioned stages 5. Co-

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products of conversion technologies are electricity for biochemical process and mixed alcohols for

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thermochemical process.

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The environmental impact assessment is definitely one of the most important issues in selecting

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lignocellulosic bioethanol production technologies. LCA-based methods are widely used to measure the

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environmental impacts of a process or product throughout its life cycle 5.

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3. Model formulation

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A multi-objective MILP optimization model is proposed that consists of mass balances, production,

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conversion, operational capacity, transportation links weight limits and demand satisfaction constraints.


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Maximization of profit, minimization of environmental impacts and maximization of created job

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opportunities are considered as economic, environmental and social objective functions.

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𝑖

4

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 𝑓𝑏,𝑖,𝑗,𝑚,𝑡

𝑗

𝑘 𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑓𝑘,𝑙,𝑚,𝑡

5 6 7

⋮

⋮

𝑩𝒊𝒐𝒎𝒂𝒔𝒔 𝒔𝒖𝒑𝒑𝒍𝒚 𝒛𝒐𝒏𝒆𝒔 𝒊 = {𝟏, … , 𝑰}

𝑩𝒊𝒐𝒓𝒆𝒇𝒊𝒏𝒆𝒓𝒊𝒆𝒔

8 9 10

⋮

𝒋 = {𝟏, … , 𝑱}

𝑩𝒊𝒐𝒆𝒕𝒉𝒂𝒏𝒐𝒍 𝒅𝒆𝒎𝒂𝒏𝒅 𝒛𝒐𝒏𝒆𝒔 𝒌 = {𝟏, … , 𝑲}

11

Figure 1. Structure of biofuel supply chain network

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Also uncertainties related to bioethanol demand & sale price, main crop selling price and environmental

13

impacts, as well as harvesting losses and deterioration of biomass during the storage are considered in the

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model. The proposed multi-objective MILP model is capable of optimizing the following decision

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variables:

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• Land area assigned to each lignocellulosic biomass feedstock in each supply zone

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• Number, capacity level, technology type and locations of biorefineries

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• Quantity of harvested biomass main crop

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• Quantity of cultivated and harvested biomass feedstocks sent to the biorefineries

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• Quantity of produced bioethanol and by-products in each time period

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• Quantity of bioethanol sent to the customer demand zones in each time period

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• Inventory levels of lignocellulosic biomass and bioethanol in biorefineries at each time period

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• Shortage quantity of each demand zone in each time period

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A planning horizon is one year and is divided into months as time periods. All continuous decision

25

variables are non-negative, while all integer variables have 0-1 (i.e. binary) restriction. The verbal

26

description of the model can be represented as follows, which includes three objective functions covering

27

the three aspects of sustainability:



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(Verbal model) maximization of total profit = revenue from selling biomass main crops, bioethanol and byproducts - biomass renting, cultivation and harvesting costs - fixed opening costs of biorefineries – variable bioethanol production costs biomass and bioethanol inventory holding costs - variable transportation costs – unmet demand penalty costs Minimization of Environmental Impact = Damage to human health + Damage to ecosystem + Damage to resources Maximization of social impact = (number of job opportunities generated per year due to biomass and bioethanol production and transportation) × project life time duration + number of job opportunities generated due to construction of biorefineries Subject to:           

Limitation of land area assigned to lignocellulosic biomass feedstocks in each supply zone Limitation of harvested biomass quantity in each supply zone according to the yield considering harvest losses Mass balances for biomass regarding deterioration during storage Mass balances for bioethanol Conversion equations of biomass to bioethanol and byproducts Limitation of produced bioethanol according to corresponding biorefinery capacity level Operational capacity of biorefineries Weight capacity of transportation links Demand satisfaction Selection of capacity level and conversion technology type for installed biorefineries Decision variables non-negativity and binary constraints

1 2

3.1. Constraints

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3.1.1. Biomass sourcing and supply

4

Land area allocation limitation: Inequality (1) restricts assigned area for cultivating each lignocellulosic

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biomass feedstock in each supply zone (𝑥𝑖,𝑏 ) where the left side of the inequality states that assigned area

6

should be greater than currently assigned area of that zone and right side constraints the maximum

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corresponding allowable area for given feedstock. 𝑓𝑟𝑖,𝑏 . 𝑎𝑟𝑒𝑎𝑖𝑚𝑎𝑥 ≤ 𝑥𝑖,𝑏 ≤ 𝑖𝑛𝑐𝑟𝑎𝑡𝑒𝑏,𝑖 . 𝑓𝑟𝑖,𝑏 . 𝑎𝑟𝑒𝑎𝑖𝑚𝑎𝑥 ,

∀𝑖, 𝑏

(1)

8

Where 𝑓𝑟𝑖,𝑏 is the currently cultivated fraction of supply zone i for biomass type b and 𝑎𝑟𝑒𝑎𝑖𝑚𝑎𝑥 is the

9

total area of zone i. 𝑖𝑛𝑐𝑟𝑎𝑡𝑒𝑏,𝑖 is the maximum allowable increasing rate for cultivating feedstock b in

10

supply zone i.


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Harvested biomass quantity Limitation: The total amount of lignocellulosic biomass type b harvested

2

𝑟𝑒𝑠𝑖𝑑𝑢𝑒 from supply zone i at time period t (ℎ𝑟𝑣𝑏,𝑖,𝑡 ) is constrained by the amount of corresponding biomass

3

yield (𝑦𝑙𝑏 ) multiplied by the area assigned to the cultivation of this biomass (𝑥𝑖,𝑏 ). Similar equation exists

4

for the main crop harvested amount limitation. 𝜇 refers to the maximum ratio of crop residues which can

5

𝑟𝑒𝑠𝑖𝑑𝑢𝑒 be sustainably removed from supply zones. It should be noted that ℎ𝑟𝑣𝑏,𝑖,𝑡 is related to crop residues

6

as a feedstock and ℎ𝑟𝑣𝑏,𝑖,𝑡 is related to the corresponding main crop. (e.g., corn as a main crop and corn

7

stover as a crop residue and feedstock).

𝑐𝑟𝑜𝑝

𝑟𝑒𝑠𝑖𝑑𝑢𝑒 ∑ ℎ𝑟𝑣𝑏,𝑖,𝑡 ≤ 𝜇. 𝑦𝑙𝑏𝑟𝑒𝑠𝑖𝑑𝑢𝑒 . 𝑥𝑖,𝑏 ,

∀𝑖, 𝑏

(2)

𝑡 𝑐𝑟𝑜𝑝

𝑐𝑟𝑜𝑝

∑ ℎ𝑟𝑣𝑏,𝑖,𝑡 ≤ 𝑦𝑙𝑏

. 𝑥𝑖,𝑏 ,

∀𝑖, 𝑏

(3)

𝑡

8

3.1.2. Mass balances

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Mass balances of biomass feedstocks in each supply zone: amount of biomass type b harvested from

10

𝑟𝑒𝑠𝑖𝑑𝑢𝑒 supply zone i at time period t (ℎ𝑟𝑣𝑏,𝑖,𝑡 ) considering the harvest loss of biomass type b equals the

11

amount of harvested biomass type b shipped from supply zone i to biorefinery j via all transportation

12

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 modes at time period t (∑𝑗 ∑𝑚 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 ). 𝑟𝑒𝑠𝑖𝑑𝑢𝑒 ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 ℎ𝑟𝑣𝑏,𝑖,𝑡 , ∀𝑏, 𝑖, 𝑡 (1 − ℎ𝑙𝑜𝑠𝑠𝑏,𝑖,𝑡 ) = ∑ ∑ 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 𝑗

(4)

𝑚

13

Mass balances of biomass feedstocks in each biorefinery: amount of harvested biomass type b shipped

14

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 from supply zone i to biorefinery j at time period t (∑𝑗 ∑𝑚 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 ) plus the inventory from

15

previous time period considering the deterioration equals the amount of biomass feedstock b used for the

16

production of bioethanol in biorefinery k at time period t (∑𝑠 𝑏𝑚𝑠𝑏,𝑗,𝑠,𝑡 ) plus the inventory level of current

17

time period t (𝑖𝑛𝑣𝑏,𝑗,𝑡

𝑏𝑖𝑜𝑚𝑎𝑠𝑠,𝑟𝑒𝑓

). 𝑏𝑖𝑜𝑚𝑎𝑠𝑠,𝑟𝑒𝑓

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 ∑ ∑ 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 + (1 − 𝑑𝑟𝑎𝑡𝑒𝑏,𝑡−1 ) 𝑖𝑛𝑣𝑏,𝑗,𝑡−1 𝑖

𝑚 𝑏𝑖𝑜𝑚𝑎𝑠𝑠,𝑟𝑒𝑓

= ∑𝑠 𝑏𝑚𝑠𝑏,𝑗,𝑠,𝑡 + 𝑖𝑛𝑣𝑏,𝑗,𝑡

,

∀𝑏, 𝑗, 𝑡

(5)

18

Mass balances of bioethanol in each biorefinery: amount of produced bioethanol in biorefinery j at time

19

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 period t (∑𝑠 𝑏𝑒𝑙𝑗,𝑠,𝑡 ) plus the inventory from previous time period (𝑖𝑛𝑣𝑗,𝑡−1 ) equals the amount of

20

bioethanol sent from biorefinery j to demand zones via all transportation modes at time period t

21

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑏𝑖𝑜𝑒𝑡𝑎𝑛𝑜𝑙 (∑𝑘 ∑𝑚 𝑓𝑗,𝑘,𝑚,𝑡 ) plus the inventory level of current time period t (𝑖𝑛𝑣𝑗,𝑡 ).



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

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑏𝑖𝑜𝑒𝑡𝑎𝑛𝑜𝑙 ∑ 𝑏𝑒𝑙𝑗,𝑠,𝑡 + 𝑖𝑛𝑣𝑗,𝑡−1 = ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 + 𝑖𝑛𝑣𝑗,𝑡 , 𝑠

𝑘

∀𝑗, 𝑡

Page 10 of 43

(6)

𝑚

1

3.1.3. Conversion constraints

2

Conversion of biomass to bioethanol and byproducts: All of the biomass feedstocks in biorefinery j at

3

𝑏𝑒𝑙 time period t are converted to bioethanol and byproducts where 𝜃𝑏,𝑠 is the conversion factor of biomass

4

type b through technology s to bioethanol and 𝜃𝑏,𝑠,𝑔

5

through technology s to byproduct g.

𝑏𝑦𝑝𝑟𝑜𝑑𝑢𝑐𝑡

𝑏𝑒𝑙 𝑏𝑒𝑙𝑗,𝑠,𝑡 = ∑ 𝜃𝑏,𝑠 . 𝑏𝑚𝑠𝑏,𝑗,𝑠,𝑡 ,

is the conversion factor of biomass type b

∀𝑗, 𝑠, 𝑡

(7)

𝑏 𝑏𝑦−𝑝𝑟𝑜𝑑𝑢𝑐𝑡

𝑓𝑔,𝑗,𝑡


= ∑ 𝜃𝑏,𝑠,𝑔

. 𝑏𝑚𝑠𝑏,𝑗,𝑠,𝑡 ,

∀𝑗, 𝑔, 𝑠, 𝑡

(8)

𝑏

6

3.1.4. Capacity of biorefineries

7

If biorefinery j with capacity level r and conversion technology s is selected, capacity amount of

8

biorefinery j should be equal to the corresponding capacity amount, e.g., capacity level 2 corresponds to

9

the capacity amount of 100 MGY (million gallons per year). 𝑟𝑒𝑓

𝑐𝑎𝑝𝑗

𝑟𝑒𝑓

= ∑ ∑ 𝑐𝑎𝑝𝑗,𝑟,𝑠 . 𝑦𝑗,𝑟,𝑠 , 𝑟

∀𝑗

(9)

𝑠

10

3.1.5. Operational capacity of biorefineries

11

All amounts of produced bioethanol in one year (∑𝑡 𝑏𝑒𝑙𝑗,𝑠,𝑡 ), should be less than the capacity of

12

biorefinery j and greater than minimum efficiency percentage of biorefinery capacity (𝜔 𝑟𝑒𝑓 ), e.g. if

13

𝑐𝑎𝑝𝑗 =150 MGY and 𝜔 𝑟𝑒𝑓 =%80, the amount of bioethanol should be greater than 120 MGY and less

14

than 150 MGY.

𝑟𝑒𝑓

𝑟𝑒𝑓

𝑟𝑒𝑓

𝜔 𝑟𝑒𝑓 . ∑ 𝑐𝑎𝑝𝑗,𝑟,𝑠 . 𝑦𝑗,𝑟,𝑠 ≤ ∑ 𝑏𝑒𝑙𝑗,𝑠,𝑡 ≤ ∑ 𝑐𝑎𝑝𝑗,𝑟,𝑠 . 𝑦𝑗,𝑟,𝑠 , 𝑟

𝑡

∀𝑗, 𝑠

(10)

𝑟

15

3.1.6. Weight capacity of transportation links

16

If the biorefinery j is installed, all amount of harvested biomass transported from supply zone i to

17

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 biorefinery j via all transportation modes at time period t (∑𝑏 ∑𝑚 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 ) should be less than

18

maximum allowed transportation quantity on the corresponding link. 𝑠𝑢𝑝,𝑟𝑒𝑓

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 ∑ ∑ 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 ≤ 𝑢𝑝𝑐𝑎𝑝𝑖,𝑗,𝑡 𝑏

𝑚

. ∑ ∑ 𝑦𝑗,𝑟,𝑠 , 𝑟

∀𝑖, 𝑗, 𝑡

𝑠


(11)

Page 11 of 43

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1

If the biorefinery j is installed, all amounts of bioethanol transported from biorefinery j to demand zone k

2

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 via all transportation modes at time period t (∑𝑚 𝑓𝑗,𝑘,𝑚,𝑡 ) should be less than maximum allowed

3

transportation quantity on the corresponding link. 𝑟𝑒𝑓,𝑑𝑒𝑚

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 ∑ 𝑓𝑗,𝑘,𝑚,𝑡 ≤ 𝑢𝑝𝑐𝑎𝑝𝑗,𝑘,𝑡

. ∑ ∑ 𝑦𝑗,𝑟,𝑠 ,

𝑚

𝑟

∀𝑗, 𝑘, 𝑡

(12)

𝑠

4

3.1.7. Demand satisfaction

5

All amounts of bioethanol shipped from all biorefineries to demand zone k at time period t plus the

6

amount of unmet bioethanol demand should satisfy the amount of demand of zone k at that time period. It

7

should be noted that ~ refers to the uncertain nature of demand parameter. 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑎𝑥 is the maximum

8

percentage of gasoline equivalent annual demand to be satisfied from bioethanol. On the other hand, a

9

special percentage of demand should be satisfied without shortage which 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑖𝑛 is the minimum

10

ratio of gasoline equivalent annual demand to be satisfied from bioethanol without shortage. 𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 ̃𝑘,𝑡 , ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 + 𝑜𝑘,𝑡 ≥ 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑎𝑥 . 𝐷 𝑗

(13)

𝑚

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 ̃𝑘,𝑡 , ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 ≥ 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑖𝑛 . 𝐷 𝑗

∀𝑘, 𝑡

∀𝑘, 𝑡

(14)

𝑚

11

3.1.8. Selection of conversion technology and capacity level

12

If biorefinery is installed in location j, one capacity level and one technology type should be selected. ∑ ∑ 𝑦𝑗,𝑟,𝑠 𝑟

≤ 1,

∀𝑗,

(15)

𝑠

13

3.1.9. Decision variables constraints

14

Binary and non-negativity constraints on the decision variables are stated as follows: 𝑦𝑗,𝑟,𝑠 ∈ {0,1}

(16) 𝑏𝑦−𝑝𝑟𝑜𝑑𝑢𝑐𝑡

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑥𝑖,𝑏 , 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 , 𝑓𝑗,𝑘,𝑚,𝑡 , ℎ𝑟𝑣𝑏,𝑖,𝑡 , 𝑏𝑚𝑠𝑏,𝑗,𝑠,𝑡 , 𝑓𝑔,𝑗,𝑡 𝑏𝑖𝑜𝑚𝑎𝑠𝑠,𝑟𝑒𝑓

𝑖𝑛𝑣𝑏,𝑗,𝑡

𝑟𝑒𝑓

𝑏𝑖𝑜𝑚𝑎𝑠𝑠,𝑐𝑜𝑙 , 𝑏𝑒𝑙𝑗,𝑠,𝑡 , 𝑜𝑙,𝑡 , 𝑖𝑛𝑣𝑏,𝑗,𝑡 , 𝑐𝑎𝑝𝑗,𝑟,𝑠 ,

𝑏𝑖𝑜𝑒𝑡𝑎𝑛𝑜𝑙 , 𝑖𝑛𝑣𝑗,𝑡 ≥0

(17)

15 16

3.2. Objective functions

17

The proposed mathematical model aims to simultaneously optimize the economic, environmental and

18

social performance of multi-objective LBSC problem. Objective functions can be stated as follows:



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

Page 12 of 43

𝑧1 𝑝𝑟𝑜𝑓𝑖𝑡 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑏𝑗𝑒𝑐𝑡𝑖𝑣𝑒 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑠: { 𝑧2 𝑒𝑛𝑣𝑖𝑟𝑜𝑛𝑚𝑒𝑛𝑡𝑎𝑙 𝑖𝑚𝑝𝑎𝑐𝑡 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑧3 𝑔𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑗𝑜𝑏 𝑜𝑝𝑝𝑜𝑟𝑡𝑖𝑛𝑖𝑡𝑖𝑒𝑠 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 1

3.2.1. Economic objective function: Maximization of total profit

2

The first objective function considered here is maximization of total profit which can be stated as follows:

3

Max z1= revenue from sales of products - total costs = revenue from selling biomass main crops +

4

revenue from selling bioethanol + revenue from selling byproducts - supply zone renting costs - biomass

5

cultivation costs - biomass harvest costs - fixed opening costs of biorefineries - variable processing costs

6

of biorefineries - unmet bioethanol demand penalty costs - transportation costs - inventory holding costs 𝑐𝑟𝑜𝑝

𝑏𝑦−𝑝𝑟𝑜𝑑𝑢𝑐𝑡

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑚𝑎𝑥 𝑧1 = ∑ ∑ ∑ ℎ𝑟𝑣𝑏,𝑖,𝑡 . 𝑝𝑟𝑖𝑐𝑒 ̃ 𝑏 + ∑ ∑ ∑ ∑ 𝑝𝑟 ̃𝑡 . 𝑓𝑗,𝑘,𝑚,𝑡 + ∑ ∑ ∑ 𝑏𝑝𝑟𝑔,𝑡 . 𝑓𝑔,𝑗,𝑡 𝑖

𝑏

𝑡

𝑗

𝑘

𝑚

𝑡

𝑔

𝑗

𝑡 𝑟𝑒𝑓

− ∑ ∑ 𝑟𝑒𝑛𝑡𝑖 . 𝑥𝑖,𝑏 − ∑ ∑ 𝑐𝑢𝑙𝑖,𝑏 . 𝑥𝑖,𝑏 − ∑ ∑ ℎ𝑖,𝑏 . 𝑥𝑖,𝑏 − ∑ ∑ ∑ 𝑓𝑖𝑥𝑒𝑑𝑐𝑜𝑠𝑡𝑗,𝑟,𝑠 . 𝑦𝑗,𝑟,𝑠 𝑖

𝑏

𝑖

𝑏

𝑖

𝑏

𝑗

𝑟

𝑠

𝑟𝑒𝑓

− ∑ ∑ ∑ 𝑣𝑎𝑟𝑐𝑜𝑠𝑡𝑗,𝑠 . 𝑏𝑒𝑙𝑗,𝑠,𝑡 − 𝛾. ∑ ∑ 𝑜𝑘,𝑡 𝑗

𝑠

𝑡

𝑘

𝑡 𝑠𝑢𝑝,𝑟𝑒𝑓

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 − ∑ ∑ ∑ ∑ ∑ 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 𝑏

𝑖

𝑗

𝑚

.(

𝑟𝑒𝑓,𝑑𝑒𝑚

𝑘

𝑚

𝑑𝑖𝑠𝑗,𝑘,𝑚


𝑗

𝑠𝑢𝑝,𝑟𝑒𝑓

𝑡𝑟𝑢𝑐𝑘𝑐𝑎𝑝𝑚 𝑟𝑒𝑓,𝑑𝑒𝑚

. 𝑡𝑐𝑜𝑠𝑡𝑗,𝑘,𝑚


. 𝑖𝑛𝑣𝑏,𝑗,𝑡

) .(

) 𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙,𝑟𝑒𝑓

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 − ∑ ∑ ℎ𝑐𝑜𝑠𝑡𝑗,𝑡 . 𝑖𝑛𝑣𝑗,𝑡

𝑡

𝑗

1 ) 1 − 𝑚𝑜𝑖𝑠𝑏


+ 𝑡𝑟𝑢𝑐𝑘𝑙𝑜𝑎𝑑𝑐𝑜𝑠𝑡𝑗,𝑘,𝑚

𝑡𝑟𝑢𝑐𝑘𝑐𝑎𝑝𝑚

𝑡

− ∑ ∑ ∑ ℎ𝑐𝑜𝑠𝑡𝑏,𝑗,𝑡 𝑏


. 𝑡𝑐𝑜𝑠𝑡𝑏,𝑖,𝑗,𝑚 + 𝑡𝑟𝑢𝑐𝑘𝑙𝑜𝑎𝑑𝑐𝑜𝑠𝑡𝑏,𝑖,𝑗,𝑚

𝑡

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 − ∑ ∑ ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 .( 𝑗

𝑑𝑖𝑠𝑖,𝑗,𝑚

(18)

𝑡

𝑐𝑟𝑜𝑝

7

Where ℎ𝑟𝑣𝑏,𝑖,𝑡 is the quantity of biomass main crop b harvested from supply zone i in time period t. It

8

should be noted that, in this study, as mentioned before, crop residues are considered as biomass

9

feedstocks where biomass main crops are not used for biofuel production and be sold directly. Also,

10

investment in biorefineries is considered as fixed opening costs of biorefineries.

11

3.2.2. Environmental objective function: minimization of environmental impacts

12

Sustainable development was introduced as “development that meets the needs of the present without

13

compromising the ability of future generations to meet their own needs” provided by the Brundtland

14

Commission in 1987. Nowadays, Stakeholders and social organizations are pressuring companies to

15

incorporate all three dimensions of sustainability, i.e., social, environmental, and economic issues known

16

as triple bottom line 27 in their business strategies.

17

Incorporating energy and sustainability issues into the optimal design of supply chain network has been

18

an active research area in recent years

28

. Additionally, sustainability assessment is now recognized 12

ACS Paragon Plus Environment

Page 13 of 43

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


29

1

imperative for bioenergy development from lignocellulosic material

2

methodology is an important tool for sustainability analysis, which is recognized as one of the best

3

approaches for evaluating environmental impacts of bioenergy supply chain

4

methodology which measures environmental loads and their potential impacts over the entire life cycle

5

stages of a product, process or activity 32-34.

6

McBride et al.

7

water quality and quantity, greenhouse gases (i.e., CO2, CH4 and NOx), biodiversity, air quality, and

8

productivity and discussed 19 measurable indicators that fall into these categories. In a recent review

9

paper, Awudu and Zhang

35

. Life Cycle Assessment (LCA) 28, 30, 31

. Notably, LCA is a

identified six categories as environmental impacts of bioenergy including soil quality,

1

mentioned the major environmental impacts of biofuel supply chain as (1)

10

GHG emission, (2) water resources quality (3) soil degradation and loss of biodiversity.

11

Several models have been presented up to now, which applied combined use of mathematical

12

programming and LCA-based methods in the optimal design and planning of biofuel supply chain.

13

Giarola et al.

14

financial performances simultaneously. Environmental objective was to minimize total GHG emissions

15

resulting from all life cycle stages of the biofuel supply chain. Mele et al.

16

linear programming problem (bi-MILP) model with the aim of maximizing simultaneously the net present

17

value (NPV) and life cycle environmental performance of the combined sugar/ethanol supply chains. The

18

environmental objective was measured through the entire life cycle of the supply chain by applying two

19

LCA-based methodologies i.e., Eco-indicator 99 and CML. The CML 2001 methodology includes a set of

20

impact categories and characterization methods developed by Center of Environmental Science of Leiden

21

University.

22

Integrating LCA with multiobjective optimization, You et al. 3 proposed a multi-objective MILP model in

23

which environmental objective was minimizing the total annual CO2 equivalent GHG emissions caused

24

by the operations of the lignocellulosic biofuel supply chain. The environmental model proposed by

25

Giarola et al. 18 assessed the impacts of whole biofuel supply chain operations on global warming through

26

a Life Cycle Assessment methodology. In order to assess the environmental impacts GHG emissions was

27

applied, which is expressed in units of CO2 equivalents. Balaman and Selim

28

environmental performance of the bioenergy supply chain through considering the total amount of waste

29

biomass, which is collected from biomass source sites and utilized to be converted to biogas. They

30

proposed environmental objective as minimizing the total waste biomass amount that is not collected

31

from the biomass source sites. To assess the environmental impact, Santibañez-Aguilar et al. 37, 38 applied

32

Ecoindicator99 which is a LCA-based methodology. The environmental objective was to minimize the

33

Eco-indicator99 of raw material production, product manufacturing, product use, and the transportation of

34

materials between biofuel supply chain components.

18

proposed a mixed integer linear programming model to optimize the environmental and


36

proposed a mixed-integer

23

assessed the


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Page 14 of 43

1

To quantify the environmental objective function, Eco-indicator 99 (EI99) is adopted here, which is a

2

LCA-based damage-oriented method proposed by Goedkoop and Spriensma 39. In order to measure the

3

total environmental impacts of a process or product, EI99 use special numbers or units called Eco-

4

indicators. The most practical application of this method is the calculation of single scores for LCA

5

results that can be used as a tool for designers to compare the design alternatives according to total

6

environmental impacts. The unit of measurement is called Eco-indicator Point (Pt) which is divided into

7

1000 millipoints (mPt). The Eco-indicator99 method focuses on three environmental damage categories

8

including:

9

(1) Damage to human health caused by:

10



Carcinogenic substances

11



Respiratory effects

12



Climate change

13



Ionizing radiation

14



Ozone layer depletion

15

(2) Damage to ecosystem quality caused by:

16



Ecotoxic substances

17



Acidification and eutrophication

18



Land-use

19 20

and (3) Damage to resources caused by: 

Depletion and fossil fuels

21

Eco-indicators are weighted based on three different perspectives, i.e., (1) Hierarchist , (2) Individualist

22

and (3) Egalitarian. Every perspective represents different weighting set to damage categories. Here, the

23

Average Hierarchist perspective is adopted to calculate Eco-indicator scores. In the Average Hierarchist

24

perspective 40%, 40% and 20% weighting set are assigned to human health, ecosystem quality and

25

resource depletion categories 33, 39.

26

In this study, the environmental objective function considers the entire scope of environmental impacts

27

over the life cycle of the concerned supply chain. Furthermore, fuzzy numbers are used to model

28

uncertainty related to environmental impacts. Although there are studies in the supply chain management

29

literature which have taken into account the effects of imprecise parameters in the environmental

30

performance (e.g., Guillén‐Gosálbez and Grossmann

31

supply chain related studies on this topic is rare. As shown in Figure 1, life cycle stages of studied LBSC

32

problem contain: (1) biomass production, (2) transportation of harvested biomass from biomass supplying

33

zones to biorefineries, (3) conversion of biomass to bioethanol in biorefineries, (4) transportation of

40

and Pishvaee et al.


25

), but the existing biofuel

Page 15 of 43

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1

bioethanol from biorefineries to customer demand zones. According to above mentioned descriptions,

2

environmental objective function is stated as follows: 𝑏𝑚𝑠𝑝𝑟𝑜

𝑚𝑖𝑛 𝑧2 = ∑ 𝑒𝑖 ̃𝑏

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 . 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 +

𝑏,𝑖,𝑗,𝑚,𝑡

+

∑


ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 . 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 . 𝑑𝑖𝑠𝑏,𝑖,𝑗,𝑚,𝑡

𝑏,𝑖,𝑗,,𝑚,𝑡

𝑟𝑒𝑓


𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑒𝑖 ̃ 𝑏,𝑠 . 𝑓𝑗,𝑘,𝑚,𝑡 + ∑ 𝑒𝑖 ̃𝑚

𝑠,𝑏,𝑗,𝑘,𝑚,𝑡


∑ 𝑒𝑖 ̃𝑚


𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 . 𝑓𝑗,𝑘,𝑚,𝑡 . 𝑑𝑖𝑠𝑗,𝑘,𝑚,𝑡

(19)

𝑗,𝑘,𝑚,𝑡

3

𝑏𝑚𝑠𝑝𝑟𝑜 𝑠𝑢𝑝,𝑟𝑒𝑓 Where 𝑒𝑖 ̃𝑏 is the (uncertain) unit Eco-indicator 99 for production of biomass type b, 𝑒𝑖 ̃𝑚 is the

4

unit Eco-indicator 99 for transportation of harvested biomass from supply zones to biorefineries via

5

𝑟𝑒𝑓 transportation mode m in time period t, 𝑒𝑖 ̃ 𝑏,𝑠 is the unit Eco-indicator 99 for conversion of biomass type b

6

𝑟𝑒𝑓,𝑑𝑒𝑚 to bioethanol via technology type s in biorefineries, and 𝑒𝑖 ̃𝑚 is the unit Eco-indicator 99 for

7

transportation of bioethanol from biorefineries to demand zones via transportation mode m in time period

8

t.

9

As can be seen, the environmental objective function considers feedstock production, bioethanol

10

production and transportation of materials between SC components. The use phase of produced

11

bioethanol is excluded from consideration because according to Mu et al. 5 the carbon dioxide which is

12

released during the bioethanol use phase (i.e., combustion in an engine) is biogenic and doesn't have

13

acidification and eutrophication impacts. Moreover, in the life cycle assessment of the system that

14

produce more than one output, allocation procedure is used to divide the environmental impacts between

15

the main product and its co-products. There are several approaches for co-product allocation. In this

16

study, for calculating eco-indicators in the feedstock production stage, we adopt the subdivision method

17

which assigns to stover and straw only those additional activities caused by their harvest.

18

Straw incorporation into the soil (if not removed) leads to building up soil carbon as well as soil nitrogen,

19

and returning valuable nutrients to the ecosystem. As a consequence, utilization of straw for bioenergy

20

targets rather than incorporation into the soil leads to environmental impacts resulting from (1) the loss of

21

the potential build-up of soil C and N, and (2) the removal of nutrients that implies an extra cost for the

22

production of the added mineral fertilizers (N, P and K) to maintain yield as well as a change in emissions

23

of e.g. NH3, NOx, N2O and NO3 41. Similarly, the collection of stover leads to loss of the potential build-

24

up of soil C and N and removal of nutrients (N, P and K) which requires addition of N, P and K fertilizers

25

in sufficient quantity to replace the N, P and K removed in stover biomass.

26

Soil carbon sequestration is the temporary storage (or release) of carbon in the soil and is expected to hold

27

a significant potential to decrease agricultural greenhouse gas emissions. However, most of the LCA-

28

based studies related to agricultural products, have not considered possible changes in soil carbon

29

sequestration 42. 15 ACS Paragon Plus Environment


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Page 16 of 43

1

In this study, in order to calculate eco-indicators for feedstock production stage, we consider the

2

environmental impacts resulted from soil carbon (C) sequestration loss and application of fertilizers (e.g.,

3

ammonia, dinitrogen monoxide and NOx air emissions) according to formulas reported in Murphy and

4

Kendall

5

carbon sequestration is according to Petersen et al.

6

straw C in to the soil (instead of utilizing it for bioenergy) in Denmark would correspond to a carbon

7

sequestration equivalent of 9.7% in a 100-year perspective. This corresponds to the loss of 39 kg soil C

8

sequestration and 3.9 kg soil N build up per tonne of straw removal (according to Nguyen et al.

9

assumed that the build up of organic nitrogen to follow carbon is in the ratio of 1:10) and 39.9 kg soil C

43

and Nguyen et al.

41

which is reported for wheat straw. It should be noted that the amount of 42

which found that the incorporation of 1 tonne of

10

sequestration and 3.9 kg soil N build up per tonne of stover removal.

11

Table 1. Summary of the main features of biomass feedstocks Wheat straw a

Corn stover

85%

88% b

C

47.3%

46.7% b

N

0.6%

0.7% b

P (as P2O5)

0.09%

0.2% c

K (as K2O)

1.5%

1.45% c

Dry matter content

44

it is

Elemental composition (dry matter basis) as %

12

a

13

According to Nguyen et al.

14

with straw, is 1.5 kg nitrogen, 0.8 kg phosphorus and 12.8 kg potassium per tonne of straw wet weight.

15

These values are based on assumption that 30% of the N and 100% of the P and K removed in straw must

16

be replaced. We assume similar rates for calculating quantity of fertilizer input for corn stover. Summary

17

of the main features of straw and stover is given in Table 1 which are used for calculation of values of

18

Table 2. Table 2 illustrates environmental impacts consequences of straw and stover removal (instead of

19

retention) based on formulas that is presented in Nguyen et al.

20

𝑏𝑚𝑠𝑝𝑟𝑜 eco-indicators for feedstock production stage (i.e., 𝑒𝑖 ̃𝑏 ), including acidification and eutrophication

21

impact categories, values reported in Table 2 are adopted.

22

Table 2. Environmental consequences of straw and stover removal concerning soli C sequestration loss, extra

23

fertilizer inputs and induced emissions (per tonne of crop residue weight) [adopted from Nguyen et al. 41, 44]

ref: Nguyen et al. 44. b Wang et al. 45. c Murphy and Kendall 43 41

the amount of fertilizer nutrient input to compensate for nutrient removal

Environmental consequences Soil C sequestration loss, 100 years perspective Extra fertilizer input

Unit

kg

44

Amount for

Amount for

wheat straw

corn stover

39

39.9

for wheat straw. Also, for calculating

kg


Comment 9.7% of the total C in crop residue a

Page 17 of 43

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1.53b

N

b

1.85

30% of the total N in crop residue

P

0.765

1.76

100% of the total P in straw & stover

K

12.75b

12.76

100% of the total k in straw & stover

0.015b

0.018

0.01 × kg N in fertilizer

0.062

0.01 × kg N in crop residues

Emissions

kg

N2O-N from extra fertilizer-N application

b

Avoided N2O-N from crop residues

0.051

NH3-N from extra fertilizer-N application

0.0306b

0.1232


NO-N from extra fertilizer-N application

0.0107b

0.0431


N2-N from extra fertilizer-N application

0.072b

0.290

0.047 × kg N in fertilizer Extra fertilizer-N input – N output in straw removed – N

NO3-N, calculated as the change in the potential leaching due to straw removal

-0.11c

-0.735

emissions from extra fertilizer-N application – (–N2O–N

-0.036c

-0.004

0.0075 × NO3–N + 0.01 × (NH3–N + NOx–N)

from crop residues – N build-up in soil)

Indirect N2O-N

1

a

2

In order to determine eco-indicators in bioethanol production stage, we have calculated eco-indicators for

3

biochemical and thermochemical conversion according to emissions associated with the various process

4

inputs (e.g., sulfuric acid, lime, ammonia, enzymes) involved in each technology according to life cycle

5

inventory data of Mu et al. 5. For each technology, amount of process inputs per tonne of corn stover and

6

wheat straw is calculated and multiplied by corresponding eco-indicator units. The sum of resulted values

7

𝑟𝑒𝑓 is eco-indicator for related technology (i.e., 𝑒𝑖 ̃ 𝑏,𝑠 ).

8

3.2.3. Social objective function: maximization of the number of job opportunities generated

9

At the 2002 World Summit on Sustainable Development (WSSD) held in Johannesburg, sustainable

10

development was reaffirmed as a development that implies the balancing of not just economic with

11

environmental protection, but also social development 46.

12

Although there is a rich literature on the environmental dimension of sustainability in supply chain, very

13

few approaches address the social dimension of sustainability 47. Measuring all aspects of social impact

14

(SI) is a fully multi-disciplinary and multi-stakeholder issue. In this regard, a number of standards such as

15

ISO 26000 (ISO, 2010), SA8000 (SAI, 2001) and AA1000 (ISEA, 1999) have been developed in order to

16

provide a framework for implementing social responsibility (SR) in firms and corporations. ISO 26000

17

provides a comprehensive framework which classifies social issues into seven core subjects including (1)

18

organizational governance, (2) human rights, (3) labor practices, (4) the environment, (5) fair operating

19

practices, (6) consumer issues, (7) community involvement and development 25, 48.

20

A number of works have been done to identify socio-economic factors of biofuel supply chains. Domac et

21

al. 49 assessed employment and other socio-economic factors of bioenergy as drivers for bioenergy sector

22

development. The authors categorized socio-economic aspects to four dimensions, including :(1) the

23

dimension of social aspects with parameters such as living standards, rural diversification, regional

ref: Peterson et al. 42. b Nguyen et al. 44. c Nguyen et al. 41



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Page 18 of 43

1

development, migration effects, education and others; (2) the macro-level dimension with parameters

2

such as security of supply, regional growth and trade balance; (3) the supply side dimension with

3

parameters such as productivity, competitiveness and labor mobility; and (3) the demand side dimension

4

with parameters such as employment, income change and induced investment. Most of mentioned factors

5

are not quantifiable

6

job creation potential in local, regional and national employment. Perimenis et al. 31 presented a decision

7

support tool in order to asses biofuel production pathways. The tool integrated technical, economic,

8

environmental and social performances along the concerned supply chain. They adopted employment or

9

job creation along the entire biofuel pathway as an indicator for social aspect which is considered one of

31, 50

. They concluded that bioenergy as a labor intensive technology has the highest

1

10

the main social drivers for development of bioenergy sector. Awudu and zhang

11

social sustainability issues of biofuel supply chains as (1) poverty reduction potential, (2) land and crop

12

indirect impacts, and (3) effects on social resources, such as water utility systems.

13

Recently, a review paper of bioenergy socio-economic indicators by Dale et al.

14

economic indicators under social well-being, energy security, trade, profitability, resource conservation,

15

and social acceptability categories across the biofuel supply chain. Social well-being category focused on

16

four indicators, including employment, household income, work days lost due to injury and food security.

17

They argued that policy makers have highlighted employment as a prime motivator of national policies

18

supporting bioenergy research, development, and use.

19

To the best of our knowledge, few works have considered quantitatively measuring environmental and

20

social impacts simultaneously in biofuel supply chain network design and planning. Indeed, multi-

21

objective optimization of biofuel supply chain design with all three components of sustainability is very

22

scarce (e.g., You et al.3, Yue et al.

23

investigated the lignocellulosic supply chain optimal design and planning under economic,

24

environmental, and social objectives in which the social objective was quantified by the number of

25

accrued local jobs (in terms of full-time equivalent for a year). Similarly, Santibañez-Aguilar et al.

26

presented an optimization model to design and planning sustainable biorefinery supply chains by

27

considering simultaneous economic, environmental and social objectives where the social objective was

28

measured by the number of jobs generated. In this study, for measuring social dimension of sustainable

29

biofuel supply chain, the number of created job opportunities which is a popular SR indicator is adopted.

30

Hence, the social objective function is measured by the number of job opportunities generated per year

31

due to the biomass production (𝑠𝑖𝑏

32

𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔 bioethanol production (𝑠𝑖𝑗,𝑠 ). Moreover, the number of job opportunities generated resulted from

33

constructing biorefineries is considered. The social objective function is formulated as follows:

52

and Santibañez-Aguilar et al.

𝑏𝑚𝑠𝑝𝑟𝑜

37

analyzed some of the

51

identified 16 socio-

). You et al.

3

and Yue et al.52

37

𝑠𝑢𝑝,𝑟𝑒𝑓 𝑟𝑒𝑓,𝑑𝑒𝑚 ), biomass and bioethanol transportation (𝑠𝑖𝑏,𝑖,𝑗,𝑚 , 𝑠𝑖𝑗,𝑘,𝑚 ) and


Page 19 of 43

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𝑚𝑎𝑥 𝑍3 = ∑ ∑ ∑ ℎ𝑟𝑣𝑏,𝑖,𝑡 . 𝑠𝑖𝑏 𝑏

𝑖

𝑡

𝑏 𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔

+ ∑ ∑ ∑ 𝑏𝑒𝑙𝑗,𝑠,𝑡 . 𝑠𝑖𝑗,𝑠 𝑗

𝑠


ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 + ∑ ∑ ∑ ∑ ∑ 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 . 𝑠𝑖𝑏,𝑖,𝑗,𝑚

𝑡

𝑖

𝑗

𝑚

𝑡 𝑟𝑒𝑓,𝑑𝑒𝑚

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 + ∑ ∑ ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 . 𝑠𝑖𝑗,𝑘,𝑚 𝑗

𝑘

𝑚

𝑡

𝑟𝑒𝑓

+ ∑ ∑ ∑ 𝑦𝑗,𝑟,𝑠 . 𝑠𝑖𝑗,𝑟,𝑠 𝑗

𝑟

(20)

𝑠

1 2

4. The proposed multi-objective robust possibilistic programming (MORPP) approach

3

In this section, first we briefly explain the robust possibilistic programming model proposed by Pishvaee

4

et al.

5

approach.

6

4.1. Robust possibilistic programming (RPP) models

7

The compact form of the LBSC model (excluding second and third objective functions) can be stated as

8

follows:

9

(𝑏𝑎𝑠𝑒 𝑚𝑜𝑑𝑒𝑙 − 𝐼)

48

and then introduce proposed multi-objective robust possibilistic programming (MORPP)

𝑚𝑎𝑥 𝑧 = 𝑝̃𝑥2 − 𝑞𝑥1 − 𝑓𝑦 𝑠. 𝑡. 𝐿𝐵 ≤ 𝑥1 ≤ 𝑈𝐵, 𝐴𝑥2 ≥ 𝑑̃, 𝐵𝑥2 = 0, 𝐶𝑥2 ≤ 𝑒𝑥1 , 𝑆𝑥2 ≤ 𝑀𝑦, 𝑇𝑦 ≤ 1, 𝑦 ∈ {0,1}, 𝑥2 ≥ 0, 10

Where vectors p, q, f and d corresponds to selling prices, variable costs of various activities related to

11

biomass sourcing, bioethanol production and distribution throughout the supply chain, fixed opening

12

costs of biorefineries and demand respectively. It is assumed that vectors p and d are imprecise

13

parameters. Basic possibilistic chance constrained programming (BPCCP) for the above mentioned model

14

according to Pishvaee et al. 48 can be stated as follows: (𝐵𝑃𝐶𝐶𝑃 𝑚𝑜𝑑𝑒𝑙) 𝑚𝑎𝑥 𝐸[𝑧] = 𝐸[𝑝̃𝑥2 ] + 𝐸[−𝑞𝑥1 − 𝑓𝑦]



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

Page 20 of 43

𝑠. 𝑡. 𝐿𝐵 ≤ 𝑥1 ≤ 𝑈𝐵, 𝑁𝐸𝐶{𝐴𝑥2 ≥ 𝑑̃} ≥ 𝛼, 𝐵𝑥2 = 0, 𝐶𝑥2 ≤ 𝑒𝑥1 , 𝑆𝑥2 ≤ 𝑀𝑦, 𝑇𝑦 ≤ 1, 𝑦 ∈ {0,1}, 𝑥2 ≥ 0, 1

As it can be seen from the model, in order to modelling the objective function expected value operator

2

and to handle chance constraints including imprecise parameters necessity fuzzy measure is applied. In

3

this study, to model the uncertain parameters, we use trapezoidal possibility distribution (see Figure 2)

4

which can be defined by their four prominent points, e.g., 𝜉̃ = (𝜉(1) , 𝜉(2) , 𝜉(3) , 𝜉(4) ). The equivalent crisp

5

model of the above mentioned model can be formulated as following: 𝑝(1) + 𝑝(2) + 𝑝(3) + 𝑝(4) 𝑚𝑎𝑥 𝐸[𝑧] = ( ) . 𝑥2 − 𝑞𝑥1 − 𝑓𝑦 4 𝑠. 𝑡. 𝐿𝐵 ≤ 𝑥1 ≤ 𝑈𝐵 𝐴𝑥2 ≥ (1 − 𝛼)𝑑(3) + 𝛼𝑑(4) , 𝐵𝑥2 = 0 𝑐𝑥2 ≤ 𝑒𝑥1 , 𝑆𝑥2 ≤ 𝑀𝑦, 𝑇𝑦 ≤ 1, 𝑦 ∈ {0,1}, 𝑥2 ≥ 0,

6


Page 21 of 43

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1

Figure 2. The trapezoidal possibility distribution of fuzzy parameter 𝜉̃

2

It is assumed that the chance constraints in the above mentioned formulation should be satisfied with a

3

confidence level greater than 0.5 (i.e., 𝛼 > 0.5) and determined by the Decision Maker (DM).

4

Based on BPCCP model, the robust possibilistic programming (RPP-I) model is stated as follows: (𝑅𝑃𝑃 − 𝐼) 𝑚𝑎𝑥 𝐸[𝑧] − 𝛾(𝑧𝑚𝑎𝑥 − 𝑧𝑚𝑖𝑛 ) − 𝛿1 [𝑑(4) − (1 − 𝛼)𝑑(3) − 𝛼𝑑(4) ] 𝑠. 𝑡. 𝐿𝐵 ≤ 𝑥1 ≤ 𝑈𝐵 𝐴𝑥2 ≥ (1 − 𝛼)𝑑(3) + 𝛼𝑑(4) , 𝐵𝑥2 = 0 𝑐𝑥2 ≤ 𝑒𝑥1 , 𝑆𝑥2 ≤ 𝑀𝑦, 𝑇𝑦 ≤ 1, 𝑦 ∈ {0,1}, 𝑥1 , 𝑥2 ≥ 0, 0.5 < 𝛼 ≤ 1

5

Just like BPCCP model, E[Z] indicates the expected value of z and seeks to maximize expected (average)

6

total performance of the concerned system. The term (𝑧𝑚𝑎𝑥 − 𝑧𝑚𝑖𝑛 ) represents the difference between the

7

two extreme possible values of z and 𝛾 is the weight (importance) of the second term against other terms

8

of the objective function. Definition of 𝑧𝑚𝑎𝑥 and 𝑧𝑚𝑖𝑛 are as follows: 𝑧𝑚𝑎𝑥 = 𝑝(4) 𝑥2 − 𝑞𝑥1 − 𝑓𝑦, 𝑧𝑚𝑖𝑛 = 𝑝(1) 𝑥2 − 𝑞𝑥1 − 𝑓𝑦,

9

As a result, the second term, i.e., −𝛾(𝑧𝑚𝑎𝑥 − 𝑧𝑚𝑖𝑛 ) results in minimization of maximum deviation over

10

and under the expected optimal value of z which controls the optimality robustness of the solution vector.

11

The third term, i.e., 𝛿1 [𝑑(4) − (1 − 𝛼)𝑑(3) − 𝛼𝑑(4) ], which determines the confidence level of each

12

chance constraint, controls the feasibility robustness of the solution vector. In this term, 𝛿1 describes the

13

penalty unit of possible violation of each constraint containing uncertain parameter(s). Also, [𝑑(4) −

14

(1 − 𝛼)𝑑(3) − 𝛼𝑑(4) ] represents the difference between the worst case value of uncertain parameter and

15

the value which is used in the corresponding chance constraint. It should be noted that 𝛿1 is not just a

16

theoretical and meaningless parameter and can be determined according to application context

17

appropriately. For instance, in our LBSC model 𝛿1 can be defined as shortage or non-satisfied demand 21 ACS Paragon Plus Environment


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1

penalty which is a common parameter in the SCM context 48. Note that unlike the BPCCP model, in this

2

model, minimum confidence levels (i.e., 𝛼) are variable and are optimized according to model objective

3

function and constraints.

4

4.2. Multi-objective robust possibilistic programming (MORPP) model: new approach

5

Now we consider the base model, including three objective functions, i.e., economic, environmental and

6

social objective functions that can be stated as follows:

7

(𝑏𝑎𝑠𝑒 𝑚𝑜𝑑𝑒𝑙 − 𝐼𝐼)

Page 22 of 43

max 𝑧1 = 𝑝̃𝑥2 − 𝑞𝑥1 − 𝑓𝑦 𝑚𝑖𝑛 𝑧2 = ℎ̃𝑥, 𝑚𝑎𝑥 𝑧3 = 𝑘𝑦 + 𝑠𝑥, 𝑠. 𝑡. 𝐿𝐵 ≤ 𝑥1 ≤ 𝑈𝐵, 𝐴𝑥2 ≥ 𝑑̃, 𝐵𝑥2 = 0, 𝐶𝑥2 ≤ 𝑒𝑥1 , 𝑆𝑥2 ≤ 𝑀𝑦, 𝑇𝑦 ≤ 1, 𝑦 ∈ {0,1}, 𝑥2 ≥ 0, 8

Where vectors h and s correspond to unit environmental impacts and number of generated job

9

opportunities resulted from various activities throughout the supply chain and k corresponds to the

10

number of jobs generated due to construction of biorefineries.

11

As expressed in the previous section, robust objective function considers three components including

12

upgrading expected (average) performance of the system, minimizing optimality robustness and

13

maximizing feasibility robustness. Therefore, to develop multi-objective robust possibilistic programming

14

we consider aforementioned concepts in separate objective functions and develop multi-objective robust

15

possibilistic programming based on 𝑏𝑎𝑠𝑒 𝑚𝑜𝑑𝑒𝑙 − 𝐼𝐼 as follows: (𝑀𝑂𝑅𝑃𝑃 𝑚𝑜𝑑𝑒𝑙) 3

𝑚𝑎𝑥 𝑂𝐹1 = ∑ 𝜆𝑚 . 𝜇𝑚 𝑚=1


Page 23 of 43

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2

𝑚𝑖𝑛 𝑂𝐹2 = ∑ 𝜆́𝑚 . 𝜇𝑚́ 𝑚=1

𝑚𝑖𝑛 𝑂𝐹3 = 𝛿1 . [ 𝑑(4) − (1 − 𝛼)𝑑(3) − 𝛼𝑑(4) ] 𝑠. 𝑡. 𝐿𝐵 ≤ 𝑥1 ≤ 𝑈𝐵, 𝐴𝑥2 ≥ (1 − 𝛼)𝑑(3) + 𝛼𝑑(4) , 𝐵𝑥2 = 0, 𝐶𝑥2 ≤ 𝑒𝑥1 , 𝑆𝑥2 ≤ 𝑀𝑦, 𝑇𝑦 ≤ 1, 𝑦 ∈ {0,1}, 𝑥2 ≥ 0, 1

OF1 is a weighted sum fuzzy aggregation function that is used to aggregate three basic objective

2

functions E[Z1], E[Z2 ] and Z3. Therefore, OF1 results in maximization of “expected (average)

3

performance” of the concerned system. 𝜆𝑚 (m is the number of basic objective functions) indicates the

4

weight (importance) of each basic objective function 𝑧𝑚 for DM. 𝜇𝑚 is the satisfaction degree of each 𝑧𝑚

5

that defined by using a linear fuzzy membership function as follows:

6

𝑖𝑓 𝐸[𝑧1 ] > 𝐸[𝑧1𝑃𝐼𝑆 ]

1, 7

𝜇1 (𝑥) =

8

𝐸[𝑍1 ]−𝐸[𝑧1𝑁𝐼𝑆 ] , 𝐸[𝑧1𝑃𝐼𝑆 ]− 𝐸[𝑧1𝑁𝐼𝑆 ]

9 10

𝜇2 (𝑥) =

15

𝐸[𝑧2𝑁𝐼𝑆 ]−𝐸[𝑍2 ] , 𝐸[𝑧2𝑁𝐼𝑆 ]−𝐸[𝑧2𝑃𝐼𝑆 ]

0,

{

12

14

𝑖𝑓 𝐸[𝑧2 ] < 𝐸[𝑧2𝑃𝐼𝑆 ]

1,

11

13

𝑖𝑓 𝐸[𝑧1 ] < 𝐸[𝑧1𝑁𝐼𝑆 ]

0,

{

1, 𝜇3 (𝑥) =

𝑍3 −𝑧3𝑁𝐼𝑆 , 𝑧3𝑃𝐼𝑆 −𝑧3𝑁𝐼𝑆

{ 0,

𝑖𝑓 𝐸[𝑧1𝑁𝐼𝑆 ] ≤ 𝐸[𝑧1 ] ≤ 𝐸[𝑧1𝑃𝐼𝑆 ]

𝑖𝑓 𝐸[𝑧2𝑃𝐼𝑆 ] ≤ 𝐸[𝑧2 ] ≤ 𝐸[𝑧2𝑁𝐼𝑆 ] 𝑖𝑓 𝐸[𝑧2 ] > 𝐸[𝑧2𝑁𝐼𝑆 ]

𝑖𝑓 𝑧3 > 𝑧3𝑃𝐼𝑆 𝑖𝑓 𝑧3𝑁𝐼𝑆 ≤ 𝑧3 ≤ 𝑧3𝑃𝐼𝑆 𝑖𝑓 𝑧3 < 𝑧3𝑁𝐼𝑆

Similarly, 𝜇́ 𝑚 is defined as follows:



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

1, 1

𝑜𝑏𝑗1𝑛𝑖𝑠 −𝑜𝑏𝑗1 , 𝑜𝑏𝑗1𝑛𝑖𝑠 −𝑜𝑏𝑗1𝑝𝑖𝑠

𝜇́ 1 (𝑥) =

Page 24 of 43

𝑖𝑓 𝑜𝑏𝑗1 < 𝑜𝑏𝑗1𝑝𝑖𝑠 𝑖𝑓 𝑜𝑏𝑗1𝑝𝑖𝑠 ≤ 𝑜𝑏𝑗1𝑝𝑖𝑠 ≤ 𝑜𝑏𝑗1𝑛𝑖𝑠

{0,

𝑖𝑓 𝑜𝑏𝑗1 > 𝑜𝑏𝑗1𝑛𝑖𝑠

1,

𝑖𝑓 𝑜𝑏𝑗2 < 𝑜𝑏𝑗2𝑝𝑖𝑠

2

3

𝑜𝑏𝑗2𝑛𝑖𝑠 −𝑜𝑏𝑗2 , 𝑜𝑏𝑗2𝑛𝑖𝑠 −𝑜𝑏𝑗2𝑝𝑖𝑠

𝜇́ 2 (𝑥) =

{0,

𝑖𝑓 𝑜𝑏𝑗2𝑝𝑖𝑠 ≤ 𝑜𝑏𝑗2𝑝𝑖𝑠 ≤ 𝑜𝑏𝑗2𝑛𝑖𝑠 𝑖𝑓 𝑜𝑏𝑗2 > 𝑜𝑏𝑗2𝑛𝑖𝑠

4

OF2 is a weighted sum fuzzy aggregation function that is used to aggregate two objective functions obj1

5

and obj2.

6

Now we can determine positive ideal solution (PIS) and negative ideal solution (NIS) for each objective

7

function as following:

8

𝑃𝐼𝑆 𝑧𝑚=1,2,3 ={

∗ )} 𝑚𝑖𝑛{𝑧𝑚 (𝑥𝑚 ,𝑚 = 2 ∗ 𝑚𝑎𝑥{𝑧𝑚 (𝑥𝑚 )} , 𝑚 = 1,3

𝑁𝐼𝑆 𝑧𝑚=1,2,3 ={

∗ )} 𝑚𝑎𝑥{𝑧𝑚 (𝑥𝑚 ,𝑚 = 2 ∗ 𝑚𝑖𝑛{𝑧𝑚 (𝑥𝑚 )} , 𝑚 = 1,3

Also, obj1 and obj2 are defined as follows: 𝑜𝑏𝑗1 = 𝑧1𝑚𝑎𝑥 − 𝑧1𝑚𝑖𝑛 , 𝑜𝑏𝑗2 = 𝑧2𝑚𝑎𝑥 − 𝑧2𝑚𝑖𝑛

9

Note that obj1 and obj2 aim at minimizing the maximum passible deviation of objective functions z1 and

10

z2; hence OF2 controls the “optimality robustness” of the solution vector over and under the economic

11

objective function (z1) and the environmental objective function (z2). Note that z1 and z2 contains

12

uncertain parameters.

13

OF3 controls the “normalized feasibility robustness” of the solution vector. First term of OF3

14

corresponds to chance constraint 𝐴𝑥 ≥ (1 − 𝛼)𝑑(3) + 𝛼𝑑(4) and 𝛿1 is penalty unit of possible violation

15

on this constraint. More important feasibility of this constraint for DM, greater value for 𝛿1 is appropriate.

16

The term (𝑑(4) − (1 − 𝛼)𝑑(3) − 𝛼𝑑(4) ) indicates the difference between the worst case value of imprecise

17

parameter, i.e., 𝑑(4) and the value that is used in chance constraint. It's worth noting that similar to RPP

18

models, the chance constraints should be satisfied with a confidence level greater than 0.5. Now to solve

19

the proposed multi-objective robust possibilistic programming (MORPP) model, we adopt ԑ-constraint

20

method.

21

4.3. ԑ-constraint method 24 ACS Paragon Plus Environment

Page 25 of 43

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1


Assume the following multi-objective problem: 𝑚𝑖𝑛 {𝑓1 (𝑥), 𝑓2 (𝑥), … , 𝑓𝑝 (𝑥)} 𝑠. 𝑡.

𝑥 ∈ 𝑆,

2

Where x is the vector of decision variables, 𝑓𝑖 (𝑥) is the ith objective function, p is the number of

3

objective functions and s is the feasible region. A feasible solution 𝑥 is said to be efficient and the

4

corresponding objective function is said to be non-dominated if there is no other feasible solution 𝑥́ such

5

as 𝑓𝑖 (𝑥́ ) ≤ 𝑓𝑖 (𝑥) for every i=1, 2, … , p with at least one strict inequality.

6

In the ԑ-constraint method, one of the objective functions is optimized and the other objective functions

7

are incorporated as constraints into the constraint part of the model as follows: 𝑚𝑖𝑛

𝑓1 (𝑥)

𝑠. 𝑡.

𝑓2 (𝑥) ≤ 𝜀2 , 𝑓3 (𝑥) ≤ 𝜀3 , ⋯ 𝑓𝑝 (𝑥) ≤ 𝜀𝑝 , 𝑥 ∈ 𝑆.

8

Where 𝜀𝑖 is the satisfaction level of objective function i and solutions can be obtained by parametrical

9

variations of satisfaction levels 𝜀2 , 𝜀3 , … , 𝜀𝑝 in the RHS of the constrained objective functions. If some of

10

the objective function should be maximized, the related constraint should be in the form of 𝑓𝑖 (𝑥) ≥ 𝜀𝑖 .

11

The steps of ԑ-constraint method can be summarized as follows:

12

Step 1: Solve (p-1) single-objective problem (SOP) and find the optimum solution and related objective

13

function value that can be stated as follows: 𝑆𝑂𝑃𝑖 ∶ 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒 𝑓𝑖 (𝑥) 𝑖=2,…,𝑝

⇒ 𝑥𝑖∗ , 𝑓𝑖 (𝑥𝑖∗ )

𝑠. 𝑡. 𝑥 ∈ 𝑆. 14

Step 2: Using the solution that optimizes ith objective function, calculate values for other objective

15

functions. These values form ith row of the payoff table. Applying this way all rows of payoff table are

16

determined. for each column i, determine the minimum and maximum values of the objective function i

17

(i.e., 𝑦𝑖𝑚𝑖𝑛 , 𝑦𝑖𝑚𝑎𝑥 ). The structure of payoff table is illustrated in Figure 3. 25 ACS Paragon Plus Environment


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Page 26 of 43

1

Step 3: vary the value of epsilon in the range of corresponding objective function resulted from payoff

2

table, i.e., 𝑦𝑖𝑚𝑖𝑛 ≤ 𝜀𝑖 ≤ 𝑦𝑖𝑚𝑎𝑥 . Often the range of objective function is segmented into equal parts and

3

the grid points are used as the value of epsilon.

4

Step 4: If the decision maker is satisfied with one of the generated solutions, stop and select the preferred

5

solution as the final decision, otherwise select the most preferred segment and vary the value of ԑ in the

6

new range and generate new pareto-optimal solutions.

7 8

𝑓2 (𝑥2∗ )

⋯ ⋯

𝑓𝑝 (𝑥2∗ )

⋮

⋮

⋯

⋮

11

𝑥𝑝∗

𝑓𝑝 (𝑥𝑝∗ )

𝑓𝑝 (𝑥𝑝∗ )

12

𝑦𝑖𝑚𝑖𝑛

𝑓2 (𝑥2∗ )

13

𝑦𝑖𝑚𝑎𝑥

𝑚𝑎𝑥 (𝑓2 (𝑥𝑖 ))

⋯ ⋯ ⋯

𝑆𝑂𝑃𝑖

𝑓2 (𝑥𝑖 )

9

𝑥2∗

10

𝑓𝑝 (𝑥𝑖 )

𝑓𝑝 (𝑥𝑝∗ ) 𝑚𝑎𝑥 (𝑓𝑝 (𝑥𝑝 ))

Figure 3. structure of payoff table in ԑ-constraint method

14 15 16

5. implementaion and evaluation

17

In order to analyze the performance and usefulness of the developed multi-objective robust possibilistic

18

programming model, the proposed model is applied to a case study to establish a lignocellulosic

19

bioethanol supply chain in Iran.

20

In this study, two types of crop residues are considered as lignocellulosic biomass feedstocks i.e., corn

21

stover and wheat straw which are available in Iran. All 31 provinces of Iran are potential lignocellulosic

22

biomass supply zones, potential biorefinery locations and bioethanol demand zones. Demand is presumed

23

to be proportional to the population in each demand zone. The information about the gasoline

24

consumption of each zone in 2012 is available by the National Iranian Oil Products Distribution Company

25

(NIOPDC)

26

demand of each zone, gasoline consumption per capita is multiplied by population of that zone.

27

We consider three production capacity levels for biorefineries including 50 MGY, 100 MGY and 150

28

MGY. In addition, two different conversion technologies are considered, including biochemical and

29

thermochemical. For the current case study, the time horizon is one year and the duration of a time period

30

is defined as a month to avoid the additional complexities in the solution approach. The proposed model is

53

. The consumption rate per capita is calculable from these data. In order to estimate the


Page 27 of 43

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1

coded in the GAMS 24 optimization software that uses the CPLEX solver and all the empirical

2

experiments are run on a Intel® core™ i5 2.67GHz processor with 4 GB memory RAM.

3

First robust counterpart of the constrains with uncertain parameters is generated according to MORPP

4

model; then for determining values of positive ideal solution (PIS) and negative ideal solution (NIS) for

5

E[Z1] , E[Z2] and Z3 we solve each model separately in order to calculate objective function OF1. As

6

mentioned before, OF1 is an aggregation of E[Z1] , E[Z2] and Z3 basic objective functions. Similarly,

7

after calculating values of positive ideal solution (PIS) and negative ideal solution (NIS) for obj1 and

8

obj2, objective function OF2 is computable through aggregating obj1 and obj2. Table 3 illustrates the

9

results for positive and negative ideal solutions related to elements of OF1 and OF2. Finally to solve

10

multi-objective problem of maximizing OF1 (aggregated objective function, including economic,

11

environmental and social objectives) and OF2 (optimality robustness), as well as, minimizing OF3

12

(feasibility robustness) we use epsilon constraint method which can be presented as follows: 𝑚𝑎𝑥

𝑂𝐹1

𝑠. 𝑡.

𝑂𝐹2 ≥ 𝜀2 , 𝑂𝐹3 ≤ 𝜀3 , 𝑥 ∈ 𝑆.

13

Where S indicates the feasible region of the problem involving the constraints (1)–(17) of the original

14

model in which constraints (13) and (14) (including uncertain parameters) are replaced with the

15

corresponding robust counterparts as follows: 𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 + 𝑜𝑘,𝑡 ≥ 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑎𝑥 . ((1 − 𝛼). 𝐷𝑘,𝑡(3) + 𝛼. 𝐷𝑘,𝑡(4) ), 𝑗

𝑚

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 ∑ ∑ 𝑓𝑗,𝑘,𝑚,𝑡 ≥ 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑖𝑛 . ((1 − 𝛼). 𝐷𝑘,𝑡(3) + 𝛼. 𝐷𝑘,𝑡(4) ), 𝑗

∀𝑘, 𝑡 ∀𝑘, 𝑡

𝑚

16

Also, the deterministic model can be shown as follows, which is solved under nominal data in order to be

17

compared with proposed model results.

18

(Deterministic model) 𝑚𝑎𝑥

𝑂𝐹1

𝑠. 𝑡.

𝑥 ∈ 𝑆́

19

Where 𝑆́ indicates the feasible region of the original model involving the constraints (1)–(17) in which for

20

̃𝑘,𝑡 in constraints (13) and (14) nominal data are used. value of uncertain parameter demand, i.e., 𝐷 27 ACS Paragon Plus Environment


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1

Page 28 of 43

Table 3. Results of positive and negative ideal solutions for basic objective functions Objective function E[z1]

E[z2]

z3

obj1

obj2

Positive ideal solution (PIS)

Negative ideal solution (NIS)

148122000000

-8744000667.49

{max E[z1]; s.t: xϵS}

{min E[z1]; s.t: xϵS}

12572100000

190622000000

{min E[z2]; s.t: xϵS}

{max E[z2]; s.t: xϵS}

327997.578

22021.357

{max z3; s.t: xϵS}

{min z3; s.t: xϵS}

153750800

2909310000

{min obj1; s.t: xϵS}

{max obj1; s.t: xϵS}

400767700

6465463000

{min obj2; s.t: xϵS}

{max obj2; s.t: xϵS}

2

Values of epsilon for OF2 and OF3 are obtained from the payoff table which are provided through Table

3

4. Table 5 summarizes computational results of solving the case problem under deterministic and

4

proposed MORPP model considering two importance weight vector of economic, environmental and

5

social objectives (i.e., E[z1], E[z2] and z3). In this Table, solutions 3, 4 and 5 are pareto optimal solutions

6

of proposed model generated under (1.5, 1, 0.5) weight vector while 6, 7 and 8 are correspond to (1, 1, 1)

7

vector of economic, environmental and social objectives. Also, solutions 1 and 2 are associated with

8

solving deterministic model under two aforementioned weight vectors. For deterministic model, values of

9

OF1 objective function and related basic objective functions, as well as, established biorefineries location

10

along with capacity level and technology type are reported. For MORPP model, values of OF2 and OF3

11

objective functions are also reported. As Table 5 shows, considering the results from solution 3 toward 5

12

or from solution 6 to 8, decreasing the limit of OF2 and increasing the limit of OF3 which means

13

decreasing the influence of OF2 and OF3 respectively, leads to more desirable values for OF1. Despite

14

the fact that the results of deterministic and robust optimization models are not comparable under nominal

15

data because of the inevitable superiority of deterministic solutions, but comparison of solutions 3, 4 and

16

5 with 1 on the basic objective functions reveals that solutions 4 and 5 dominate 1 in two objective

17

functions even under nominal data. Moreover, solution 3 dominates 1 in terms of first objective function

18

and have a close performance in the third objective function. Likewise, solutions 7 and 8 dominate 2 in

19

two objective functions under nominal data.

20

Table 4. Payoff table for OF2 and OF3 objectives 𝑺𝑶𝑷𝒊 𝒙∗𝟐

OF2

OF3

1.834

1426476

{max OF2; s.t: xϵS}

{OF3(x=𝑥2∗ )}


Page 29 of 43

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1.6234

-971406

{OF3(x=𝑥3∗ )}

{min OF3; s.t: xϵS}

𝒚𝒎𝒊𝒏 𝒊

1.6234

-971406

𝒚𝒎𝒂𝒙 𝒊

1.834

1426476

𝒙∗𝟑

1

In order to validate the proposed model under nominal data, we formulate a deterministic linear

2

programming model called “realization model” which is somehow a simulation of reality. In the

3

realization model values of imprecise parameters are produced randomly in the corresponding interval

4

under each realization (e.g.,𝑑𝑟𝑒𝑎𝑙 ) and the realization model is solved for obtained solutions from the

5

deterministic and proposed model (i.e., x1*, x2*, y*). As mentioned before, all the uncertain parameters are

6

represented by trapezoidal possibility distribution function (e.g., 𝑑̃= (𝑑(1) , 𝑑(2) , 𝑑(3) , 𝑑(4))). Here uniform

7

distribution is used to generate random values for imprecise parameters under each realization which

8

produces a random number uniformly between two extreme points of the corresponding interval (i.e.,

9

𝑑𝑟𝑒𝑎𝑙 ∼ [𝑑(1) , 𝑑(4) ]). Compact form of the realization model can be stated as follows: (Realization Model) 𝒎𝒂𝒙 𝑶𝑭𝒓𝒆𝒂𝒍 = 𝝀𝟏 .

(𝒑𝒓𝒆𝒂𝒍 𝒙∗𝟐 − 𝒒𝒙∗𝟏 − 𝒇𝒚∗ ) − 𝒛𝑵𝑰𝑺 𝟏

+ 𝝀𝟑 .

∗

𝒛𝑷𝑰𝑺 − 𝒛𝑵𝑰𝑺 𝟏 𝟏 (𝒌𝒚∗ + 𝒔𝒙∗𝟐 ) − 𝒛𝑵𝑰𝑺 𝟑 ∗

𝒛𝑷𝑰𝑺 − 𝒛𝑵𝑰𝑺 𝟑 𝟑

∗

∗

∗

+ 𝝀𝟐 .

𝒛𝑵𝑰𝑺 − (𝒉𝒓𝒆𝒂𝒍 𝒙∗𝟐 ) 𝟐 ∗

𝒛𝑵𝑰𝑺 − 𝒛𝑷𝑰𝑺 𝟐 𝟐

∗

∗

−𝝅𝑹𝒅 𝒔. 𝒕. 𝑳𝑩 ≤ 𝒙∗𝟏 ≤ 𝑼𝑩, 𝑨𝒙∗𝟐 + 𝑹𝒅 ≥ 𝒅𝒓𝒆𝒂𝒍 , 𝑩𝒙∗𝟐 = 𝟎, 𝑪𝒙∗𝟐 ≤ 𝒆𝒙∗𝟏 , 𝑺𝒙∗𝟐 ≤ 𝑴𝒚∗ , 𝑻𝒚∗ ≤ 𝟏, 𝑹𝒅 ≥ 𝟎, 10 11

In which Rd is the only decision variable that determine the violation of chance constraint under random

12

realization and 𝜋 is the penalty cost of this violation which is assumed to be equal to the penalty of unmet

13

demand because it is corresponds to the demand satisfaction constraint. The results obtained under

14

realizations are summarized in Table 6. As the objective function of realization model is meaningless,

15

values of infeasibility penalty (i.e., 𝜋𝑅 𝑑 ) are reported in Table 7 in order to compare results of

16

deterministic and proposed model under 10 realizations. As can be seen from Table 7, all of the MORPP



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

Page 30 of 43

1

model pareto optimal solutions have better performance in terms of average as well as the standard

2

deviation of the infeasibility penalty values compared with the deterministic model solutions. Besides,

3

from solution 3 toward 5, the value of average performance and standard deviation worsen because with

4

respect to results of Table 5 the impact of OF2 and OF3 limits is reduced. Since the optimality robustness

5

objective function (OF2) seeks to minimize the maximum deviation of the solution vector from the

6

optimal value in (almost) all possible values of uncertain parameters, reducing the impact of OF2 leads to

7

increasing the standard deviation. Also, disregarding OF3 limits leads to increasing amount of

8

infeasibility and hence, increasing the average penalty values.

9

Also, we calculate the basic objective function values under each realization and compare performance in

10

terms of average and standard deviation of these objective functions under realizations for all solutions.

11

Computational results are illustrated in Table 8.

12 13

Figure 4. Comparison of obtained solutions in terms of z1, z2 and z3 objective functions and corresponding standard

14

deviations under realizations

15

From the results of Table 8 we can observe that in comparison of solution 1 with 3, 4 and 5, performance

16

of 4 in terms of z1 and z2 average is better than 1 and have an almost similar performance in z3 average. 30 ACS Paragon Plus Environment

Page 31 of 43

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1

Also, from the aspect of the standard deviation solution 4 outperforms 1. Solution 7 outperforms 2 in

2

terms of all basic objective functions. Additionally, solutions 3, 4 and 5 outperform 1 in at least 2

3

objective function averages. Similarly, solutions 6, 7 and 8 have better performance than 2 in at least 2

4

objectives. Figure 4 compares the performance of obtained solutions in terms of z1, z2 and z3 objectives

5

as well as corresponding standard deviations under realizations as mentioned in Table 8. It should be

6

noted that since the scales of objective function values are different, the results of objective function

7

values are normalized through dividing each objective function value by the maximum value of

8

corresponding objective function among compared solutions. As can be seen, pareto solutions dominates

9

the corresponding deterministic solution in at least two objective function value. The DM can prefer one

10

of the pareto solutions according to the importance of economic, environmental and social objectives. In

11

the case that DM Prefers economic objective than environmental and social objectives, solutions 4, then 7

12

and then 8 are proper. If deviation over and above the optimal value are undesirable for DM, solution 7 is

13

better than 4. In the case that economic and social objectives are important for DM, solutions 5, 7 and 8

14

are better than 4. If social and environmental objectives are as important as economic objective, solutions

15

3 and 5 seems good. On the other hand, if DM is very sensitive to deviation from objectives optimal

16

values, solutions 4, 6 and 7 have better performance than others. Finally, it seems that solution 4 is a good

17

choice because has a superior performance in economic and environmental objectives with a low amount

18

of standard deviation, although has the least performance in terms of social objective function.

19

Figure 5 and Figure 6 displays the resulting lignocellulosic bioethanol supply chain network involving

20

biorefineries locations, capacities and technology type related to solution 1 and 4. According to solution 1

21

two biorefineries are established with a capacity of 50 MGY, one with 100 MGY and three with 150

22

MGY capacity. Technology type of all the biorefineries is biochemical except in the case of Khorasan,

23

North. In solution 4, four biorefineries are established with a capacity of 50 MGY, one with 100 MGY

24

and two with 150 MGY capacity. All of the established biorefineries are based on biochemical

25

technology. As can be seen, locations of biorefineries in solution 4 are more sporadic than solution 1.

26

Moreover, Table 9 illustrates the Results of optimal land area allocation to lignocellulosic biomass

27

feedstocks in supply zones corresponds to solutions 1 and 4. Input data related to the current land area

28

allocation fractions are available by the agricultural ministry of Iran 54.

29 30



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

Objective function values

OF1 Soluti-

Model

on No.

Epsilon

Aggregated

Limits

of Z1, Z2

(*)

& Z3 OFs (**)

Deterministic

1

-

model

2.232

Page 32 of 43

OF2

OF3

Z1

Optimality

Feasibility

Profit

Robustness

Robustness

($M)

-

-

(1.5,1,0.5)

Z2 Environmental Impact (mPt)

11.4497E+1

2.76197E+1

0

0

Z3 Social

established

biorefineries

Location(***)

Responsibility

107015.42

Ardabil(1,2)Gilan(1,2)Golestan(3,2)K horasan,North(3,1)

Markazi(2,2)

Qom(3,2) Deterministic

2

-

model MORPP

-

-

11.936E+10

(1,1,1) 3

model MORPP

1.930

4

model

OF2≥1.7872

2.229

OF3≤-252041.4

(1.5,1,0.5)

OF2≥1.7638

2.578

OF3≤-12253.2

(1.5,1,0.5)

4.37721E+1

110092.14

Markazi(3,2) Mazandaran(3,2)

0 1.788

1.783

-252041.4

-12253.20

11.8907E+1

3.39030E+1

0

0

14.5800E+1

1.26498E+1

0

0

Ardabil(1,2) Isfahan(2,2)

100553.25

Ardabil(1,2) Fars (3,2) Gilan (3,2) Khorasan, South (3,2)

83412.39

Chahar Mahaal and Bakhtiari(1,2) Zanjan(1,2)Mazandaran(3,2) Ilam(3,2)Qazvin(1,2)Semnan

(1,2)

Sistan and Baluchestan (2,2) MORPP

5

model

OF2≥1.6234

2.651

OF3≤ 1426476

(1.5,1,0.5)

1.625

1426476

12.4110E+1

4.90489E+1

0

0

130373.34

Bushehr(1,2)Hormozgān(3,2)Ilam(1,2 )Khuzestan(1,1)Kohgiluyeh

and

Boyer-Ahmad(3,2) Yazd(3,2) MORPP

6

model

OF2≥1.6936

1.692

OF3≤707111.4

(1,1,1)

1.995

707111.40

6.77237E+1

1.26701E+1

0

0

85269.49

Chahar Mahaal and Bakhtiari (3, 2)Hormozgān (3, 1) Kurdistan (3, 2)Mazandaran (3, 1)

MORPP

7

model

OF2≥1.7404

1.893

OF3≤227535

(1,1,1)

1.740

227535

13.6911E+1

3.88894E+1

0

0

117621.80

Fars(3,2)Ilam(3,2)Khorasan, Razavi(1,2)Kurdistan(2,2)

Lorestan

(2,2) Qazvin (1,2) MORPP model

Table 5.

8

OF2≥1.6234

2.087

OF3≤1426476

(1,1,1)

1.631

1426476

13.9459E+1

5.01377E+1

0

0

129992.90

Azerbaijan,East(1,2)Fars(3,2)Golesta n (3, 2) Qom(3,2) Zanjan (1, 2)

Computational results of deterministic and proposed MORPP model under different weight of objective functions and epsilon limits

* Limits of OF2 & OF3 objective functions (ɛ2, ɛ3). ** Importance weight of OFs (Z1, Z2, Z3). *** (Capacity level, Technology type)


Page 33 of 43

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1

6. Conclusions and future research

2

This paper has presented a multi-objective MILP model for design and planning of lignocellulosic biofuel

3

supply chain, including biomass supply zones, candidate biorefinery locations and demand zones under

4

various types of uncertainties. The optimization model determines biomass sourcing and allocation,

5

locations, capacity level and technology type selection of biorefinery facilities, inventory levels,

6

production amounts, and shipments among the network. Uncertainty of input data involving market

7

prices, biofuel demand and environmental impacts are treated as fuzzy numbers and dealt with using a

8

robust possibilistic programming approach.

9

Table 6. The performance of the deterministic and proposed model under 10 realizations.

𝑶𝑭𝒓𝒆𝒂𝒍 Realization No.

Deterministic model

MORPP model solutions

solutions 1

2

3

4

5

6

7

8

1 (nominal data)

2.23

1.93

2.23

2.58

2.24

1.69

1.89

2.09

2

-43915.46

-45376.55

-19.43

-466.96

-2345.44

-1404.62

-935.45

-2341.77

3

-41046.37

-41432.1

-0.36

-10.38

-12.19

-13.85

-5.68

-21.23

4

-53687.14

-54826.11

-24.36

-668.79

-2489.83

-1584.98

-292.13

-2057.05

5

-64263.65

-66724.83

-51.97

-842.05

-2770.72

-4470.62

-4355.85

-6517.92

6

-76777.11

-78548.65

-17.78

-1564.97

-6031.80

-4905.92

-2366.23

-6635.53

7

-46665.98

-47834

-17.56

-96.40

-108.05

-117.09

-57.29

-176.08

8

-47092.24

-63890.94

-55.23

-783.04

-4808.19

-3151.21

-2838.17

-4604.54

9

-61530.37

-48340.46

-15.69

-5291.69

-3610.51

-4198.96

-2936.60

-8703.06

10

-59001.48

-59421.22

-60.61

-1.70

-14.87

20.43

-31.09

-34.78

10

The major contribution of this study is to develop a multi-objective robust possibilistic programming

11

(MORPP) approach which extends robust possibilistic approach concepts to deal with multi-objective

12

nature of the problem. To the best of our knowledge, it is the first time that robust possibilistic

13

programming approach is developed for multi-objective problem in the presence of uncertain parameters

14

in objective functions. Additionally, sustainability issues are involved through considering economic,

15

environmental and social objective functions in the concerned problem.

16

Table 7. Penalty of infeasibility for the deterministic and proposed model under 10 realizations.

𝝅𝑹𝒅 Deterministic model Realization No.

MORPP model solutions

solutions 1

2

3

4

5


6

7

8


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

Page 34 of 43

1 (nominal data)

0

0

0

0

0

0

0

0

2

43917.69

45378.49

21.659

469.54

2343.86

1640.70

937.54

1643.38

3

41048.60

41434.03

2.591

12.96

23.32

21.45

7.77

25.91

4

53689.37

54828.04

26.592

671.37

2278.74

1391.88

294.22

2293.51

5

64265.89

66726.77

54.201

844.63

5945.86

3911.33

4357.94

6466.88

6

76779.34

78550.59

20.016

1567.55

6789.45

4259.73

2368.33

7005.39

7

46668.22

47835.93

19.797

98.98

178.17

168.92

59.39

197.97

8

47094.47

48342.39

57.46

785.62

4680.57

3443.81

2840.26

3073.58

9

61532.60

63892.87

17.92

5294.27

7834.63

5854.07

2938.70

7646.99

10

59003.711

59423.16

62.841

4.279

36.87

33.178

33.178

42.794

Average

49399.99

50641.23

23.98

974.92

3011.15

2072.51

1383.73

2839.64

Standard deviation

20497.68

21076.82

27.36

1598.39

3069.36

2141.66

1603.01

3094.55

1 2

Table 8. Results of z1, z2 and z3 values of solutions and corresponding standard deviations under 10 realizations model Deterministic model Deterministic model MORPP model MORPP model MORPP model MORPP model MORPP model MORPP model

Solution

Z1

Z2

Z3

No.

Average

SD

Average

SD

Average

SD

1

114.56E+10

13.5E+07

2.75E+10

2.33E+08

110092.1

0

2

119.44E+10

15.6E+07

43.6E+10

3.70E+08

107015.4

0

3

118.94E+10

9.95E+07

3.38E+10

2.87E+08

100553.3

0

4

145.89E+10

12.7E+07

1.26E+10

1.07E+08

83412.4

0

5

124.2E+10

14.7E+07

4.89E+10

4.16E+08

130373.3

0

6

67.74E+10

3.70E+07

12.6E+10

1.07E+08

85269.5

0

7

136.95E+10

11.4E+07

38.8E+10

3.30E+08

117621.8

0

8

139.51E+10

14.7E+07

50.0E+10

4.25E+08

129992.9

0

3

A case study of lignocellulosic supply chain established in Iran is applied to indicate the effectiveness of

4

the proposed model. Diverse solutions achieved by the proposed MORPP approach outperform

5

deterministic solutions in terms of performance measures. Regarding the obtained results, it can be

6

concluded that deterministic solutions are not realistic and effective in the presence of uncertainty.


Page 35 of 43

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1

The direction for future research is to consider all types of uncertainty sources for input data. Another

2

future research path could be accounting for considering interval model of uncertainty for imprecise

3

parameters.

4 5

Table 9. Results of optimal land area allocation (hectare) to lignocellulosic biomass feedstocks in supply zones related to solutions 1 and 4 Current Name of supply zone

land

area

allocation

Solution #1

Solution #4

(Deterministic model)

(MORPP model)

Corn

wheat

Corn

Wheat

Corn

Wheat

Alborz

0

6892

38.632

13784

38.632

13784

Ardabil

9299

352976

37196

529464

37196

529464

Azerbaijan, East

414

382090

41400

573135

41400

573135

Azerbaijan, West

5343

398310

53430

597465

53430

597465

Bushehr

266

126290

26600

138919

26600

138919

Chahar Mahaal and Bakhtiari

126

72219

15750

86662.8

15750

86662.8

Fars

43992

389346

87984

467215.2

87984

467215.2

Gilan

60

5818

24000

29090

24000

29090

Golestan

770

326286

53900

358914.6

53900

358914.6

Hamadan

9910

356983

49550

392681.3

49550

392681.3

Hormozgān

6704

13713

100560

41139

100560

41139

Ilam

8028

130776

160560

143853.60

160560

143853.60

Isfahan

1867

90404

56010

108484.8

56010

108484.8

Kerman

37668

114134

45201.6

125547.4

45201.6

125547.4

Kermanshah

38990

424928

116970

446174.4

116970

446174.4

Khorasan, North

140

140977

14000

148025.85

14000

148025.85

Khorasan, Razavi

469

391986

70350

431184.6

70350

431184.6

Khorasan, South

10

32927

7000

36219.7

7000

36219.7

Khuzestan

97804

623910

102694.2

627029.55

102694.2

627029.55

Kohgiluyeh and Boyer-Ahmad

799

88000

79900

92400

79900

92400

Kurdistan

1682

603477

84100

663824.7

84100

663824.7

Lorestan

7915

261052

55405

287157.2

55405

287157.2

Markazi

272

253730

68000

266416.5

68000

266416.5

Mazandaran

404

48487

40400

145461

40400

145461

Qazvin

8280

169635

82800

178116.75

82800

178116.75

Qom

0

12138

57.090

20634.6

57.090

20634.6

Semnan

56

43717

28000

48088.7

28000

48088.7

Sistan and Baluchestan

5521

73327

165630

80659.7

165630

80659.7

Tehran

8

41510

16000

45661

16000

45661

Yazd

3209

26573

32090

29230.3

32090

29230.3

Zanjan

10

397382

10000

417251.1

10000

417251.1

6 35 ACS Paragon Plus Environment


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

1 2 3 4 5 6 7 8

Legend Biorefinery locations, capacity level & technology type Capacity 50 MGY Thermochemical Capacity 100 MGY Thermochemical Capacity 150 MGY Thermochemical Capacity 50 MGY Biochemical

9

Capacity 100 MGY Biochemical

10


11

Biomass supply zones

12

Biomass Cultivation Sites

13

Caspian Sea

Figure 5. The illustration of lignocellulosic bioethanol supply chain (LBSC) network nodes related to solution#1

14 15 16 17

Legend Biorefinery locations, capacity level & technology type

18

Capacity 50 MGY Thermochemical

19


20


21


22 23 24 25 26 27

Caspian Sea

Capacity 100 MGY Biochemical Capacity 150 MGY Biochemical

Biomass supply zones Biomass Cultivation Sites

Figure 6. The illustration of lignocellulosic bioethanol supply chain (LBSC) network nodes related to solution#4


Page 36 of 43

Page 37 of 43

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1

ASSOCIATED CONTENT

2

Supporting Information

3

Values of input parameters used in the case study are available in Tables S1-S8. Key deterministic

4

parameters and selling prices of commodities values are provided in Tables S1 and S2. Table S3

5

illustrates maximum available area and cultivated current fraction for each feedstock of each supply zone.

6

The values of the imprecise parameter demand and the distance between potential biorefinery locations

7

and biomass supply zones/demand zones are provided through Tables S4 and S5, respectively. Demand

8

values of each realization in time period 7 are displayed in Table S6. Table S7 summarizes satisfied demand

9

related to solutions 1 and 4 in time period 7 under 10 realizations . Environmental impacts related data are

10

summarized in Table S8. This information is available free of charge via the Internet at

11

http://pubs.acs.org/.

12 13

AUTHOR INFORMATION

14

Corresponding Author

15

*E-mail: [email protected].

16 17

NOMENCLATURE

18

Indices

19

𝑖 = Biomass supply zones, i=1,…,I

20

𝑗 = Candidate locations for biorefineries, j=1,…, J

21

𝑟 = Capacity levels available for biorefineries, r=1,…, R

22

𝑠 = Conversion technology types available for biorefineries, q=1,…, Q

23

𝑘 = Bioethanol demand zones, k=1,…, K

24

𝑏 = Lignocellulosic biomass feedstock types, b=1,…, B

25

Parameters

26

𝑎𝑟𝑒𝑎𝑖𝑚𝑎𝑥 = Maximum available area of supply zone i, hectare

27

𝑓𝑟𝑖,𝑏 = Current fraction of supply zone i assigned for lignocellulosic biomass feedstock type b cultivation

28

𝑖𝑛𝑐𝑟𝑎𝑡𝑒𝑏,𝑖 = Maximum allowable increasing rate for cultivating feedstock b in supply zone i

29

𝑦𝑙𝑏𝑟𝑒𝑠𝑖𝑑𝑢𝑒 = Yield of biomass feedstock b, tonne/hectare

30

𝑦𝑙𝑏

31

ℎ𝑙𝑜𝑠𝑠𝑏,𝑖,𝑡 = Fraction of harvesting loss of biomass feedstock b in supply zone i at time period t

𝑐𝑟𝑜𝑝

= Yield of biomass main crop b, tonne/hectare



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

Page 38 of 43

1

𝑑𝑟𝑎𝑡𝑒𝑏,𝑡 = Biomass feedstock b deterioration rate during storage in collection facility at time period t

2

𝜇 = Maximum ratio of crop residues that can be removed from supply zones

3 4

𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑎𝑥 = Maximum percentage of gasoline equivalent annual demand to be satisfied from bioethanol

5 6

𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑚𝑖𝑛 = Minimum percentage of gasoline equivalent annual demand to be satisfied from bioethanol

7

𝑏𝑒𝑙 𝜃𝑏,𝑠 = Conversion factor of biomass feedstock type b through technology s to bioethanol, gallon/drytonne

8

𝜃𝑏,𝑠,𝑔

9

or kw/tonne


= Conversion factor of biomass feedstock type b through technology s to bioethanol, kg/tonne

10

𝜔 𝑟𝑒𝑓 = Minimum efficiency percentage of biorefinery capacity

11

𝑏𝑝𝑟𝑔,𝑡 = By-product sale price at time period t, $/gallon or $/Mwh

12

𝑟𝑒𝑛𝑡𝑖 = Renting cost of biomass supply zone i, $/hectare

13

𝑐𝑢𝑙𝑖,𝑏 = Cultivation cost of biomass feedstock type b, $/hectare

14

ℎ𝑖,𝑏 = Harvesting cost of biomass feedstock type b, $/tonne

15

𝛾 = Unit penalty cost of unmet bioethanol demand, $/gallon

16

𝑑𝑖𝑠𝑖,𝑗,𝑚

17

𝑡𝑐𝑜𝑠𝑡𝑏 𝑖,𝑗,𝑚 =Transportation cost of biomass feedstock b via transportation mode m per unit of distance

18

between supply zone i & biorefinery j, $/km

19

𝑑𝑖𝑠𝑗,𝑘,𝑚

20

𝑡𝑐𝑜𝑠𝑡𝑘,𝑙,𝑚

21

biorefinery k & demand zone l, $/km

22 23

𝑡𝑟𝑢𝑐𝑘𝑙𝑜𝑎𝑑𝑐𝑜𝑠𝑡𝑏,𝑖,𝑗,𝑚 = Truck loading and unloading cost of biomass feedstock b via transportation mode

24

between supply zone i & biorefinery j ($)

25 26

𝑡𝑟𝑢𝑐𝑘𝑙𝑜𝑎𝑑𝑐𝑜𝑠𝑡𝑏,𝑖,𝑗,𝑚

27

biorefinery k & demand zone l ($)

28

𝑡𝑟𝑢𝑐𝑘𝑐𝑎𝑝𝑚 = Capacity of truck type m (dry tonne)

29

𝑡𝑟𝑢𝑐𝑘𝑐𝑎𝑝𝑚 = Capacity of truck type m (gallon)

30 31

ℎ𝑐𝑜𝑠𝑡𝑏,𝑗,𝑡

32

t, $/ tonne.month

33


= Distance from supply zone i to biorefinery j via transportation mode m, km



= Distance between biorefinery j & demand zone k via transportation mode m, km


= Transportation cost of bioethanol via transportation mode m per unit of distance between 𝑠𝑢𝑝,𝑟𝑒𝑓

m 𝑟𝑒𝑓,𝑑𝑒𝑚

= Truck loading and unloading cost of bioethanol via transportation mode m

between


= Inventory holding cost of biomass feedstock b per month in biorefinery j at time period

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 ℎ𝑐𝑜𝑠𝑡𝑗,𝑡 = Holding cost of bioethanol per month in biorefinery j at time period t, $/gallon.month


Page 39 of 43

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



1

𝑠𝑖𝑏

2

b production, job/tonne

3 4

𝑠𝑖𝑏,𝑖,𝑗,𝑚 = Number of local jobs generated pear year due to the unit harvested biomass type b shipped from

5

supply zone i to biorefinery j via transportation mode m, job/tonne

6

𝑠𝑖𝑗,𝑘,𝑚

7

to demand zone k via transportation mode m, job/gallon

8 9

𝑠𝑖𝑗,𝑟,𝑠 = Number of local jobs generated per year due to the construction of biorefinery j with capacity level

= Number of local jobs generated pear year due to the unit production of biomass feedstock type



= Number of local jobs generated per year due to the unit bioethanol shipped from biorefinery j

𝑟𝑒𝑓

10

r and technology type s, job

11

𝑠𝑖𝑗,𝑠

12

biorefinery j with technology s, job/gallon

13

𝑢𝑝𝑐𝑎𝑝𝑖,𝑗,𝑚,𝑡 = Maximum allowed transportation quantity of link between supply i and biorefinery j via

14

transportation mode m at time period t, tonne/year

15 16

𝑢𝑝𝑐𝑎𝑝𝑗,𝑘,𝑚,𝑡

17

k via transportation mode m at time period t, tonne/year

18

𝑣𝑎𝑟𝑐𝑜𝑠𝑡𝑗,𝑠 = Variable cost of biorefinery j with technology type s, $/gallon

19

𝑓𝑖𝑥𝑒𝑑𝑐𝑜𝑠𝑡𝑗,𝑟,𝑠 = Fixed cost of biorefinery j with capacity level r and technology type s, $

20

𝑙𝑡𝑑𝑢𝑟 = Project life time duration, year

21

Uncertain parameters

22

𝑝𝑟𝑡 = Bioethanol selling price at time period t, $/gallon

23

𝑝𝑟𝑖𝑐𝑒𝑏 = Main crop type b selling price, $/tonne

24

𝐷𝑘,𝑡 = Bioethanol demand of demand zone k at time period t, gallon

25

𝑒𝑖𝑏

26

𝑒𝑖𝑏,𝑖,𝑗,𝑚,𝑡 = Unit environmental impact of transportation of biomass feedstock b from supply zone i to

27

biorefinery j via transportation mode m at time period, mp/tonne×km

28

𝑒𝑖𝑏,𝑠 = Unit environmental impact of bioethanol production at biorefinery from biomass type b with

29

technology s, mp/tonne

30

𝑒𝑖𝑗,𝑘,𝑚,𝑡

31

k via transportation mode m at time period t, mp/ gallon.km

32

Binary variables

𝑝𝑟𝑜𝑐𝑒𝑠𝑠𝑖𝑛𝑔

= Number of local jobs generated per year due to the unit processing of bioethanol in



= Maximum allowed transportation quantity of link between biorefinery j and demand zone

𝑟𝑒𝑓

𝑟𝑒𝑓


= Unit environmental impact of biomass type b production at supply zones, mp/tonne


𝑟𝑒𝑓


= Unit environmental impact of transportation of bioethanol from biorefinery j to demand zone



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

1

𝑦𝑗,𝑟,𝑠 = Equals 1 if biorefinery with capacity level r and technology type s is opened at location j and 0

2

otherwise

3

Continuous variables

4

𝑥𝑖,𝑏 = Land area dedicated to lignocellulosic biomass feedstock b cultivation in supply zone i, hectare

5

𝑟𝑒𝑠𝑖𝑑𝑢𝑒 ℎ𝑟𝑣𝑏,𝑖,𝑡 = Quantity of biomass feedstock b harvested from supply zone i in time period t, tonne

6

ℎ𝑟𝑣𝑏,𝑖,𝑡 = Quantity of biomass main crop b harvested from supply zone i in time period t, tonne

7

ℎ𝑎𝑟𝑣𝑒𝑠𝑡𝑒𝑑 𝑏𝑖𝑜𝑚𝑎𝑠𝑠 𝑓𝑏,𝑖,𝑗,𝑚,𝑡 = Quantity of biomass feedstock b shipped from supply zone i to biorefinery j via

8

transportation mode m in time period t, tonne

9

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙 𝑓𝑗,𝑘,𝑚,𝑡 = Quantity of bioethanol produced at biorefinery j and shipped to demand zone k via

Page 40 of 43

𝑐𝑟𝑜𝑝

10

transportation mode m at time period t, gallon

11

𝑜𝑘,𝑡 = Quantity of unmet bioethanol demand in demand zone k at time period t, gallon

12

𝑓𝑔,𝑗,𝑡

13

𝑖𝑛𝑣𝑏,𝑗,𝑡

14

𝑖𝑛𝑣𝑗,𝑡

15

𝑏𝑚𝑠𝑏,𝑗,𝑠,𝑡 = Quantity of biomass feedstock b used for the production of bioethanol via technology s in

16

biorefinery j at time period t, tonne

17

𝑏𝑒𝑙𝑗,𝑠,,𝑡 = Amount of produced bioethanol at biorefinery j through technology q at time period t, gallon

18

𝑏𝑦𝑝𝑔,𝑗,𝑡 = Amount of produced byproduct g at biorefinery j at time period t, gallon

19

𝑐𝑎𝑝𝑗,𝑟,𝑠 = Capacity of biorefinery j with capacity level r and technology type s, gallon/year

20

𝑐𝑎𝑝𝑗,𝑠 = Capacity of biorefinery j with technology type j, gallon/year

21

𝑧1 = amount of total profit, $

22

𝑧2 = amount of environmental impacts, mp

23

𝑧3 = number of generated job opportunities


= Quantity of byproduct g produced g produced in biorefinery k at time period t, kg


= Inventory level of biomass type b in biorefinery j at time period t, tonne

𝑏𝑖𝑜𝑒𝑡ℎ𝑎𝑛𝑜𝑙,𝑟𝑒𝑓

= Inventory level of bioethanol in biorefinery j at time period t, gallon

𝑟𝑒𝑓 𝑟𝑒𝑓

24 25

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26 27 28 29 30 31 32 33 34

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Multiobjective Robust Possibilistic Programming Approach to

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