Sustainability Enhancement under Uncertainty: A Monte Carlo Based Simulation and System Optimization Method

Transcription

1 Sustanablty Enhancement under Uncertanty: A Monte Carlo Based Smulaton and System Optmzaton Method Zheng Lu and Ynlun Huang* Department of Chemcal Engneerng and Materals Scence Wayne State Unversty, Detrot, Mchgan 4822 Orgnal: August 4, 24 Revson: December 24, 24 Abstract Known methods for sustanablty enhancement are typcally scenaro based and the uncertanty surroundng avalable data and nformaton s usually not addressed holstcally, due to nherent problem complexty. Thus the solutons dentfed by those methods could be not suffcently effectve n many ndustral applcatons. In ths paper, we ntroduce a Monte Carlo based smulaton and system optmzaton method for dervng sustanablty enhancement strateges, where uncertantes are systematcally taen nto account. The methodologcal effcacy s llustrated through the study of an ndustral sustanablty enhancement problem nvolvng a number of sectors. Keywords: Industral sustanablty, uncertanty, system optmzaton, Monte Carlo smulaton For publcaton n Clean Technologes and Envronmental Polcy. * All correspondence should be addressed to Prof. Ynlun Huang (Phone: ; Fax: ; E-mal: yhuang@wayne.edu).

2 Introducton Sustanablty, n a general sense, s the capacty to mantan a certan process or state ndefntely. As appled to the human socety, sustanable development s development that meets the needs of the present wthout compromsng the ablty of future generatons to meet ther own needs (WCED, 987). The economc, envronmental and socal sustanablty are normally accepted as the trple bottom lnes, whch should be systematcally assessed and enhanced. Industral sustanablty s pursued to acheve the sustanable development (SD) of ndustral organzatons or systems. Decsons and strateges for SD are usually jontly derved by busness leaders, planners, techncal personnel, and staeholders. Decson mang could be a very challengng process, especally when an ndustral system s large and where uncertanty s pervasve. A large-scale ndustral system may be composed of a few sectors, each of whch has a number of manufacturng plants. The plants have ther own busness development goals and may share supply chans. Decsons and strateges for the SD of ths type of herarchcally structured systems must ensure a healthy development, for all enttes, through synergstc collaboraton and decson maers should be able to coordnate the SD objectves n a decson herarchy under varous constrants and uncertantes. Sustanablty orented decson-mang s mostly scenaro based n practce, where a scenaro refers to a detaled plan or possblty. For nstance, one scenaro could call for mprovng proftablty by ncreasng water reuse and chemcal recovery, as well as reducng energy consumpton n certan processes. In a decson-mang process, the frst step s to dentfy the possble scenaros, followed by a comparson aganst each other, and fnally 2

3 selecton of the most preferable scenaro, based on group expertse. In most decson mang processes, nformaton and data uncertanty s not thoroughly consdered, whch could mae the derved decsons not suffcently effectve n the mplementaton phase. Note that the uncertanty assocated wth sustanablty problems s frequently pervasve, whch appears due to ncomplete or mprecse nformaton and lac of deep nowledge about the nteractons of partcpatng ndustral unts wthn the system or surroundng envronment (Pluso and Huang, 29). Accordng to Parry (996), uncertantes can be classfed nto two types: aleatory and epstemc. Aleatory uncertanty refers to the nherent varatons assocated wth the physcal system and/or the envronment under consderaton; t s objectve and rreversble. By contrast, epstemc uncertanty denotes a lac of nowledge and/or nformaton; t s subjectve and reducble. The uncertantes encountered n the study of large-scale ndustral sustanablty problems can be ether aleatory or epstemc. They are most lely related to parametrc uncertantes assocated wth models and/or due to lmted understandng on sustanablty problems (Dorn et al., 2). A varety of mathematcal technques and computer or cogntve scence based methods are avalable for handlng uncertantes, such as those utlzng fuzzy logc theory, statstcs theory, and artfcal ntellgence (Graham and Jones 988; Ayyub and Gupta, 997; Menrath, 2; Yang, 2; Blgc, 2; Hanss, 25; Kanovch and Vauzelles, 27; Cawleya et al., 27). Despte the exstence of numerous types of nherent uncertantes and uncertanty handlng methods, ths wor s concerned wth the uncertantes that appear n the sustanablty problems of large-scale ndustral systems. We formulate sustanablty problems as a class of system optmzaton problem, whch requres the dentfcaton of soluton alternatves. We

4 then ntroduce a Monte Carlo based smulaton approach to evaluate soluton alternatves when varous uncertantes are ncorporated. Optmal solutons wll be determned for achevng the hghest level of sustanablty mprovement whle eepng below the gven budget constrants. Ths wor s methodologcal effcacy s llustrated by analyzng sustanablty ssues and developng strateges to enhance the sustanablty of a metal fnshng ndustral system that nvolves three sectors and sx plants. 2 System Modelng and Alternatve Scenaro Identfcaton Industral sustanablty s largely reflected by materal and energy effcences, product qualty and productvty, envronmental cleanness, safety, etc. A varety of methods can be used to generate the system nformaton that s needed for a sustanablty assessment, such as Materal Flow Analyss (MFA), Total Materal Requrement (TMR), Materal Intensty Per Unt Servce (MIPS), and Substance Flow Analyss (SFA). The other type of flow analyss method s Input-Output Analyss (IOA) and ts varants. Baley et al. (24) provded a comprehensve revew on sector-based IOA approaches that are ntegrated wth materals, energy, and/or envronmental mpacts, and ntroduced an Ecologcal Input-output Analyss (EIOA) method. Pluso et al. (28) extended the EIOA method (named e-eioa method here) by separatng the output streams nto two sets, the product stream set and the waste stream set, whch facltates a system performance analyss. An e-eioa-based system model can provde the necessary nformaton for decson maers to develop alternatve scenaros, each of whch may adopt one or more techncal approaches, or smply called technologes here, that can be further studed for system performance mprovement. The most effectve scenaro wll then be selected for 4

5 mplementaton. Detaled nformaton of the e-eioa method can be obtaned n Pluso et al. (28). In ths wor, the e-eioa based system modelng method s adopted due to ts capablty of provdng comprehensve system nformaton. System descrpton. Accordng to Pluso et al. (28), a complex ndustral system, named R (for example, an ndustral regon), s assumed to have n sub-systems (e.g., plants), each of whch s named H, and t s a basc element n nput-output flow analyss. As shown n Fg. (a), the sub-system s nputs nclude the raw materal and/or energy streams (denoted as z ), the nternal flow from sub-system H j to sub-system H (symbolzed as f,j ), and flow from H to H (.e., f, ), whle the sub-system s outputs nclude the product stream (p ) and the waste stream (w ). For the system, R, composed of n sub-systems, the system matrx s shown n Fg. (b), whch can be expressed as: R R 2 R R 22 2 () where z R Dag,,, n (2) 2 f, j n n R,, j,, n () 22 R 2 Dag y,,, n (4) T y p w,, n (5) The throughflow ( T ) of sub-system the sub-system and s defned as follows: H s defned as the rate of materal flow through 5

6 T n f j,j z,,, n (6) T n f, p w,,, n (7) Note that throughflow s ether the sum of all nflows to a sub-system (Eq. 6, whch equals the sum of the rows n R) or the sum of all outflows from the sub-system (Eq. 7, whch equals the sum of the columns n R); the two throughflows are equal to each other. Gven the system matrx, R, and throughflows, an nflow analyss can be performed, whch allows one to trace the system outputs bac to ther orgns by determnng the amount of drect and ndrect flows wthn the system needed to generate that outflow. The detaled mathematcal descrpton can be found n Pluso et al (28). Assessment of system sustanablty. It s assumed that a set of sustanablty metrcs s selected by decson maers, each of whch contans three subsets and can have a number of specfc ndces (Zhou et al., 22): S E, V, L, (8) where E E, 2,, M E, the set of economc sustanablty ndces, V V, 2,, M L L, 2,, M V L, the set of envronmental sustanablty ndces,, the set of socal sustanablty ndces. For convenence, all ndces are normalzed ( to ). By usng the selected sustanablty ndces, the status quo of the sustanablty of system R can be assessed usng the data collected from the system. Ths data can be used to estmate the categorzed sustanablty for the system,.e., E R, 6

7 V R, and L R usng the followng formulas: E R M, each of whch are called the composte sustanablty ndces and can be evaluated e a E M e a R, (9) V L R R G H bv G b R, () c L H c R, () where a, b, and c [, ] are weghtng factors assocated wth the ndvdual ndces, reflectng the relatve mportance of an ndvdual ndex aganst others n the sustanablty assessment (Sdar, 29). Pluso et al. (2) ntroduced a sustanablty status representaton scheme, whch s called the sustanablty cube and s shown n Fg. 2. The three coordnates are desgnated for the composte economc ndex, the composte envronmental ndex, and the composte socal ndex. Each composte ndex s set to have a value between (meanng no sustanablty) and (meanng complete sustanablty). In the cube, the corner coordnate of (,, ) represents the system s status of no sustanablty, whle the opposte corner havng the coordnate (,, ) ndcates complete sustanablty. The pont, S(t), represents the system s overall sustanablty status at tme t, whch s determned by the values of three categorzed sustanablty,.e., E(t), V(t), and L(t), as dsplayed n the fgure. The sustanablty cube can be used to represent both the categorzed and overall sustanablty status at any tme nstant. In an ndustral organzaton, the personnel at a 7

8 lower admnstratve level may pay the most attenton to the values of the ndvdual sustanablty ndces (.e., E (t), V j (t), and L (t)), whle those at a hgher admnstraton level may be more nterested n nowng the values of the three categorzed sustanablty (.e. E(t), V(t), and L(t) and the overall sustanablty performance (S(t)). The overall sustanablty can be estmated as follows: R R, V R, LR,, E S, (2) where,, and each have a value of (default) to, and S R s normalzed. System state transton. For operatonal convenence, we can restructure the system matrx, R(t), n Eq. by removng all zero sub-matrces. The new matrx, namely R (t), can be obtaned as follows: R' T t I R I R I I R t t 2 t 22 R2 T R () Note that the values of the parameters, z, f,j, p, and w, n matrx R (t) wll be used to evaluate the system sustanablty performance by usng the ndces n Eq s. 9-. Thus, E V ' t g z t, f t, p t, w t E,j R,, j,, n (4) ' t g z t, f t, p t, w t V,j R,, j,, n (5) ' t g z t, f t, p t, w t L R,, j,, n (6) L, j T and, S ' t g z t, f t, p t, w t S, j R,, j,, n (7) Sustanablty performance can be mproved f approprate actons, e.g., new technology mplementaton, are taen, whch normally requres some form of an nvestment. Let U(t) be a vector of nvestments at tme t, and X(t) be the system parameter vector. A system state transton model can be expressed as: 8

9 t hxt Ut X,, (8) where t h z t, f t, p t, w t X, j X, j,, n (9) t u t u t u t 2 Ju T U (2) System optmzaton model. Alternatve scenaros for sustanablty enhancement can be dentfed by solvng a sustanablty optmzaton problem (Wang et al., 2). The optmzaton problem, formulated below, s desgned to acheve the best sustanablty performance under a number of system, nvestment, and other relevant constrants. J Max S R' t U t (2) s.t. t hxt Ut X, (8) t t max u j u j j,,ju (22) J U u max, total t Ut (2) E V L E V R' t ER' t E (24) R' t V R' t v (25) R' t LR' t L L (26) t E t E,, n t V t V,, n t L t L,, n L (27) (28) (29) In the above model, the objectve functon n Eq. 2 s to maxmze the total sustanablty of the 9

10 system, and the decson varables are the nvestment vector, U(t ). Equaton 8 s the system model. The nvestment constrants are lsted n Eq s. 22 and 2, ncludng the upper lmt of each nvestment type and the total budget constrants. There are two sets of categorzed sustanablty mprovement constrants. The frst set (Eq s. 24 to 26) ensures that the categorzed sustanablty performance of the whole system s at least % better than the status before mprovement, whle the second set (Eq s. 27 to 29) requres at least % of a categorzed sustanablty mprovement for each sub-system after tang certan actons. Alternatve scenaro dentfcaton. The optmzaton model lsted above s a non-lnear optmzaton model. Whle there are a number of avalable mathematcal programmng technques to solve the problem, n ths wor, the model s solved usng a Genetc Algorthm (GA) technque, by whch a number of local optmal solutons can be readly dentfed. GA applcaton methods have been mplemented n many other wors (e.g., Ruszczyńs, 26; Bartholomew and Mchael, 25). These local optma are used as alternatve scenaros that are to be further studed by ncorporatng uncertantes, whch wll be dscussed n a later secton. Let be the set of dentfed alternatve scenaros, whch can be expressed as: where * * S R' t, t U GA, 2,, N () * N s the total number of alternatve scenaros; R' t GA value of the system n the -th scenaro; -th scenaro. * t S s the sustanablty U s the dentfed nvestment strategy for the

11 Uncertanty Incorporaton and Optmal Strategy Development As stated earler, the uncertanty assocated wth sustanablty problems s usually pervasve, whch appears due to ncomplete and mprecse nformaton and a lac of deep nowledge about the nteractons of partcpatng ndustral members wthn the system and the surroundng envronment. For nstance, raw materals and product prcng, maret demand, technology uncertanty, envronmental regulatons, and organzatonal nvestment and development capabltes could all change over tme. Thus, n the development of sustanablty mprovement strateges, the evaluaton of alternatve scenaros must consder varous forms of uncertanty n order to dentfy practcal and effectve solutons. Khajura and Pstopoulos (2) also expressed ths concern when solvng optmzaton problems under uncertanty, and proposed a post-dynamc feasblty test after solvng an optmal desgn problem of pressure swng adsorpton processes. Smlarly, Zhou et al. (2) proposed a two-stage stochastc programmng model for the optmal desgn of dstrbuted energy systems, where the second stage employs Monte Carlo based samplng to estmate an average value under uncertanty for each model parameter that s used by the programmng at the frst stage. In ths wor, uncertantes are ntroduced to the system by utlzng a Monte Carlo smulaton technque, whch s wdely used for uncertanty analyss (Chettouh et al., 24; Kazantz et al., 2). The smulaton wll then reevaluate the sustanablty performance of each canddate scenaro after the uncertantes have been ntroduced. Parameters that nvolve uncertanty, each s requred to specfy a parameter varaton range. For nstance, f the antcpated sale prce of a product s $/lb, ts fluctuaton range may be set at $8/lb to $2/lb. Note that there could be nfntve combnatons of uncertan parameter values, whch adds to the

12 dffculty of evaluatng scenaros under uncertanty. Here, the Monte Carlo based method developed by Geltle (998) and then Kolos and Whtloc (28) s used to randomly sample a large number of uncertanty combnatons for scenaro evaluaton. Such a Monte Carlo samplng approach was also successfully used by Shastr and Dwear (26) for solvng stochastc nonlnear programmng (SNLP) problems, and for performng the stochastc smulaton that was appled to the GREET Model (Subramanyan et al., 28) under uncertanty. Optmal scenaro determnaton. An optmal strategy for sustanablty performance enhancement can be derved usng the followng procedure, whch s shown n Fg.. Step. Collect all of the necessary system nformaton, budget avalablty data, sustanablty goals for ndvdual sub-systems and for the entre system, etc. Identfy the uncertan parameters and defne ther varaton ranges. Select sustanablty ndces for each of the three categorzed sustanablty groups (see Eq. 8) and assgn preferred values for coeffcents, a, b j, and c n Eq s. 9 through, and α, β, and γ n Eq. 2. Step 2. Create a system model usng the e-eoia modelng method. Ths wll lead to the generaton of Eq s. through 7 and, therefore, Eq s. 4 through 2. Step. Generate a sustanablty-orented optmzaton model (see Eq s. 2 through 29). Step 4. Use the gven parameter uncertanty data to conduct the Monte Carlo smulaton to generate N MC sets of random parameter values; N MC should be large, e.g.,,. Step 5. Calculate the total sustanablty for each alternatve scenaro usng each of the N MC sets of parameter values and obtan an average total sustanablty value for each scenaro. Ths step wll contnue untl all alternatve scenaros have been evaluated, whch leads to the generaton of the strateges lsted n Eq.. Step 6. Ran all N MC scenaros usng Eqs. and 2, whch are lsted below. 2

13 Step 7. Output the best scenaro for sustanablty enhancement, for whch the optmal budget allocaton and specfc sustanablty assessment results are ncluded. Note that n Step 5, for each scenaro, the calculated value of total sustanablty s averaged based on all N MC smulatons. Due to the stochastc nature of a Monte Carlo smulaton, among these smulatons, there could be a number of calculatons that result n the largest total sustanablty value as compared wth other scenaros. There could also be some other number of calculatons that result n the second largest value of the total sustanablty compared wth the smulatons for all remanng scenaros, and so on.. Ths results n many optons for the decson maers and some decson maers may prefer to tae ths nto account n ther scenaro ranng. For nstance, the followng scenaro selecton rule may be used: =, 2,..., N GA () ς θ ξ υ ρ where s the score for the -th alternatve scenaro;,, and ρ are the number of tmes that the sustanablty values are the largest, the second largest, and the thrd largest among N MC Monte Carlo smulatons for the -th scenaro as compared wth other scenaros; ϛ, ξ, and υ are constants to be selected based on a decson maer s preference. For example, one may set ϛ =, ξ = 6, and υ = 2. The best scenaro can be easly selected usng the followng formula: N MC Max, 2,, (2) 4 Case Study System and alternatve scenaros. Pluso et al. (28) studed an nterestng sustanablty enhancement problem for a large-scale ndustral system. As shown n Fg. 4, the

14 system s a surface-fnshng-centered networ nvolvng three sectors: a chemcal supply sector consstng of two chemcal solvent plants, a surface fnshng sector contanng two electroplatng plants, and an automotve manufacturng sector wth two OEM plants. The parameter values for the system nputs, outputs, and nternal materal flow streams for sub-matrces R 2, R 22, and R 2 n Eqs. through 5 are lsted n Table, where each stream s unt prce nformaton s also shown. Usng the e-eioa modelng method, four alternatve scenaros for sustanablty performance mprovement were dentfed. Whle ther method s systematc and sound, data and nformaton uncertanty ssues were not consdered. In ths secton, we study the same ndustral system, but tae varous uncertantes nto account n the strategy development process. For the system shown n Fg. 4, Pluso et al. (28) proposed four canddate scenaros for sustanablty performance enhancement. These are: Scenaro : Improve materal recyclng for Chemcal Suppler # ( H ). The process stream nvolved s f,. Scenaro 2: Improve materal recyclng for Chemcal Suppler #2 ( H 4 ). The process stream nvolved s f4, 4. Scenaro : Improve materal recyclng from Automotve OEM # ( H 5 ) to Chemcal Suppler # ( H ) as well as Chemcal Suppler #2 ( H 4 ). The recycle streams are f, 5 and f 4, 5. Scenaro 4: Improve process effcency of Chemcal suppler 2 ( H ) to reduce ts waste generaton that s quantfed by stream w. Sustanablty assessment of exstng system. A number of sustanablty metrcs can 4

15 be used for studyng ths problem, such as AIChE Sustanablty Index TM (Sdar et al., 2) and IChemE Sustanablty Metrcs System (IChemE, 22). For smplcty, n ths case study, only one ndex from each sustanablty category s selected and they are lsted below. Economc sustanablty ndcator (E). Ths ndcator s defned as the total proft, whch s the dfference between the revenue ganed from the sale of products and the sum of the raw materal cost, producton cost, and waste treatment cost. E R Revenue from product Operatngcost Raw materal cost Waste treatment cost () Envronmental sustanablty ndcator (V). Only the mass ntensty of the system s consdered, whch s the rato between the materals used for the fnal products and the raw materals consumed n the plant (Tang et al., 2; Smth et al., 2). Materals for products V R (4) Raw materal consumed Socal sustanablty ndcator (L). The collaboraton level among all sx plants s taen as the ndex for measurng ther synergstc efforts. Ths collaboraton level s quantfed by the amount of materals recycled and reused n the entre ndustral system. R L Massrecycled and reused (5) Usng these ndces, the sustanablty performance of the exstng system, S(R(t )), can be evaluated usng Eq. 2, where weghtng factors, α, β, and are all set to for convenence. The sustanablty assessment results are summarzed n Table 2. Budget avalablty for scenaro based system mprovement. The mplementaton of each of the four scenaros requres an nvestment. The cost parameters are desgnated as u t,, 2, 4, each of whch has an upper lmt, u max, t. The cost requred for 5

16 mplementng each scenaro s related to the level of materal recyclng (for the ncrease of f, (for Scenaro ), f4, 4 and f, 5 (for Scenaro 2), f 4, 5 (for Scenaro ) or the decrease of w (for Scenaro 4)). As an llustraton, the followng relatonshps are used n ths study. Note that n the exstng system, materal recycles as well as waste reducton actons have already been taen, but not n an optmal way. The followng relatonshps are expressed on an ncremental bass. Δf, j t t t max, j 9u log Δf max u, = or 4; j =, 4, or 5; =, 2, or (6) t t 4 max u 4 max 9u Δw t log Δw (7) Assume that max Δf, = 4 lbs/yr, max Δf 4, 4 = 2 lbs/yr, max Δf, 5 =.2 lbs/yr, max, Δf 4 5 =.8, lbs/yr, and Δw 4 t max e = 4.2 lbs/yr. The budget lmts for the mplementaton of the four scenaros are: u max t = $75 K, u max 2 t = $9 K, max t u = $, K, and max t dscharge. u 4 = $5 K, whch refer to complete materal recycle or zero waste Optmzaton model. Based on the gven system nformaton, sustanablty assessment results, relatonshps between system mprovement measures and nvestments, as well as budget constrants and mnmum expectatons on sustanablty mprovement, a specfc system optmzaton model, descrbed n Eqs. 2 through 29, can be establshed and s shown below. The goal of the optmzaton s to dentfy the best strategy for budget allocaton and to acheve the hghest level sustanablty. Note that at ths stage, no uncertanty s consdered. J Max E (8) u t,,, 4 Rt,V Rt, LRt 6

17 s.t. Δf Δf Δw,, 5 u t t u 4 u t 9u log u max 9u log u max 9u log u 4 max 4 t t t t t t max Δf ; Δf t max Δf ; Δf t,, 5 Δw max 5 5 t 4 ; u2t ; 5 5 t 2 ; u t 5 t 5 4 4, 4 4, 5 9u log u max 2t t t t max 2 9u log u Δf Δf 4, 4 4, 5 max max ; ; (9) (4) (4) E Rt. 8772; VRt. 769; LRt 592. (42) E E E E E E te. 85; V te. 9; L te. 5 te. 7842; V2 te. 88; L2 te. 5 te. 8572; V te. 85; L te. 55 te. 87; V4 te. 8; L4 te te. 847; V5 te. 9; L5 te. 685 t. 656; V t. 92; L t. 882 e 6 e 6 e ; ; ; ; ; (4) The above optmzaton problem s solved usng a Genetc Algorthm (GA) technque. The soluton dervaton process nvolves a total of generatons, each of whch ncludes populatons. Fnally, a set of local optmal cases (.e., N n Eq. ) are obtaned, whch consst of sets of alternatve budget dstrbuton strateges, lsted n Table, where the evaluated system sustanablty performance for each set of budget dstrbuton strateges s also ncluded. GA Uncertanty ncorporaton va Monte Carlo based smulaton. The sets of alternatve budget dstrbuton strateges developed should be further nvestgated by 7

18 ncorporatng uncertantes that appear n system parameters and performng a Monte Carlo based smulaton. The parameters experencng uncertantes are lsted n Table 4. In the Monte Carlo based smulaton, a set of parameter values are randomly generated from ther varaton range. These values are used to evaluate the sustanablty performance for each of the sets of nvestment strateges. For nstance, one set of parameter values generated randomly from the domans are: z =.58 $/lb, z 2 =.54 $/lb, p 5 = 6.6 $/lb, p 6 = 2.99 $/lb, u max t = $795 K, u max 2 t = $928 K, u max t = $984 K, and max t u 4 = $47 K. The evaluated sustanablty performance for each of the sets of strateges s lsted n Table 5. Note that the Monte Carle smulaton nvolves, random samples. These results, smlar to the case n Table 5, should be averaged (see the averaged sustanablty values, S * R t, n the 6 th column of Table 6). Applyng Eqs. and 2, we are able to ran the sets of alternatve strateges. In ths case, the coeffcents n Eq.,.e., ς,, and, are set to, 6, and 2, respectvely. Column 7 n Table 6 lsts the ranng results. As shown, the alternatve strategy set, No. 5, s the best, whch receves the hghest score (9,4); the optmal budget dstrbuton of the total funds of $5, for t u*, u*, u*, and 2 t t u* are 4 t $9K, $9K, $22K, and $97, respectvely. The categorzed and the overall sustanablty values, * * * E Rt, V Rt, L Rt, and S * R t are.92,.8,.767, and.8, respectvely. By comparng the sustanablty performance of the exstng system, the economc, envronmental, socal and overall sustanablty mprovement after mplementng technologes are 5.2%, 4.2%, 29.5%, and.%, respectvely. Ths comparson s clearly depcted n Fg. 5. Prortzed sustanablty mprovement. In prncple, a balanced sustanablty development based on the three-pllars s always preferred, however, there could be cases where an organzaton, durng a certan perod of tme, emphaszes one categorzed sustanablty (e.g., 8

19 envronmental sustanablty) more than another categorzed sustanablty. The model n Eq. 2 provdes such an opportunty, as decson maers can assgn dfferent values to the weghtng factors, α, β, and. As an example, f we let α, β, and be 5, 2, and respectvely, then we can re-evaluate the alternatve budget dstrbuton strateges. In ths scenaro, t s found that the best strategy for the dstrbuton of $5K s as follows: t u*, u*, u*, and 2 t t u* are 4 t 255, 68, 5, and 9, and the overall sustanablty, S * R t, s ncreased to.876. Table 7 provdes a comparson between ths unbalanced development strategy and the balanced strategy. 5 Concludng Remars The mprovement of the sustanablty performance of ndustral systems s always very challengng, especally when systems are complex and the avalable data and accessble nformaton are uncertan. The ntroduced Monte Carlo smulaton and system optmzaton methodology s effectve n developng sustanablty mprovement strateges where uncertantes are systematcally taen nto account. Ths methodology s partcularly useful for evaluatng canddate solutons and dentfyng the best soluton, as well as determnng the optmal nvestment strategy for achevng the hghest level of sustanablty mprovement under pre-specfed system and budget constrants and performance mprovement requrements. Acnowledgment and 44277). Ths wor was supported n part by Natonal Scence Foundaton Grants (No. 4, 9

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23 Table. Stream parameter values of cost data of the system before modfcaton Varable Flow ( lbs/yr) Unt value ($/lb) z z f, f, f, f, f 4, f4, f 4, f4, f 5, f 5, f 6, p p w.5.25 w w w w w

24 Table 2. System sustanablty assessment result before mplementng mprovement strategy Interested E Rt System V Rt L Rt S Rt Z H H H H H H

25 Table. Budget dstrbuton strateges wth sustanablty evaluatons for ten alternatve strateges Strategy Budget dstrbuton ( $) Sustanablty evaluaton result No. u* 2 u* 4 E Rt V Rt L Rt S Rt

26 Table 4. Lst of uncertan parameters Parameter Nomnal value Varaton range z.58 $/lb ( ) $/lb z 2.55 $/lb ( ) $/lb P $/lb ( ) $/lb P $/lb ( ) $/lb u max t 4 5 $ (.5 4.5) 5 $ u max 2 t 5 $ (2.5.5) 5 $ u max t 2 5 $ (.5 2.5) 5 $ u 4 5 $ (2.5.5) 5 $ max t 26

27 Table 5. Sustanablty assessment and nvestment strategy ranng after one Monte Carlo smulaton Strategy No. Budget dstrbuton ( $) t u* u* u* u* 2 t t 4 t S R t Ran

28 Table 6. Sustanablty assessment and nvestment strategy ranng after, Monte Carlo smulaton runs. Strategy No. Budget dstrbuton ( $) t u* u* u* u* 2 t t 4 t S * R t Score

29 Coeff s n Eq. 2 (α, β, ) Table 7. Comparson of the best sustanablty mprovement strateges wth dfferent emphases on categorzed sustanablty Budget dstrbuton ( $) Sustanablty after mprovement t u* u* t 2 t u* u* t * * * * 4 E Rt V Rt L Rt S Rt (,, ) (5, 2, )

30 z H P w f, j f, (a) From z z2... z... n H H 2 H n p w... w p2 2 pn wn z z 2 M z n H z... f,, 2 f... f, n To H 2 M H n p w p 2 w 2 M M z 2... M O M... z n f 2, M f n, p w M f 2,2 M f n,2 p 2 w 2... f 2 n M, O... O f n, n M M p n w n p n w n (b) Fg.. Structure of an e-eioa model: (a) a basc element n a system, and (b) a system model that conssts of n sub-systems.

31 Socal (L) (,,).5 L(t) (,,) V(t) E(t) S(t) S Fg. 2. Sustanablty status representaton scheme: the Sustanablty Cube.

32 Input system nformaton, budget data, uncertanty data, sustanablty goal, etc. Generate an e-eoia model for the system under study Generate a parameterzed system optmzaton model Solve the optmzaton model to dentfy alternatve strateges Conduct Monte Carlo smulaton by ncorporatng uncertan nformaton Generate sustanablty assessment result for each strategy No All scenaros evaluated? Yes Ran sustanablty mprovement strateges and dentfy the best one Output the best strateges wth complete sustanablty and cost nformaton Fg.. Flowchart of the procedure for uncertanty ncorporaton and optmal strategy development. 2

33 Supplers (Chemcals) Ter I Manufacturng (Metal Platng) OEM (Automotve Assembly) z H (Chemcal Suppler # ) f, H (Platng Shop # ) f, f 5, H 5 (Automotve OEM # ) f,5 p 5 Product z 2 H 2 (Chemcal Suppler # 2) f 4,2 f,2 H 4 (Platng Shop # 2) f 4,4 f 4,6 f 4,5 f 5,4 f 6,4 H 6 (Automotve OEM # 2) p 6 w 6 w 5 w 4 w w 2 w Waste Fg. 4. Setch of a mult-sector nvolved ndustral system.

34 Socal (,,).8 S(R(t ) S(R(t ) (,,) Fg. 5. Sustanablty performance comparson of the system before and after optmal strategy mplementaton. 4