151 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 61, 2017 Guet Editor: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš Copyright 2017, AIDIC Servizi S.r.l. ISBN 978-88-95608-51-8; ISSN 2283-9216 The Italian Aociation of Chemical Engineering Online at www.aidic.it/cet DOI: 10.3303/CET1761023 Deign a Sutainable Supply Chain under Uncertainty uing Life Cycle Optimiation and Stochatic Programming Jiyao Gao, Fengqi You* Cornell Univerity, Ithaca, New York 14853, USA Thi work addree the life cycle economic and environmental optimiation of a upply chain network conidering both deign and operational deciion under uncertainty. A general modelling framework i propoed that integrate the functional-unit-baed life cycle optimiation methodology and the two-tage tochatic programming approach for utainable upply chain optimiation under uncertainty. a tochatic mixed-integer linear fractional programming (SMILFP) model i developed to tackle multiple uncertaintie regarding feedtock upply uncertainty and product demand uncertainty. To addre the computational challenge of olving large-cale SMILFP problem, an efficient olution algorithm that take advantage of the efficiency of parametric algorithm and the decompoition-baed multi-cut L-haped method i ued. A cae tudy baed on a patially explicit model for the county-level hydrocarbon biofuel upply chain i preented in Illinoi to demontrate the applicability of the propoed modelling and algorithmic framework. 1. Introduction Recently, a functional-unit-baed life cycle optimization approach ha been propoed (Yue et al., 2016), which ytematically optimize the economic and environmental performance of a biofuel upply chain baed on a functional unit aociated with the production ytem. The product-centric perpective embedded in thi approach not only capture the major feature of a proce-baed life cycle analyi (LCA), but potentially lead to more cot-effective and utainable upply chain (Gao and You, 2015a). Depite the wide application of LCA-baed approache, criticim are raied for their vulnerability to uncertainty. Uncertaintie are ubiquitou in the biofuel upply chain and inherent in quantitative meaurement of environmental impact (Yue and You, 2016). Simply doing utainable optimiation of a biofuel upply chain without conidering uncertainty would be reckle (Emara et al., 2016), ince both the optimality and feaibility of a upply chain deign can be eaily impaired (Garcia and You, 2015). Therefore, it i imperative to develop a general modelling framework that enable u to effectively handle multiple uncertaintie in utainable deign and operation of upply chain. In thi paper, a novel integrated modelling framework for a utainable biofuel upply chain deign under uncertainty i propoed. It imultaneouly addree economic and environmental concern baed on the functional-unit-baed life cycle optimization framework. Major deciion including upply chain network deign, converion technology election, capital invetment regarding biorefinerie, production planning, tranportation and torage, etc. are fully addreed. Meanwhile, a two-tage tochatic programming tructure i ued to quantitatively account for uncertainty in thi deign and planning problem. In thi way, all poible future outcome are taken into account. Conequently, the economic objective i minimizing the expected unit cot per functional unit aociated with biofuel product. The environmental objective i defined a minimizing the life cycle GHG emiion (in term of CO2 equivalent baed on 100-y time horizon) per functional unit (Yue et al., 2013). Becaue the quantity of functional unit generated in the ytem i an important deciion variable to optimize along with the production deciion, the reulting problem i a bi-criterion tochatic mixed-integer linear fractional programming (SMILFP) problem, which i extremely challenging to olve, featuring both a twotage tochatic tructure and fractional objective function. Thu, a tailored olution algorithm that integrate both a parametric algorithm (Zhong and You, 2014) and the multi-cut L-haped method (You et al., 2009) i ued efficient olution of the reulting bi-criterion SMILFP. Pleae cite thi article a: Gao J., You F., 2017, Deign a utainable upply chain under uncertainty uing life cycle optimiation and tochatic programming, Chemical Engineering Tranaction, 61, 151-156 DOI:10.3303/CET1761023
152 2. Problem tatement To illutrate the application of the propoed modelling framework and tailored olution algorithm, a county-level cae tudy on hydrocarbon biofuel upply chain in Illinoi i conidered. It focue on the utainable deign under uncertainty of county-level hydrocarbon biofuel upply chain in the tate of Illinoi. The functional unit i defined a unit gaoline-equivalent gallon (GEG) liquid biofuel characterized in term of energy content (Yue et al., 2014). Correpondingly, the economic objective i to minimize the expected unit cot per GEG of biofuel. The environmental objective i to minimize the life cycle GHG emiion (in term of CO2 equivalent baed on 100 y time horizon) per GEG of biofuel. The goal i to determine the optimal upply chain configuration (including location, capacitie, and technologie of biorefinerie), and correponding operational deciion (including the amount of material flow, inventory level, and product ale) under different cenario. A upply chain upertructure i preented in the following Figure 1. Figure 1. Supply chain network for hydrocarbon biofuel In thi problem, it i given a et of bioma feedtock, including agricultural reidue (e.g., corn tover), wood reidue (e.g., foret reidue and urban wood reidue), and energy crop (e.g., witchgra). The bioma feedtock can be converted to a et of hydrocarbon biofuel (e.g., gaoline and dieel) through a et of converion technologie (Ng et al., 2015). Thi work focue on integrated biorefinerie, and the pecific technologie conidered include gaification followed by Ficher-Tropch (FT) ynthei (Wang et al., 2013) and fat pyrolyi followed by hydroproceing (Zhang et al., 2014). On the bai of the annual production amount, two range of capacitie are conidered for both converion technologie. The total invetment cot of biorefinerie in each capacity level are modelled uing piecewie linear cot curve to account for the economy of cale. In addition to direct converion, the bioma feedtock can alo be tored at biorefinerie temporarily a inventory. However, degradation and extra charge for inventory will occur at thi torage phae. Similarly, biofuel can either be ditributed directly to demand zone for ale or be held a inventory at biorefinerie. Two major biofuel product are conidered in thi work, namely gaoline and dieel. In addition, demand zone can alo purchae gaoline and dieel through external ource. Accordingly, a penalty cot will be charged. Uncertaintie are in bioma feedtock availability and biofuel demand imultaneouly, both of which follow normal ditribution with a 10 % deviation (Gebrelaie et al., 2012). In order to reduce the number of cenario required, thi approach further incorporate the ample average approximation (SAA) approach for thi twotage tochatic programming problem (Kleywegt et al., 2002). By etting an initial ample ize of 25 cenario and conider a 98 % confidence interval. The number of cenario i finalized a 80. 3. Model formulation and global optimiation algorithm 3.1 Model formulation Following the propoed modelling framework, the reulting problem i a multi-objective SMILFP problem. The economic objective i to minimize the expected unit cot per GEG of biofuel. Here tc1 tand for the um of firt-tage cot correponding to deign deciion and tc2, tand for the econd tage cot correponding to operational deciion in cenario. qt i the variable quantity of functional unit generated in cenario, and cenario probability i denoted by p. The environmental objective i to minimize the life cycle GHG emiion per GEG of biofuel. te tand for the econd tage GHG emiion in cenario. For the compactne of thi paper, we do not provide the detailed model formulation for all the contraint.
153 Economic Objective: min p tc + p tc 1 2, S S qt Environmental Objective: min S S p te p qt (1).t. Ma balance contraint Capacity contraint Logic contraint The component of the firt-tage cot tc1 include the capital invetment, fixed O&M cot, and incentive received for biorefinerie; the econd-tage cot tc2, equal the ummation of cot regarding: bioma acquiition, biofuel production, tranportation, torage, backorder, and incentive; the total GHG emiion te include imilar component for bioma acquiition, biofuel production, tranportation, and torage. 3.2 Tailored global optimiation algorithm The SMILFP problem, a a combination of tochatic programming and MILFP problem, require pecial olution technique to be olved efficiently (Gao and You, 2015b). After exploiting the problem tructure, a tailored global optimization algorithm that integrate the parametric algorithm (Chu and You, 2013) for handling the fractional term, a well a the multi-cut L-haped method (You et al., 2013) i ued for dealing with the cenario planning tructure of SMILP problem. Figure 2 ummarize thi olution algorithm in a peudo code, and note that thi i by far the mot computationally efficient algorithm for globally optimizing general SMILFP problem to 0% optimality gap. Global Optimiation Algorithm F( qw) min N x, y qw D y min N x, y D y 1: Tranform out 2: Initialization: qw 0, Iter 1 out 3: while (objective function F( qw) Tol ) do 4: out out Iter Iter 1 5: in LB, UB, Iter 1, Gap 6: Solve Mater Problem (MP) to obtain x * 7: in while ( Gap Tol ) do 8: in in Iter Iter 1 9: while (Terminate =fale) do 10: Scenario +1, 11: Solve Subproblem (SP) with fixed x * 12: Generate optimality cut: e y d 13: if count S then 14: Terminate true 15: end if 16: end while 17: Add ey d to MP, update UB 18: Solve MP with updated cut Gap UB LB 1 LB 19: Update LB, 20: end while * * * 21: Update parameter qw N x, y D y 22: end while 23: Output qw * Figure 2. Peudo-code of the tailored olution algorithm 4. Cae tudy In thi county-level hydrocarbon biofuel upply chain network, a total of 102 region are conidered, each of which correpond to a ingle county in Illinoi (Gebrelaie et al., 2012). The reulting biofuel upply chain network conit of 20 bioma harveting ite, 8 potential integrated biorefinery facilitie, and 35 demand region (Tong et al., 2014). A 10 y planning horizon i conidered, and each year i further divided into 12 time period, correponding to 12 month/y, to account for the eaonality of bioma upply (You et al., 2012). A
154 10 % dicount rate i adopted for each year (You and Wang, 2011). The reulting problem ha 52,094,579 continuou variable (Stage I: 170; Stage II: 52,094,409), 32 dicrete variable (Stage I: 32; Stage II: 0), and 3,412,636 contraint (Stage I: 222; Stage II: 3,412,414). All of the model and olution procedure are coded in GAMS 24.4.1. The MILP problem are olved uing CPLEX 12.6. The olution of Point C wa obtained after 5 outer iteration within a total of 2,311 CPU econd. The reulting multi-objective SMILFP problem i olved by the algorithm propoed above. By olving 10 intance with uniform interval of GHG emiion per GEG biofuel, an approximated Pareto-curve i obtained in Figure 3. The x-axi repreent the GHG emiion correponding to unit GEG of biofuel. The y-axi repreent the total cot per GEG of biofuel. On the Paretocurve, three point are choen for further demontration. Point A and C are two extreme olution with the lowet GHG emiion per GEG biofuel and lowet cot per GEG biofuel, repectively. Point B i a compromied olution that feature with good economic performance and decent emiion performance. In addition to the curve itelf, we add pie chart above the curve to how the cot breakdown for different olution. Similarly, the donut chart below the curve are emiion breakdown. The ize of thee chart are proportional to the abolute value of total cot and emiion, and the percentage correpond to different activitie/procee in the hydrocarbon biofuel upply chain. Figure 3. Pareto-optimal curve of the cae tudy with breakdown Figure 4. Optimal biofuel upply chain deign in different olution: (a) Point A, (b) Point B, (c) Point C The Pareto-curve how that the mot utainable olution point A ha the lowet GHG emiion per GEG biofuel of 10.22 kg CO2-eq/GEG, and it ha the highet cot per GEG biofuel of 4.21 $/GEG. By contrat, point C ha the lowet cot per GEG biofuel of 3.39 $/GEG and the highet GHG emiion per GEG biofuel of 22.50 kg CO2-eq /GEG. The cot per GEG biofuel for point B i 3.65 $/GEG, and the GHG emiion per GEG biofuel i 14.31 kg CO2-eq /GEG. Next, we preent the upply chain profile of all the olution, given in Figure 4. The number and location of integrated biorefinerie are depicted on a county-baed map of Illinoi.
The capacity for each biorefinery in term of million gallon per y (MGY) i provided a well. A can be een, for point A, a total of 6 biorefinerie are built, all of which adopt pyrolyi and hydroproceing technology. For point C, there are alo 6 biorefinerie to be built with gaification and FT technology. The optimal upply chain deign for point B i a combination of point A and B, where both technologie are adopted. In order to review and compare the reult related to operational deciion. One pecific cenario out of the 80 cenario i conidered to demontrate the different operational deciion. The bioma feedtock compoition i provided in Figure 5. Additionally, due to the eaonality of bioma availability, and taking the uncertaintie of bioma upply and product demand into account, the inventory planning become one important ection in the operation of biofuel upply chain (Yue and You, 2016). The inventory profile i ummarized in Figure 6. 155 Figure 5. Bioma feedtock compoition for (a) point A, (b) point C Figure 6. Biofuel inventory level for point A and point C Obviouly, due to the competitive acquiition cot for agricultural reidue and wood reidue, they are choen a major bioma feedtock in the cot-minimization cae. Meanwhile wood reidue become a popular choice in the emiion-minimization cae thank to it much lower carbon footprint generated in the bioma acquiition proce. Energy crop account for 5 % of the feedtock upply in point A becaue of it relatively lower carbon footprint compared with agricultural reidue. Additionally, in region uch a Cook County where wood reource i abundant, it eaily become the dominant bioma feedtock. For the inventory trategy, an obviou ditch of inventory level can be oberved near Augut, which i the month before the harveting period of agricultural reidue. In point A, more gaoline i tored; while in that of point C, dieel i major tored product. Thi difference i mainly driven by the underlying converion technology choice. For gaification and FT technology, with unit amount of bioma input, more dieel i produced; in contrat, fat pyrolyi and hydroproceing will yield more gaoline than dieel with unit bioma input. 5. Concluion In thi work, a general modelling framework wa propoed that integrate the functional-unit-baed life cycle optimiation methodology with tochatic programming framework. The reulting problem i a bi-criterion SMILFP problem and can be olved efficiently by a tailored global olution algorithm. Furthermore, a countylevel hydrocarbon biofuel upply chain model in Illinoi wa preented to demontrate the propoed modelling framework and correponding olution algorithm. The mot environmentally utainable deign achieve a point with 10.22 kg CO2-eq/GEG emiion per GEG biofuel and 4.21 $/GEG cot per GEG biofuel. The mot economical deign correpond to a point with 22.50 kg CO2-eq/GEG emiion per GEG biofuel and 3.39
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