Business Process Improvement using Multi-objective Optimisation K. Vergidis 1, A. Tiwari 1 and B. Majeed 2

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1 Busness Process Improvement usng Mult-objectve Optmsaton K. Vergds 1, A. Twar 1 and B. Majeed 2 1 Manufacturng Department, School of Industral and Manufacturng Scence, Cranfeld Unversty, Cranfeld, MK43 0AL, U.K. Phone: +44 (0) Fax: +44 (0) e-mals: [k.vergds, 2 Computatonal Intellgence Group, IS Lab, BT Research and Venturng, Oron Buldng, Adastral Park, Martlesham, IP5 3RE, U.K. Phone: +44 (0) Fax: +44 (0) e-mal: Abstract Busness process redesgn and mprovement has become an ncreasngly attractve subject n the wder area of busness process ntellgence. Although there are many attempts to establsh a busness process redesgn framework, there s lttle work on the actual optmsaton of busness processes wth gven objectves. Furthermore, most of the attempts to optmse a busness process are manual wthout nvolvng a formal automated methodology. Ths paper proposes a process mprovement approach for automated mult-objectve optmsaton of busness processes. The proposed framework uses a generc busness process model that s formally defned. The formal defnton of busness process s necessary to ensure that the optmsaton wll take place n a clearly defned, repeatable and verfable way. Mult-objectvty s expressed n terms of process cost and duraton as two key objectves for any busness process. The busness process model s programmed and ncorporated nto a software optmsaton platform where a selecton of mult-objectve optmsaton algorthms can be appled to a busness process desgn. Ths paper proposes a case study of busness process desgn that s optmsed by the state-of-the-art mult-objectve optmsaton algorthm NSGA2. The results ndcate that, although busness process optmsaton s a hghly constraned problem wth fragmented search space, a number of alternatve optmsed busness processes that meet the optmsaton crtera can be produced. The paper also provdes drectons for future research n ths area.

2 1. Introducton In the modern compettve busness world there s a frequent need for enterprses to modfy the structure of ther busness processes to become more successful n the market place. The desgn and management of busness processes s a key factor for companes to effectvely compete n today s volatle busness envronment. By focusng on the optmsaton and contnuous mprovement of busness processes, organsatons can establsh a sold compettve advantage by reducng cost, mprovng qualty and effcency, and enablng adaptaton to changng requrements. Multobjectve optmsaton of busness processes can result n novel approaches and more effcent ways of busness process mprovement. The advantages le n two aspects: () more than one optmsaton crtera can be selected and satsfed smultaneously and () nstead of a sngle optmsed process, mult-objectve optmsaton can produce a populaton of alternatve optmsed busness processes. The next secton examnes the relevant work n the specfc subject area; the rest of the paper ntroduces a multobjectve optmsaton framework for formally defned busness process models. 2. Related work Process modellng methodologes, such as the IDEF famly, Computer Integrated Manufacturng Open Systems Archtecture (CIM-OSA), Object-orented Modellng and Petr-nets, allow for a systematc and a well-defned representaton of processes. Based on some of the above methodologes, a number of process modellng tools have been developed, such as ARIS, FrstStep, PrmeObjects and TEMAS [1]. These approaches provde powerful methods for vsualsng busness processes, evaluatng ther partcular characterstcs (such as resource utlsaton, cost and speed) and checkng ther structural and resource consstency [2], [3]. Zakaran [1] ntegrated the Fuzzy-rule-based Reasonng Approach wth IDEF methodology for quanttatve analyss of process models to model effcently the uncertan and ncomplete nformaton n process varables. Grgor et al. [4] recently proposed a Busness Process Intellgence tool sute that uses Busness Intellgence Technologes (n partcular data mnng) for analysng busness processes. Also n [5] an overvew of busness process analyss technques and tools s presented and n [6] product data engneerng prncples are appled to the representaton of busness processes but there - 2 -

3 s no formal optmsaton attempt n these papers. Hofacker and Vetschera [7] propose a busness process modellng approach that can be optmsed wth three dfferent technques. They defne a sequental busness process usng a sngle-objectve mathematcal model. The qualtatve nature of busness process models explans the dffculty of developng parametrc models of busness processes. There s therefore a lack of formal methods to support the desgn of busness processes [7]. One of the man reasons for ths s that desgn elements and constrants on process desgns are hard to characterse n a formal way amenable to analytcal methods. Therefore, although a consderable number of algorthms exst for dealng wth process optmsaton problems n areas such as Manufacturng, there s a lack of algorthmc approaches for the optmsaton of busness processes [8]. Much of the recent research n the area of busness process optmsaton has dealt wth ether selecton of a process model from a set of alternatves [9] or smple sngle-objectve optmsaton [7] that does not address the strong synergstc/ant-synergstc effects among ndvdual actvtes that consttute a process desgn. Therefore, the current research suffers from serous lmtatons n dealng wth the scalablty requrements and complexty of real-lfe processes. In summary, the optmsaton attempts for busness processes have a long way ahead due to three man ssues: 1. Most busness process models are dagrammatc approaches not capable of quanttatve analyss and algorthmc optmsaton. 2. The busness process optmsaton attempts have been mostly manual. 3. There s no attempt to optmse a busness process under multple crtera. Ths paper addresses the above three ssues. 3. A formal busness process model The frst step towards busness process optmsaton s the busness process model specfcaton. The model has a mathematcal bass to ensure formalty, consstency and rgour. The busness process model has a seres of mathematcal constrants that defne the feasblty of the busness process and a set of objectve functons that consst of - 3 -

4 the varous busness process objectves. Representng a busness process usng a formal mathematcal model guarantees the constructon of consstent and rgorous busness processes followng a formally correct, repeatable and verfable approach [10]. Fgure 1. A feasble busness process desgn wth actvtes and resources Fgure 1 sketches a feasble busness process desgn usng two key concepts: actvtes (n squares) and resources (n crcles). Apart from the resources that are generated wthn the process, the busness process desgn of fgure 1 has two other sets of resources, the ntal (I glob ) and the fnal (O glob ) resources. The ntal resources are avalable at the begnnng of the busness process and the fnal resources form the fnal output. The resources flow through the process and belong to two categores: physcal and nformaton resources. The actvtes are perceved as the transformaton steps wthn the process that use some resources as nputs and produce others as outputs. The busness process model receves as nput parameters the partcpatng actvtes and ther startng tmes. The am s to produce an optmsed process n terms of mnmsng two objectves, the process duraton and cost. For each process desgn there s a lbrary of canddate actvtes wth attrbutes such as actvty duraton and actvty cost. The mathematcal model of busness process defnes the two objectve functons and ensures the busness process consstency and feasblty wth thrteen constrants. Further objectves can be added wth extra functons. The complete mathematcal model s the followng: - 4 -

5 f ( P) = max( q ) mn, j : b go 1 f ( P) = u x mn 2 1 s. t. 1. x r,, j : b I, b B, 2. x y,, j : b I, b B, 3. go + r M g + t x, j : b B, 4. y g + t x, j : b B, 5. y go, j j j j j j P j j j I j j j j P j j j j I j j 6. p q M (1 x ),, j : b I, j j 7. q p + δ + M (1 x ), : b O j 8. q p + δ M (1 x ) M (1 λ ), : b O, 9. λ x,, j : b O, 10. λ r + og M (1 y ), j : B, g = 0, j j j P j : bj O 11. λ 1 M (1 y ), j : b B, g = 0, : bj O 12. x {0,1},, j j j j j j j j j P j 13. λ {0,1},, j : b j j O. Parameter Explanaton u1 Cost of executon for actvty a. x Bnary varable that ndcates whether a canddate actvty a partcpates n the busness process desgn. yj Bnary varable that ndcates whether resource bj s or becomes avalable durng the busness process. t,j Matrx of bnary varables that lnks the actvtes wth ther output resources. rj Matrx of bnary varables that ndcate f a unt of physcal resource bj s avalable for use by actvty a. gj & goj One-dmensonal bnary constants that ndcate whch resources belong to global nputs and/or global outputs. M Large constant ndcatng that physcal resources contaned n the set of global nputs are avalable n unlmted amounts. p Startng tme of actvty a. qj The tme resource bj becomes avalable. δ Duraton of actvty a. λj Bnary varable ndcatng that actvty a s used to create resource bj. I / O Sets of nput/output resources of actvty a. BP / BI Set of physcal / nformaton resources bj. Table 1. Man Parameters n Mathematcal Model The mathematcal model conssts of a number of bnary varables and bnary matrces that have an mpact on the producton of feasble process desgns snce they result n a fragmented search space. Table 1 explans the man parameters used n the mathematcal model. The frst objectve functon (f1) of the model calculates the duraton of the busness process. The total duraton for a feasble process equals the tme that the last resource belongng to global outputs s produced. The second objectve functon (f2) calculates the busness process cost as the sum of costs of all partcpatng actvtes. The mathematcal model constrants ensure that the model produces feasble busness processes by examnng dfferent aspects of the busness process model. The proposed mathematcal model s an extenson of the sngleobjectve model n [7]. It s mportant to hghlght two features of the busness process model. The mathematcal model conssts of many dscrete bnary varables that ncrease the complexty of the search space by makng t fragmented. Another feature of the busness process model s, that although t s smple to conceve, understand and vsualse, t proves to be hghly constraned when t comes to formal mathematcal - 5 -

6 defnton. Ths can create dffcultes n locatng the optmum solutons snce even feasble solutons are hard to produce. Table 2 provdes a short descrpton of each constrant of the mathematcal model n order to enhance ts understandng. The next secton optmses the busness process model usng a mult-objectve evolutonary algorthm. 4. Case study Ths secton descrbes the constructon of a test busness process desgn problem. In total, fve dfferent test process desgns were constructed for optmsaton, but only the constructon of one of these problems s descrbed here n detal. The test problems constructed have an ncreasng number of actvtes partcpatng n the process desgn. Each of the problems has a fxed predefned number of partcpatng actvtes n the process. The ntal and fnal resources of the busness process are gven. The optmsaton algorthm that s selected s NSGA2. Non-domnated Sortng Genetc Algorthm II (NSGA2) s non-domnated, sortng-based, mult-objectve evolutonary algorthm [12]. NSGA2 has been qute popular due to ts robustness and performance. NSGA2 attempts to optmse the process desgns by selectng dfferent sets of actvtes and defnng ther startng tmes. Note that for each process desgn there s a lbrary of canddate actvtes that can potentally partcpate n the process. The case study dscussed here s a busness process desgn under the name ActvtesST4 and t s based on the mathematcal busness process model descrbed n the prevous secton. It nvolves four partcpatng actvtes. The lbrary of canddate actvtes contans ten actvtes that can be alternatvely used n varous combnatons of four. Process optmsaton depends on two crtera: 1. The approprate actvtes need to be selected and combned from the lbrary based on ther duraton and cost attrbutes and 2. The startng tmes of actvtes need to be determned n order for the process outputs to be produced as early as possble, thus mnmsng the total process duraton

7 1. x r,, j : b I, b B j j j P Bref descrpton of constrants All nput physcal resources of an actvty must be avalable (r j=1) at some stage of the process f the actvty s partcpatng (x =1). 2. x y,, j : b I, b B j j j I All nput nformaton resources (y j) of an actvty must be avalable at some stage of the process f the actvty s partcpatng (x =1). 3. go + r M g + t x, j : b B j j j j P The output physcal resources -fnal or not- must not exceed the sum of ntal and produced -durng the process. 4. y g + t x, j : b B j j j j I An nformaton resource (y j) can be avalable ether at the begnnng of the process -as ntal resource (g j)- or as an output resource of a partcpatng actvty. 5. y j go j A resource (y j) cannot be part of the output wthout frst beng avalable at some stage of the process (go j). 6. p q M (1 x ),, j : b I j j In terms of tme, a partcpatng actvty must start (p ) only after the tme that all ts nput resources have become avalable. 7. q p + δ + M (1 x ), : b O j j 8. q p + δ M (1 x ) M (1 λ ), : b O j j j In terms of tme, an output resource must become avalable exactly when the generatng actvty has been completed (q j=p ). 9. λ x,, j : b O j j A non-partcpatng actvty (x =0) cannot have output resources (λ j=1). 10. λ r + og M (1 y ), j : B, g = 0, j j j P j : bj O When a physcal resource does not belong to ntal resources, t must be produced durng the process n greater or equal amounts to the requred resource nputs of the partcpatng actvtes. 11. λ 1 M (1 y ), j : b B, g = 0 j j j P j : b j O Each physcal resource that does not belong to ntal resources but appears n the output of a partcpatng actvty must be produced at least once. 12. x {0,1}, The varable x (ndcatng partcpatng actvtes) must be bnary. 13. λ {0,1},, j : b O j j The varable λ (ndcatng output resource j of actvty ) must be bnary

8 Table 2. Summary of constrant explanatons The process desgn sketch of ActvtesST4 problem s demonstrated n fgure 2 and can be descrbed as follows: There are two global nput resources to start the process. These two resources together wth the two global outputs are consdered as constants. The system varables of the problem are the four partcpatng actvtes and ther startng tme attrbute. Ths means that the optmsaton algorthms wll attempt to satsfy the optmsaton objectves by selectng a set of four actvtes (from a lbrary of 10 alternatves) and defnng the startng tme for each of them. All the potental actvtes are stored n a bult-n lbrary and the algorthms can select any four. For a process to consdered feasble, the four potental actvtes of the process desgn must be combned n a way that the gven output resources are produced. Fg. 2. ActvtesST4 ntal process sketch 5. Results Ths secton descrbes the expermental results for the test problem sketched n the prevous secton (fg. 2) as those were generated by NSGA2 evolutonary algorthm. In ths paper, the focus s on the effect of optmsaton algorthm to busness process n terms of mprovng the performance of the busness objectves. The optmsed solutons were produced by executng NSGA2 30 tmes wth dfferent random seed values. 28 of these 30 runs produced smlar results. The results presented here belong to one of the typcal runs. The generated solutons represent feasble busness processes wth mnmsed process duraton and cost

9 Fg. 3. ActvtesST4 optmsaton results wth NSGA2 mult-objectve evolutonary algorthm Legend: x random solutons NSGA2 generated solutons 1 optmsed solutons Fgure 3 demonstrates the NSGA2 generated busness processes and also a set of randomly generated solutons n order to provde a comparson measure for the optmsed results. The dotted ponts represent the NSGA2-generated solutons whereas the x ponts random solutons that demonstrate feasble busness process desgns. The numbered-dotted ponts correspond to the sub-set of optmsed solutons among the NSGA2-generated results. As llustrated n fgure 3, the numbered-dotted solutons are better than both random and the rest of NSGA2-generated solutons as the have both shorter process duraton and lower cost. However, none of the three numbered-dotted solutons s consdered better among them as they are optmsed alternatves wth dfferent trade-offs between the two objectves. These three solutons are further dscussed below. Fgure 4 provdes a pctoral vew of the three numbered-dotted solutons of fgure 3 and gves the opportunty to see what each soluton represents. Fgure 4 demonstrates graphcally that each optmsed process holds a dfferent tradeoff between process duraton and cost. At tme 0 the two nput resources are avalable and the process starts. The grey boxes represent the actvtes and ther length depcts ther duraton. Each box states the name of the actvty used (e.g. a4) and n brackets the cost of ts executon. The process cost s calculated by addng all the actvty costs, whle the process duraton s defned by the tme that the last resource s beng produced

10 Fgure 4. Optmsed busness process values for 3 dfferent solutons

11 Busness processes - usng the same resources to produce standard outputs- can have dfferent performance. Optmsed process 1, for example, has the shortest duraton (8 unts) but t s also the most expensve. Optmsed process 2 on the other hand, has reduced cost but has a 50% ncrease on process duraton. Optmsed process 3 costs less than half of the frst nstance but t lasts twce as long. Therefore, the optmsed solutons provde a range of selecton to the busness analyst to make a decson. The decson makng crtera could be the company s prortes or polcy at a gven tme or external factors such as compettor s performance. Havng the opportunty to shape a busness process accordng to two or more objectves and beng able to revew the trade-offs between the objectves empowers the process analyst when t comes to busness process selecton and realsaton. 6. Dscusson Ths secton dscusses the practcal mplcatons of the framework, along wth ts lmtatons and drectons for future research. The test problem demonstrates that the proposed framework s capable of applyng mult-objectve optmsaton to busness process desgns and generatng optmsed alternatve busness processes wth tradeoffs between the process objectves (duraton and cost). Ths gves the capablty to the process analyst to select, accordng to decson makng prortes, a busness process from a range of optmsed ones. The results are promsng and future research can lead to better qualty results. Durng the development of the proposed mult-objectve optmsaton methodology a number of lmtatons were unveled. The frst lmtaton orgnates from the mathematcal model of the busness process. The mathematcal model focuses on actvtes and resources as ts two man concepts and t gnores the partcpatng (physcal or mechancal) actors. Ths results n what s crtcsed as a mechanstc vewpont of busness processes [11]. However, t s more dffcult for a formal busness process modellng technque to capture the roles of the partcpants than a dagrammatc approach whch vsualses the flow of the process. Another lmtaton les n the selecton of a process desgn as test problem. The busness process optmsaton capabltes can be better demonstrated usng a seres of test busness

12 process desgns nvolvng a wde range of actvtes and patterns lke decson boxes or feedback loops. Future research n the relevant area should focus on areas such as buldng more complete process models and testng more complcated process desgns. The constructon of a busness process model that can cover more aspects of a closer to real world busness process can prove a challengng research area. Modellng and optmsaton of closer to real world process patterns can sgnfcantly ncrease the problem complexty. Future research should also focus on selectng the most approprate technques for busness process mult-objectve optmsaton from a wder set of technques and algorthms and thus locatng more accurately the most sutable optmsaton method. 7. Conclusons Ths paper presented a framework for applyng mult-objectve optmsaton to busness processes. By developng a formal busness process model and orentng t to mult-objectvty, the generaton of optmsed busness processes s facltated and demonstrated by a case study. What makes the busness process optmsaton problem dstnctve s ts hghly constraned nature and the fragmented search space that has a sgnfcant mpact on locatng the optmum solutons. It s shown that state-of-the-art mult-objectve optmsaton algorthms, such as NSGA2, can produce satsfactory results by managng to generate and preserve optmal solutons on a process desgn. Ths provdes an adequate number of alternatve optmsed process desgns for the busness analyst to decde the trade-offs between the dfferent objectves. The results presented here are encouragng for further research n the area of busness process mult-objectve optmsaton. References [1] A. Zakaran, Analyss of process models: A fuzzy logc approach, The Internatonal Journal of Advanced Manufacturng Technology, vol. 17, pp , [2] W. Sadq and E. M. Orlowska, Analysng process models usng graph reducton technques, Informaton Systems, vol. 25, pp ,

13 [3] H. L, Y. Yang and T.Y. Chen, Resource constrants analyss of workflow specfcatons, The Journal of Systems and Software;, vol. 73, pp , [4] D. Grgor, F. Casat, M. Castellanos, U. Dayal, M. Sayal and M.C. Shan, Busness Process Intellgence, Computers n Industry, vol. 53, pp , [5] Y. Cheung and J. Bal, Process analyss technques and tools for busness mprovements, Busness Process Management;, vol. 4(4), pp , [6] A. McKay and Z. Radnor, A characterzaton of a busness process, The Internatonal Journal of Operatons and Producton Management, vol. 18(9/10), pp , [7] I. Hofacker and R. Vetschera, Algorthmcal approaches to busness process desgn, Computers & Operatons Research, vol. 28, pp , [8] A. Twar, Evolutonary computng technques for handlng varables nteracton n engneerng desgn optmzaton, PhD Thess, SIMS, Cranfeld Unversty, Cranfeld, UK, [9] Y. Shmzu and Y. Sahara, A supportng system for evaluaton and revew of busness process through actvty-based approach, Computers and Chemcal Engneerng, vol. 24, pp , [10] M. Koubaraks and D. Plexousaks, A Formal Framework for Busness Process Modellng and Desgn, Informaton Systems, vol. 27, pp , [11] A. Lndsay, D. Downs and K. Lunn, Busness processes - attempts to fnd a defnton, Informaton and Software Technology, vol. 45, pp , [12] K. Deb, Multobjectve optmsaton usng evolutonary algorthms, New York: John Wley & Sons, Author bographes Kostas Vergds s currently a Doctoral Researcher at Cranfeld Unversty n the area of Busness Process Optmsaton. He holds a BSc n Busness IT from Unversty of Macedona, Greece and an MSc n IT for Product Realsaton from Cranfeld Unversty, UK. Dr. Ashutosh Twar s a Lecturer n Decson Engneerng at the Manufacturng Department, School of Industral and Manufacturng Scence, Cranfeld Unversty (UK). He has a strong academc, research and ndustral background n Appled Soft Computng, Process Modellng and Re-desgn, and Mult-crtera Decson Makng. Dr. Basm Majeed s a Prncpal Research Professonal at the Intellgent Systems Research Centre wthn BT Research and Venturng. He holds a Masters degree (1987) and a PhD degree (1992) n Intellgent Control Systems from the Unversty of Manchester. He s a part of a team workng n the area of real-tme busness ntellgence and busness process management. He s a Member of the IEE and IEEE, and a Chartered Engneer

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