Project Scheduling Based on Multi-Agent Systems

Transcription

1 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 Project Schedulig Based o Multi-Aget Systems Fu-Shiug Hsieh Departmet of Computer Sciece ad Iformatio Egieerig Chaoyag Uiversity of Techology [email protected] Jim-Bo Li Chaoyag Uiversity of Techology s @cyut.edu.tw ofte relies o etwor plaig methods such as critical path method (CPM ad project evaluatio ad review techique (PERT. However, such traditioal etwor plaig methods caot be applied to real costructio projects. PERT ad CPM are helpful schedulig techiques oly whe the project deadlie is ot fixed ad the resources are ot costraied. May project schedulig methods [1]-[5] have bee proposed. I [6], the authors reviewed meta-heuristics for project ad costructio maagemet. They idicated that the existig studies to solve real project schedulig problems ca be classified ito the followig categories: (1 timecost tradeoff [7]-[9]; (2 resource allocatio [10]-[12]; (3 resource-costraied project schedulig; (4 resource levelig [13]-[14]; ad (5 itegrated models that cosider more tha oe category above [15]-[16]. However, these studies did ot provide a framewor for schedulig projects i a costructio supply chai. I this paper, we will cocetrate o the developmet of a project schedulig system that ca be applied i a costructio supply chai. Executio of tass that hadle physical parts i a costructio project may deped o locatio. Although worflow maagemet problems have bee extesively studied for decades, locatio aspect of worflows has ot bee cosidered i the existig literature. I this paper, we study how to exploit recet advacemets i multiaget systems (MAS [17]-[21], iformatio techologies (IT [22]-[24] ad geographic iformatio system (GIS to reduce cost ad time i the developmet of locatioaware worflow schedulig systems based o a sustaiable architecture. We propose a methodology that icludes modelig of locatio-aware worflows of costructio projects based o worflow models, develop a techique to trasform worflow models to formulate ad solve a schedulig problem. We propose a framewor to implemet a prototype system based o a FIPA-compliat MAS platform ad Google API. Our solutio methodology combies IT, MAS architecture with Petri et models, a effective model for modelig ad aalysis of worflows [25]-[27]. I our architecture, the worflow to be performed by a aget is represeted by a worflow aget ad each resource is Abstract Oe of the most importat ad challegig issues i costructio project maagemet is to schedule activities to meet the costructio project requiremets uder resource costraits. I this paper, we will cocetrate o the developmet of a worflow schedulig system that ca be applied i costructio supply chais based o the iteractios of etities/parters. Executio of worflows that hadle physical parts i a costructio project may deped o locatio. Although worflow maagemet problems have bee extesively studied for decades, locatio iformatio of worflows has ot bee cosidered i existig literature. We propose a methodology that icludes modelig of locatio-aware worflows i costructio projects based o formal worflow models ad develop a techique to trasform worflow models to formulate ad solve a project schedulig problem. We propose a framewor to implemet a prototype system based o a FIPA-compliat multi-aget system platform ad Google API. Idex Terms locatio aware worflow, project schedulig, multi-aget system I. INTRODUCTION As costructio projects become larger ad more complex i terms of scale, cost ad time, effective costructio project maagemet is very importat for the success of a costructio compay. There are several research issues i the maagemet of costructio projects. Oe of the most importat ad challegig issues i costructio project maagemet is the schedulig of activities to meet the requiremets uder resource costraits. Compaies i a typical costructio supply chai eed to egotiate with each other to create a feasible schedule for a costructio project. Developmet of a schedulig software system to support ad facilitate cooperatio ad project schedulig betwee the parters of a costructio supply chai is required. Project schedulig is oe of the fudametal fuctios of costructio project maagemet. Project schedulig Mauscript received May 13, 2014; revised July 30, This paper is supported i part by the Miistry of Sciece ad Techology of Taiwa uder Grat NSC H MY3. doi: /joams

2 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 modeled by a resource aget. I MAS, the most wellow protocol for coordiatio ad egotiatio is the cotract et protocol (CNP [28]-[29]. There are a lot of wors o distributig tass i MAS with CNP [30]-[33]. To edow each aget with the owledge to perform locatio-aware operatios i the worflows, we propose a locatio-aware timed Petri et (LTPN model, which exteds time Petri et, for each worflow aget ad resource aget. The Petri Net Marup Laguage (PNML [34]-[35] is used as the format for represetig the Petri et models. The locatio iformatio i LTPN is used to calculate the firig time iformatio based o Google Distace Matrix API. Our approach uses a software module to formulate the project schedulig problem based o the LTPN models ad the project requiremets. The cost ad time ivolved i the developmet of schedulig software ca be sigificatly reduced. The worflow schedulig problem is solved based o iteractio of a umber of iterrelated optimizatio agets. We adopt a FIPA-compliat MAS platform, JADE, which provides built i service publicatio/discovery capabilities, to realize our system. The remaider of this paper is orgaized as follows. I Sectio II, we describe the locatio-aware worflow schedulig problem. We itroduce our scheme i Sectio III. I Sectio IV, we propose our problem formulatio ad schedulig method based o locatio-aware worflow models. We preset our implemetatio ad a case study i Sectio V. We coclude this paper i Sectio VI. II. SUPPLY CHAIN PROJECT SCHEDULING PROBLEM Retailers Raw Material Suppliers Wholesalers Figure 1. Example of a typical supply chai Maufacturers A costructio project usually relies o cooperatio of a umber of compaies to maufacture ad supply parts or compoets. These compaies form a supply chai. Supply chai activities trasform atural resources, raw materials, ad compoets ito a fiished product that is delivered to the ed customer. Fig. 1 shows a typical supply chai that provides parts or compoets. I additio to the supply chai that provides parts or compoets, compaies that tae part i a costructio project also form a costructio supply chai. Fig. 2 shows the cofiguratio of a typical costructio supply chai [36]. The participats of a typical costructio supply chai eed to egotiate with each other to create a feasible schedule for the give costructio project. A importat issue is to develop a software system to support ad facilitate egotiatio ad cooperatio betwee the parters of a costructio supply chai. I this paper, we will cocetrate o the worflow schedulig problem i costructio supply chais. We will propose a flexible schedulig system to optimize the costructio project schedule based o cooperatio of parters of a costructio supply chai. Residet Pricipal Direct Suppliers/Subcotractor Architect & Cosultat Mai Cotractor Idirect Suppliers Figure 2. Cofiguratio of a typical costructio supply chai Locatio iformatio plays a importat role i schedulig the activities ad resources that move materials, parts or compoets from oe parter to the ext i a costructio supply chai. Although worflow maagemet problems have bee extesively studied for decades, locatio aspect of worflows has ot bee cosidered i existig literature. I this paper, we will study how to develop locatio-aware worflow schedulig systems. The locatio-aware worflow schedulig system aims to fid the schedule of resources ad activities based o the locatio iformatio of the etities i the system. The etities i a costructio supply chai ca be classified ito several categories: (1 orders that trigger the activities of a costructio project, (2 activities that specify the operatios to be performed for the fulfillmet of costructio project requiremets ad (3 resources that execute activities i a costructio project. I this paper, a resource refers to costructio equipmet specially desiged for executig costructio tass. Each etity has certai properties ad maes decisios proactively ad iteracts with other etities. To propose a schedulig methodology based o MAS, we model each etity as a aget i multi-aget systems. Let OA, WA ad RA deote the set of order agets, worflow agets ad resource agets, respectively. A order aget o has several attributes, ( d o, q o, l o, icludig order due date, demads ad the locatio of the customer. A worflow aget has the attributes, ( t, l, w, to describe its worflow type, locatio ad the structure of worflow. A resource aget r has the attributes, ( l r, a, to describe its locatio ad the structure of activities that it ca perform i the worflow. Give a set of etities OA, WA ad RA, icludig orders, activities, resources ad their associated locatio iformatio, the problem is to optimize the schedule of each etity to meet the customers order requiremets such that the overdue cost ca be miimized subject to (I resource capacity r 212

3 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 architecture to cofigure agets to achieve a goal. The egotiatio protocol used i this paper exteds the origial CNP. Let s illustrate the multi-level CNP by a example. costraits, (II precedece costraits betwee the worflow agets ad (III demad costraits. Applicatio Libraries Worflow Aget Resource Aget Worflow Model Activity Model Order Aget Google API Solve SP1 Schedule S1 Solve SP2 MySQL driver W1 W2 Schedule S 2 W1 W2 Optimizatio Aget Other API Java Aget DEvelopmet Framewor AMS Schedule P3 Solve SP3 DF W3 W3 Figure 3. Architecture of the proposed schedulig system Fig. 3 shows our architecture for the developmet of locatio-based worflow schedulig system. There are four types of agets, icludig order agets, worflow agets, resource agets ad optimizatio agets. All these four types of agets are desiged ad implemeted based o JADE, a FIPA-compliat MAS platform. Agets i Fig. 3 may ivoe third party libraries such as Google API to obtai the processig time for locatio depedet operatios i worflows. The locatio-aware worflow schedulig system is developed by applyig a egotiatio protocol betwee agets based o Petri et models of worflow agets ad resource agets. A solutio methodology will be proposed based o trasformatio of the Petri et models of worflow agets ad activity models i this paper. III. W4 W4 (a (b Figure 4. A hybrid approach based o combiatio of multi-level CNP ad optimizatio algorithms Fig. 4 shows how the multi-level CNP wors for a costructio supply chai etwor with four compaies. Fig. 4(a shows the tas aoucemet messages propagate from the dowstream to upstream i the supply chai. O receivig the messages, each compay must solve the worflow schedulig problem. I Fig. 4(a, the worflow schedulig problem to be solved by compay W is deoted as SP. Let S deote the schedule of compay W. Each compay draws up a proposal based o its schedule ad the submits the proposal to its parter at the dowstream as show i Fig. 4(b. The dowstream parter the decides whether to accept the proposal. A HYBRID SCHEME FOR SCHEDULING LOCATION AWARE WORKFLOWS Our scheme to solve the locatio-aware worflow schedulig problem combies the cotract et protocol (CNP with optimizatio theories to optimize the schedules based o collaboratio of worflow agets, resource agets ad optimizatio agets. I CNP, a aget may play the role of a maager or a bidder. CNP specifies a four steps procedure to establish a cotract betwee a maager ad oe or more bidders. Step 1: The maager aouces a tas to the potetial bidders. Step 2: The potetial bidders draw up proposals ad submit the proposals to the maager. Step 3: The maager awards the cotracts to the best bidder(s. Step 4: The awarded bidder may either commit itself to carry out the tas or refuse to accept the cotract. As the origial CNP oly defies the iteractio betwee oe maager ad multiple bidders, it must be exteded properly to capture the iteractio betwee the etities i a costructio supply chai. I this paper, a multi-level CNP is proposed i this paper to capture the iteractio betwee parters i a supply chai. The multilevel CNP ca be applied i a supply chai to form a VE base o establishmet of cotracts betwee a set of worflow agets ad a set of resource agets to fulfill order requiremets. By combiig CNP with optimizatio theories, our approach provides a flexible Schedule S 4 Solve SP4 IV. PROJECT SCHEDULING BASED ON LOCATION AWARE WORKFLOW MODELS Wheever a worflow aget eeds to optimize the worflow schedule, a request will be set to a optimizatio aget. The optimizatio aget will tae two actios. First, it will automatically formulate the schedulig problem based o the requiremets of the order aget, PNML models of the worflow aget ad the relevat resource agets. Secod, it will ivoe optimizatio algorithms based o optimizatio theories to fid good schedules for resource agets efficietly. Fig. 5 illustrates the flow chart for a optimizatio aget. There are three steps i the flow chart: (1 costructio of aget models, (2 schedulig problem formulatio based o extractio of parameters from the aget models ad (3 applicatio of algorithms for solvig schedulig problem. As algorithms for solvig schedulig problems have bee extesively studied i the existig literature, we will oly apply a existig algorithm i our proposed system. I the discussio as follows we will preset the details of Step (1 ad (2 oly. 213

4 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 A. Step (1: Costructio of Aget Models I this step, the models for all worflow agets ad resource agets are first created based o Petri et. A timed Petri et (TPN G is a five-tuple G ( P, T, F, m0,, where P is a fiite set of places, T is a fiite set of trasitios, F ( PT ( T P is the flow relatio, m0 : P Z is the iitial marig of the TPN with Z as the set of oegative itegers ad :T R is a mappig that specifies the firig time for each trasitio performed by RA. The marig of G is a vector m Z that idicates the umber of toes i each place ad is state of the system. Worflow Model i PNML Activity Model i PNML P Order Requiremets P sequetial locatio-aware Mared Graph (ASLMG. I this paper, the worflow model for a worflow aget is described by a timed augmeted sequetial locatioaware Mared Graph (TASLMG. Formally, the Petri et models for worflow agets ad resource agets are defied as follows. t 1 t 2 p 1 p 2 p 3 (a Start Locatio 1 p 1 Start Trasitio 1 t 1 Operatio 2 p 2 Ed Trasitio 2 t 2 Ed Locatio 3 p 3 Resource Idle Place r 1 ( x r, y 1 r 1 t 1 1 t 1 p 2 t 2 2 t 2 (c Start Trasitio Operatio 2 p 2 Ed Trasitio Start Locatio Automated Schedulig Problem Formulatio t 3 p 4 4 p 4 Start Trasitio 3 t 3 Resource Idle Place r 1 t 3 3 t 3 Start Trasitio p 5 Operatio p 5 Operatio Algorithm for Solvig Schedulig Problem 5 p 5 t 4 Ed Trasitio 4 t 4 ( x r, y 1 r 1 t 4 4 t 4 Ed Trasitio Schedule i XML p 6 (b Ed Locatio 6 p 6 (d Figure 5. Dyamic worflow schedulig problem formulatio ad solutio As the origial TPN model does ot tae locatio iformatio ito cosideratio, it caot be used to describe locatio-aware worflows. I this paper, we exted the origial TPN model by augmetig it with locatio elemets for each place ad trasitio to edow it with the capability to describe locatio-aware worflows. This ew class of time Petri ets is called locatio-aware time Petri ets (LTPN. More specifically, a LTPN GL = ( P, T, F, L, m0, is defied based o TPN G ( P, T, F, m0,, where L : P T R R s a mappig that specifies the locatio for each place ad trasitio. I this paper, we use L ( p = x, y to deote ( p p the locatio of place p P ad L (t = ( xt, yt to deote the locatio associated with trasitio t T. I costructig the model of a worflow aget w, we use a subclass of LTPN called locatio-aware timed sequetial Mared Graph (MG. A mared graph is a ordiary Petri et such that each place has exactly oe iput trasitio ad exactly oe output trasitio. A mared graph with sequetial structure is called a sequetial Mared Graph (SMG. The subclass of Petri ets for modelig a worflow aget is a SMG augmeted with a set of termial iput places ad termial output places. We call this subclass of Petri ets augmeted Figure 6. LTPN models Defiitio 4.1: The model of worflow aget, where w WA, is a TASLMG W ( P, T, F, L, m0,. As each trasitio represets a distict operatio i a costructio project, we have T T for j. j Defiitio 4.2: LTPN A P, T, F, L, m, r ( r r r r r0 deotes the th activity of resource aget r, where r RA. The iitial marig m r is determied by the umber of resources allocated to the th activity. There is o commo trasitio betwee A r ad for. Two examples of Petri et models for worflow agets are illustrated i Fig. 6(a ad (b. A resource aget may be able to perform several activities i the worflows. Fig. 6(c ad (d shows two Petri et models for two activities of a resource aget. For locatio-aware worflows, the processig time (firig time for the executio of operatios (trasitios depeds o their locatio. The worflow schedulig problem eeds to be formulated ad solved dyamically based o real geographic iformatio system (GIS or database. The Google Distace Matrix API is a service that provides travel distace ad time for a matrix of origis ad destiatios. The iformatio retured is based o the recommeded route betwee start ad ed r A r 214

5 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 poits, as calculated by the Google Maps API, ad cosists of rows cotaiig duratio ad distace values for each pair. I this paper, we apply the Google Distace Matrix API to fid the processig time (firig time for trasitios i our LTPN models. I other words, the firig time (t of trasitio t T is calculated by ivoig the Google Distace Matrix API accordig to the locatio of its iput place ad locatio of its output place. B. Step (2: Schedulig Problem Formulatio Based o Extractio of Parameters from Aget Models The schedulig problem for worfloww is to fid a allocatio of resource capacities over the schedulig horizo that miimizes the total productio costs while satisfyig all productio costraits. Let O deote the umber of order agets. Let N deote the umber of worflow agets i the system. That is, N WA ad O OA. Let K deote the umber of differet resource activities ivolved i W. The -th resource activity i W is represeted by A r, 1, 2,, K. Suppose the -th resource activity i W is performed by resource aget r. The the processig time of the -th resource activity Ar i W is = ( r ts + ( r te, where t s ad t e deote the startig ad edig trasitios of the -th activity of resource aget a r. Let T deote the total umber of time periods. Each t 1, 2, 3,, T represets a time period idex. Let C rt deote the capacity of resource r at time period t, where C rt = m r 0 ( r. Let d deote the due date of worflow aget w. Note that the due date d for worflow aget w is set by its dowstream worflow agets i the egotiatio processes. Let v ot deote the umber of parts of order o loaded oto the correspodig resource r for processig the -th resource activity i W durig time period t, where vot 0 ad v ot Z, the set of o-egative itegers. Let y be the umber of parts of order o i ot worfloww fiished durig time period t ; i.e., Let ot h be the umber of parts of order o at the iput buffer of the -th resource activity iw at the begiig of period t, where hot 0 ad h ot Z, the set of oegative itegers. We defie the earliess/tardiess pealty coefficiet ot for each product of worflow W completed at time t as E ( d t, t d ot L ( t dt, t d Mathematically, it is formulated as O ( SP v o o1 t 1 t y ot C r t mi s. t. O T o1 t1 ( y ot ot 1, 2,, K v o, t ok ( t K h o Q 11, ho1 ( t 1 ho1 t vo1t o ( t 1 hot vot vo ( 1( t 2, 3,, K ( 1 h h h v o( K 1( t1 o( K 1( t1 ok ( t I our schedulig system, we apply a subgradiet based algorithm to solve the project schedulig problem. V. IMPLEMENTATION We have developed a multi-aget locatio-aware worflow schedulig system based o JADE, a middleware that facilitates the developmet of multiaget systems, to realize our methodology. Messages exchaged by JADE agets have a format specified by the ACL laguage defied by the FIPA iteratioal stadard for aget iteroperability. To apply the cotract et protocol, a maager must be able to search for the services provided by the other bidders. Each time a aget is added to the system, its services are published ad discovered through the DF aget i JADE. I our schedulig system, order agets, worflow agets ad resource agets are accompaied with proper graphical user iterface (GUI for users to iput the required data. Optimizatio agets, which are ivoed by worflow agets, have o GUI as they wor behid the scees. Figure 7. GUI for settig the properties of a worflow aget To specify the locatio of a worflow, we have implemeted a GUI to set the latitude ad logitude of the start locatio ad ed locatio of a activity i a 215

6 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 costructio project. Fig. 7 illustrates the GUI for settig the parameters of a worflow aget. Similarly, we have implemeted a GUI to set the latitude ad logitude of the start locatio ad ed locatio of a resource aget. Fig. 8 illustrates the GUI for settig the parameters of a resource aget. Fig. 9 illustrates the graphical user iterface (GUI for settig costructio order requiremets. The output of our schedulig software icludes the schedules for executig each worflow ad the schedules for performig the operatios of worflows by each resource agets. Worflow ID TABLE I. Iput(s PROPERTIES OF WORKFLOW AGENTS Output W1 Null 1 W2 1 2 W3 2 3 TABLE II. Start Locatio ( , ( , ( , Ed Locatio ( , ( , ( , INITIAL LOCATION OF RESOURCE AGENTS Resource Iitial Locatio R1 ( , R2 ( , R3 ( , TABLE III. ORDER REQUIREMENTS Order ID Due date Product type Quatity Earliess Cost Lateess Cost /6/24-17: Figure 8. GUI to set the properties of a resource aget TABLE IV. ORDER REQUIREMENTS Worflow Start time Ed time Quatity W1 2014/6/24-14:4 2014/6/24-14: W2 2014/6/24-15: /6/24-15:50 50 W2 2014/6/24-15: /6/24-16:30 50 W3 2014/6/24-16: /6/24-17: TABLE V. SCHEDULE FOR RESOURCES Resource Start time Ed time Quatity R1 2014/6/24-14:4 2014/6/24-14: R2 2014/6/24-15: /6/24-15:50 50 R2 2014/6/24-15: /6/24-16:30 50 R3 2014/6/24-16: /6/24-17: Figure 9. GUI for settig order requiremets Cosider a applicatio sceario with three worflow agets ( W1 through W 3 ad three resource agets ( R1 through R 3 i a costructio supply chai. Table I shows the three worflows i the system. Each worflow represets a process required for maufacturig compoets or products required for the costructio project or executio of a costructio tas. Suppose a costructio order is received. Table II shows the iitial locatio of resource aget. Table III shows the requiremets of the costructio order. Table IV illustrates the schedule for worflow agets to hadle Order 1. It idicates that the due date of Order 1 ca be met as the required quatity ca be fiished at 17:30 o 2014/6/24. Table V shows the schedule for resource agets. VI. CONCLUSION The worflows i a costructio project are dyamic ad cross orgaizatioal boudary. More importatly, locatio iformatio plays a importat role i schedulig the worflow activities ad resources that move materials, parts or compoets from oe parter to the ext i a costructio supply chai. Although worflow maagemet problems have bee extesively studied for decades, locatio aspect of worflows has ot bee cosidered i existig literature. I this paper, we study how to exploit recet advacemets i multi-aget systems (MAS, iformatio techology ad geographic iformatio system (GIS to reduce cost ad time i the developmet of locatio-aware worflow schedulig systems based o a sustaiable architecture. The locatioaware worflow schedulig system aims to fid the schedule of resources ad activities based o the locatio 216

7 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 iformatio of the etities i the system. We propose a methodology that icludes modelig of locatio-aware worflows based o formal worflow models, develop a techique to trasform worflow models to formulate ad solve project schedulig problem. We propose a framewor to implemet a project schedulig system for costructio supply chais. ACKNOWLEDGMENT This paper is supported i part by the Miistry of Sciece ad Techology of Taiwa uder Grat NSC H MY3. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] X. Jiag, N. Y. Che, J. I. Hog, K. Wag, L. Taayama, ad J. A. Laday, Sire: Cotext-aware computig for firefightig, i: Proc. 2d It. Cof. o Pervasive Computig, PERVASIVE 04, Spriger, 2004, pp R. Yus, E. Mea, S. Ilarri, ad A. Illarramedi. SHERLOCK: Sematic maagemet of locatio-based, services i wireless eviromets, pervasive ad mobile computig. [Olie]. Available: T. Murata, Petri ets: Properties, aalysis ad applicatios, i Proc. the IEEE, vol. 77, o. 4, 1989, pp M. E. Georgy, Evolutioary resource scheduler for liear projects, Automatio i Costructio, vol. 17, o. 5, pp , July D. W. Johsto, Liear schedulig method for highway costructio, Joural of the Costructio Divisio, vol. 107, o. 2, pp , Jue R. B. Harris ad P. G. Ioaou, Schedulig projects with repeatig activities, Joural of Costructio Egieerig ad Maagemet, ASCE, vol. 124, o. 4, pp , July-August R. A. Yamí ad D. J. Harmeli, Compariso of liear schedulig model (LSM ad critical path method (CPM, Joural of Costructio Egieerig ad Maagemet, vol. 127, o. 5, pp , R. M. Reda, RPM: Repetitive project modelig, Joural of Costructio Egieerig ad Maagemet, vol. 116, pp. 2, pp , D. J. Harmeli, Liear schedulig model: Float characteristics, Joural of Costructio Egieerig ad Maagemet, vol. 127, o. 4, pp , T. W. Liao, P. J. Egbelu, B. R. Sarer, ad S. S. Leu, Metaheuristics for project ad costructio maagemet-a stateof-the-art review, Automatio i Costructio, vol. 20, o. 5, pp , August H. Li ad P. Love, Usig improved geetic algorithms to facilitate time-cost optimizatio, Joural of Costructio Egieerig ad Maagemet, vol. 123, o. 3, pp , B. C. Que, Icorporatig practicability ito geetic algorithmbased time-cost optimizatio, Joural of Costructio Egieerig ad Maagemet, vol. 128, o. 2, pp , H. Ke ad B. Liu, Project schedulig problem with stochastic activity duratio times, Applied Mathematics ad Computatio, vol. 168, pp , C. K. Chag, M. J. Christese, ad T. Zhag, Geetic algorithms for project maagemet, Aals of Software Egieerig, vol. 11, pp , Y. S. Dai, M. Xie, K. L. Poh, ad B. Yag, Optimal testigresource allocatio with geetic algorithm for modular software systems, The Joural of Systems ad Software, vol. 66, pp , P. Y. Yi ad J. Y. Wag, A coloy optimizatio for the oliear resource allocatio problem, Applied Mathematics ad Computatio, vol. 174, pp , Z. Re ad C. J. Aumba, Learig i multi-aget systems: A case study of costructio claims egotiatio, Advaced Egieerig Iformatics, vol. 16, pp , [18] X. L. Xue, X. D. Li, Q. P. She, ad Y. W. Wag, A agetbased framewor for supply chai coordiatio i costructio, Automatio i Costructio, vol. 14, o. 3, pp , [19] F. Peña-Mora ad C. Y. Wag, Computer-supported collaborative egotiatio methodology, Joural of Computig i Civil Egieerig, vol. 12, o. 2, pp , [20] J. So ad M. J. Sibiewsi, Multiheuristic approach for resource levelig problem i costructio egieerig: Hybrid approach, Joural of Costructio Egieerig ad Maagemet, vol. 125, o. 1, pp , [21] S. S. Leu, C. H. Yag, ad J. C. Huag, Resource levelig i costructio by geetic algorithm-based optimizatio ad its decisio support system applicatio, Automatio i Costructio, vol. 10, pp , [22] T. Hegazy, Optimizatio of resource allocatio ad levelig usig geetic algorithms, Joural of Costructio Egieerig ad Maagemet, vol. 125, o. 3, pp , [23] M. Wooldridge, A Itroductio to MultiAget Systems, New Yor: Joh Wiley & Sos Ltd, [24] M. Wooldridge ad N. R. Jeigs, Itelliget agets: Theory ad practice, The Kowledge Egieerig Review, vol. 10, o. 2, pp , [25] W. M. P. va der Aalst, The applicatio of petri ets to worflow maagemet, J. Circuit. Syst. Comput., vol. 8, o. 1, pp , [26] W. M. P. va der Aalst ad A. Kumar, A referece model for team-eabled worflow maagemet systems, Data & Kowledge Egieerig, vol. 38, o. 3, pp , September [27] M. Wese, W. M. P. va der Aalst, ad H. M. W. Verbee, Advaces i busiess process maagemet, Data & Kowledge Egieerig, vol. 50, o. 1, pp. 1-8, July [28] R. G. Smith, The cotract et protocol: High-level commuicatio ad cotrol i a distributed problem solver, IEEE Trasactios o Computers, vol. 29, pp , [29] D. C. McFarlae ad S. Bussma, Developmets i holo-ic productio plaig ad cotrol, Iteratioal Joural of Productio Plaig ad Cotrol, vol. 11, o. 6, pp , [30] H. V. D. Parua, Maufacturig experieces with the cotract et, i Distributed Artificial Itelligece, M. Huhs Ed. Lodo: Pitma, 1987, pp [31] C. Ramos, A holoic approach for tas schedulig i maufacturig systems, i Proc IEEE Iteratioal Coferece o Robotics ad Automatio, 1996, pp [32] R. W. Brea ad D. H. Norrie, Evaluatig the performace of reactive cotrol architectures for maufacturig productio cotrol, Computers i Idustry, vol. 46, pp , [33] T. Neligwa ad M. Fletcher, A HMS operatioal model, i Aget-Based Maufacturig: Advaces i the Holoic Approach, S. M. Dee Ed. Berli: Spriger-Verlag, 2003, pp [34] M. Weber ad E. Kidler. (2002. The Petri Net Marup Laguage. [Olie]. Available: [35] J. Billigto, S. Christese, K. V. Hee, E. Kidler, O. Kummer, L. Petrucci, R. Post, C. Steho, ad M. Weber, The petri et marup laguage: Cocepts, techology, ad tools, Lecture Notes i Computer Sciece, vol. 2679, pp , [36] R. Vrijhoef ad L. Kosela, The four roles of supply chai maagemet i costructio, Europea Joural of Purchasig & Supply Maagemet, vol. 6, pp , Fu-Shiug Hsieh received the B.S. ad M.S. degrees i cotrol egieerig from Natioal Chiao-Tug Uiversity, Taiwa, Republic of Chia i 1987 ad 1989, respectively. He received the Ph.D. Degree from Natioal Taiwa Uiversity i He served as research fellow i Idustrial Techology Research Istitute (ITRI, Taiwa, from 1994 to He was a Assistat Professor ad Associate Professor with The Overseas Chiese Istitute of Techology from 1999 to July 2004 ad August 2004 to July 2005,

8 Joural of Advaced Maagemet Sciece Vol. 3, No. 3, September 2015 respectively. Sice August 2005, he has bee with Chaoyag Uiversity of Techology, where he is curretly a Associate Professor at the Departmet of Computer Sciece ad Iformatio Egieerig. He has over sevety publicatios, icludig iteratioal joural ad coferece papers. He served as a Guest Editor for Asia Joural of Cotrol. He has also served as a referee for Automatica, Fuzzy sets ad systems, IEEE Trasactios o Systems, Ma, & Cyberetics, IEEE Trasactios o Robotics & Automatio ad Joural of Iformatio Sciece ad Egieerig, Joural of Itelliget Maufacturig, Iteratioal Joural of Productio Research, Iteratioal Joural of Advaced Maufacturig Techology, Measuremet, Asia Joural of Cotrol, Iteratioal Joural of Cotrol, Automatio i Costructio, ad IEEE Trasactios o Idustrial Iformatics. He chaired/co-chaired several iteratioal cofereces, icludig 2001 ad 2006 IEEE Iteratioal Coferece o Systems, Ma& Cyberetics, IFAC 2008 World Cogress, 2009 Iteratioal Coferece o Flexible Automatio ad Itelliget Maufacturig, 2010 Iteratioal Coferece o Iformatio Society (i-society 2010, Iteratioal Coferece o Computatioal Collective Itelligece --- Techology ad Applicatios (ICCCI 2010, 2012 Iteratioal Coferece o New Treds i Iformatio Sciece, Service Sciece ad Data Miig (ISSDM 2012 ad the 10th Iteratioal Coferece o Service Systems, ad Service Maagemet (ICSSSM 13. He is listed i Marquis Who s Who i the World 2006, 2007 ad 2009 ad Marquis Who s Who i Asia 2007 ad His area of iterest icludes electroic commerce, worflows, multi-aget systems, itelliget systems ad maufacturig systems. Jim-Bo Li received the B.S. degree from Lig Tug Uiversity, Taichug, Taiwa, Republic of Chia i His research iterests are i Petri ets, worflows, multi-aget systems, itelliget systems ad maufacturig systems. 218