CHAPTER 2 OBJECTIVES AND METHODOLOGY

Transcription

1 28 CHAPTER 2 OBJECTIVES AND METHODOLOGY The objectve of ths research s to mprove shop floor performance through proper allocaton of jobs n the machnes by consderng due tme, whch reduces the overall penalty and maxmzes the utlzaton tme of the machne. Ths problem s a generalzaton of the weghted tardness problem. More specfcally, the objectve s to fnd the schedule that mnmzes the total earlness and total tardness costs of all jobs subject to the constrants that no preempton of jobs s allowed, no dle tme s nserted and all jobs are avalable before the startng tme of the schedule. 2.1 OPTIMALITY CRITERIA Generally the performance of any schedule can be evaluated wth respect to some objectve functon to be optmzed. Below are some of the most common objectve functons used to evaluate the performance of any schedule. The mportance of multple objectve functons arses from the fact that a sngle objectve can be optmzed at the expense of others. Flow tme s the tme requred to complete all the n operatons n n machnes. It s represented by the notaton of F F n t (2.1) 1 Where t s the completon tme of the nth operaton of job. Mean Flow Tme s defned as rato of flow tme and total number of jobs (m). It s represented by the notaton of F

2 29 F 1 n Fj n j 1 (2.2) Makespan (C max ) s the most wdely used performance measurng parameter of schedules. It s the total tme requred to complete all the jobs n a schedule. The longest duraton n whch all jobs are completed s referred to as the makespan. max (2.3) 1 n Cmax F Lateness s the dfference between the completon tme of the job and the due date s termed as lateness. L F D (2.4) where F s the flow tme of th job and D s the due date of th job. Earlness: If the job s completed before the due date, then the perod between the completon tme of the job and the due date s termed as earlness. E max( D F,0) (2.5) where F s the flow tme of th job and D s the due date of th job. Tardness: If the job s completed after the due date, then the perod between the due date and the completon tme of the job s termed as tardness. T = max (F - D, 0) (2.6) where F s the flow tme of th job and D s the due date of th job. Total weghted tardness s the sum of the weghted length of the tme taken to complete the job after ts due date. Weghted tardness takes

3 30 nto account only the postve dfference between completon tme and due date. n 1 w max(0, t d ) (2.7) Where w s the weght (early or late penalty) of the th job. Tardy jobs are the jobs whch are completed after the common due date and ncurs late penalty. Machne Utlzaton has qute a sgnfcant nfluence on the tardness of the optmal sequence. Therefore t s mportant to make proper allocaton of jobs on all the avalable machnes. The machne, whch s utlzed upto the makespan are taken as 100% utlzed machne. Percentage of Machne Utlzaton s calculated for each machne n the set of n machnes usng the formula machneutlzaton of correspondng machne % of machneutlzaton x100 (2.8) Maxutlzaton 2.2 MULTICRITERIA SCHEDULING Multcrtera optmzaton problems are characterzed by the fact that several objectves have to be optmzed smultaneously. In most cases or n real case a schedule has multple crtera. Multple crtera models nvolvng multple machnes for a shop represent the most general class of schedulng models. The schedulng of jobs n a faclty wth fnte resources has been a problem of nterest to researchers for a number of years. The crtera s very mportant n producton schedulng to assgn orders or jobs effectvely to avalable producton resources accordng to the one or more schedulng crtera.

4 31 The optmal soluton wth one crteron could perform bad result wth respect to some other crtera. Therefore, a non-optmal soluton wth satsfactory performance on other measures mght be consdered as a better alternatve by the decson maker. Recognzng the need of multcrtera schedulng, Van Wassenhove and Gelders (1980) sequenced the jobs wth the two objectve functons as mnmzng the holdng cost and the maxmzng the tardness. After ntroducng the concept of effcency they developed an algorthm fulfllng the two crtera () mnmzng the total flow tme and () mnmzng the maxmum tardness. Sdney (1977) presented an algorthm for solvng sngle machne schedulng problem to mnmze the maxmum penalty wth some restrctve assumptons on the target start tme, along wth a method for generatng alternatve optma. Sankaran (1978) proposed an algorthm subject to certan assumptons on penalty functon wth the tme complexty of O(n log n). The paper gves the complexty of varous steps nvolved n the algorthm and compared wth the algorthm proposed by Sdney (1977). Raman et al (1989) proposed a schedulng procedure whch performs well n both balanced and unbalanced systems. The approach decomposed the dynamc schedulng problem nto a seres of statc problems. Tallard (1993) dscussed the job shop, open shop and flow shop schedulng problems for mult machnes and generated benchmarks for basc schedulng problems to mnmze the makespan. Chen et al (2006) presented b-crtera schedulng problem wth two domnance propertes for non-adjacent jobs to reduce the searchng scope. Yume Huo et al (2007) proposed an algorthm wth bcrtera as: the maxmum tardness and the maxmum weghted tardness. Quan-Ke pan (2009) presented a novel dscrete dfferental evoluton algorthm for solvng the schedulng problems wth makespan and maxmum tardness crtera. The studes of schedulng problem wth secondary crtera dentfy the best sequence for secondary measure among the set of alternatve optma wth respect to the prmary measure.

5 METHODOLOGY The focus of ths research s to solve the Job Schedulng Problem usng two dfferent methods for mult machnes and three methods for sngle machne schedulng. To meet the objectves, the followng algorthms are proposed.. Deep Memory Greedy Search (DMGS). Deep Memory wth Partcle Swarm Optmzaton (DMPSO). Rato Schedulng Algorthm (RSA) v. Robust Heurstc Algorthm (RHA) v. Set-based Partcle Swarm Optmzaton (SPSO) Mult Machne Job Schedulng Problem Job schedulng s a branch of producton schedulng, whch s among the hardest combnatoral optmzaton problems. Not only t s hard, but also among the members of the latter class, t appears to belong to the more dffcult ones. The problem conssts of a fnte set J of n jobs to be processed on a fnte set of m dentcal machnes. Each job J has to be processed on a machne wth processng tme p wthout nterrupton and preempton. In recent years the new unversal search technques have been gvng reason for the hope that these methods could be successfully appled to solve the JSP. Enumeratve approaches wth exponental worst-case tme complexty to obtan exact solutons. Ths secton has focused on two man approaches namely Deep Memory Greedy Search algorthm and Deep Memory wth Partcle Swarm Optmzaton algorthm on mult machne job schedulng problem provdes near-optmal solutons n short computaton tmes.. Deep Memory Greedy Search

6 33 Many algorthms proposed over the years can be descrbed as greedy procedures for the stagewse mnmzaton of an approprate cost functon. In ths work we focus on the job schedulng problem for a specfc regularzed form of greedy stagewse optmzaton. She Mannor et al (2003) proved the consstency of greedy approach under general condtons. The paper explans the smoothness parameter of the decson boundary, convergence rate wth and wthout knowng the smoothness parameter. Carsten Franke (2007) appled Evoluton Strateges to generate a method that specfcally consders the preferences of the system owner when automatcally generatng an onlne schedulng process for Massvely Parallel Processng (MPP) systems. The schedulng problem s taken from real MPP nstallatons: Dfferent user submt ndependent, non-clarvoyant parallel jobs to the MPP system over tme. The schedulng process s responsble to assgn those jobs to the avalable dentcal machnes of the MPP system. For the development of a schedulng process that supports prortzaton of the shop and the customer, we propose Deep Memory Greedy Search algorthm. In ths research we address the schedulng problem on mult machnes to mnmze the makespan and maxmum tardness by DMGS method. An attempt s made to construct an optmum soluton n stages. At each stage, a decson s made that appears to be the optmum under some crteron at that nstant. A decson made at one stage s not changed at later stage, so each decson assumes feasblty. The Best decson s taken rght now, wthout regard for future consequences. Deep Memory Greedy Search Method s a way to an optmal task assgnment n stages. The Schedulng decsons have analyzed accordng to the followng crtera Due date as per company requrements (DC o R) Due date as per customer requrements (DC u R) Common Due Date (CDD). When workng wth job schedulng accordng to the crtera n Deep Memory Greedy Search approach s tryng to evaluate and make a choce of where to go next from the current poston. The C max values obtaned through Deep Memory Greedy Search algorthm are compared wth benchmark values. Ths shows that the algorthm s one of the better ways to

7 34 fnd the optmal soluton for job schedulng problems. The result shown through smulaton experment that adopts ths approach over crtera leads to an mprovement n tardness and n makespan.. Deep Memory wth Partcle Swarm Optmzaton The majorty of research on schedulng problems addresses on Partcle swarm optmzaton as a global optmzaton algorthm for dealng wth problems n whch the best soluton can be represented as a pont or surface n a n-dmensonal space wth dspatchng rules. Partcle Swarm Optmzaton (PSO) s an evolutonary computaton technque developed by Eberhart and Kennedy (1995) nspred by socal behavor of brd flockng or fsh schoolng. Smlar to Genetc Algorthms (GA), PSO s a populaton based optmzaton tool. Compared to GA, the advantages of PSO are that PSO s easy to mplement and there are few parameters to adjust. In recent years there have been a lot of reported works focused on the PSO whch has been appled wdely n the functon optmzaton, artfcal neural network tranng, pattern recognton, fuzzy control and some other felds where GA can be appled. In DMPSO, PSO algorthm s ntalzed wth a group of Deep Memory Greedy Search partcles (solutons) and then searches for optma by updatng generatons. The majorty of research on schedulng problems addresses on Partcle Swarm Optmzaton s a global optmzaton algorthm for dealng wth problems n whch the best soluton can be represented as a pont or surface n a n-dmensonal space wth dspatchng rules (Lan et al 2006). Xngsheng Gu (2006) has developed a smlar PSO algorthm (SPSOA) to solve Flow Shop Schedulng Problem (FSSP). The paper proposes SPSOA and attempts to apply t for permutaton n FSSP to mnmze makespan. The SPSOA dffers from PSO at least n three aspects: the frst s to propose a SPSOA for permutaton flow-shop schedulng to mnmze makespan. The second s to nvestgate the effect of varous operators (crossovers) under the framework of dffcult combnatoral problems such as the FSSP. The thrd s the computatonal experments whch are performed on dfferent sze FSSP testng nstances to compare the effcency of GAs and SPSOA and t shows

8 35 that the SPSOA s more obvously effcacous than GAs. The smulaton programs are wrtten n java language. PSO s an evolutonary algorthm that the system s ntalzed wth a populaton (named swarm n PSO) of random solutons and searches for optma by updatng generatons. Each ndvdual or potental soluton, named partcle fles n the dmensonal problem space wth a velocty whch s dynamcally adjusted accordng to the flyng experences of ts own and ts colleagues. The PSO algorthm mmcs the behavor of flyng brds and ther means of nformaton exchange to solve optmzaton problems. In chapter 4, Deep Memory Partcle Swarm Optmzaton s ntalzed wth a group of Deep Memory Greedy Search Partcles (solutons) and t searches for optma by updatng the process teratvely. In all teratons, each partcle s updated by the followng two "best" values. The frst one s the best soluton acheved so far through DMGS technque and the ftness value s stored. Ths value s called as sequence best. When a partcle takes part n the populaton as ts topologcal neghbours, the best value s called partcle best. Another "best" value that s tracked by the Partcle Swarm Optmzer s the best value, obtaned so far by any partcle n the populaton. Ths best value s called global best. Each partcle updates ts movement vector based on the experence of the local best and the global best n order to update ts poston wth the currently updated movement n search space. When there s no mprovement n the teraton or all the partcles updates ts local best, the process wll be culmnated. The dspatchng rules are appled to obtan reasonable schedule. Dspatchng Rules are categorzed as Shortest Processng Tme (SPT) Crtcal Rato Rule (CRI) Longest Processng Tme (LPT) Prorty selecton (PRI) Frst-Come-Frst-Serve (FCFS)

9 36 SPT ranks the jobs accordng to the length of ther processng tme. Shortest processng tme means a hgher probablty of beng chosen, whereas Longest Processng tme s opposte, job wth longer processng tme has the hgher probablty. The results of DMPSO s encouragng, to determne the sequence of jobs for producton wth global best penalty. The comparson done for makespan, global best penalty and machne utlzaton by valdatng wth benchmark results through tabulatons and charts. The DMPSO algorthm s chosen to solve the problem and ts performance s compared wth varous dspatchng rules. Smulatons are used to evaluate them and the varous tables and charts shows the smulaton results. The dspatch prorty rules are proposed and tested for ths NP hard problem. These were found to perform far better than known heurstc methods. Peng S ow (1989) proposed a varaton of Beam Search method developed n artfcal ntellgence. Ths varant, called Fltered Beam Search was consstent n provdng near-optmal solutons wth a relatvely small search tree. The method was tested on twenty test problems, each wth dfferent parameter settngs gvng a total of 1440 problems wth maxmum job sze of 25 jobs. Ths paper nvestgates three dspatchng rules. The Shortest Processng Tme (SPT) rule s effectve when due dates are tght. The Crtcal Rato rule (CRI) wll chose the job wth lowest rato between tme untl due date and the processng tme. The Longest Processng Tme (LPT) rule gves prorty to the lot wth the hghest amount of processng tme at the current work staton. The prorty selecton rule selects lots accordng to a random number generated at the tme of allocatng. The Frst-In-Frst-Out (FIFO or FCFS) rule chooses job accordng to ther arrval tmes at work statons Sngle Machne Job Schedulng Problem The problem s to schedule a set of jobs on a sngle machne to mnmze total early and tardy costs. More specfcally, the objectve s to fnd the schedule that mnmzes the total earlness and tardness costs of all jobs, subject to the constrants that no preempton of jobs s allowed, no dle tme

10 37 may be nserted and all jobs are avalable from tme t=0 onwards. Ths research presents three algorthms for sngle machne schedulng problem wth n jobs, all havng common due date to be delvered.. Rato Schedulng Algorthm Rato Schedulng Algorthm (RSA) consders most of the possble nstances of the problem based on the sum of the processng tme of the early set p, the tme gap J E ( J ) d and p. The early set E(J) s the set of jobs wth 1and the late set L(J) s the set of jobs wth 1. In a sequence, f d then there s a tme gap (d - ) before the due date d. Also f p ( d ), J L( J ) then the startng tme of the global optmal sequence s ether t mn(0, d) or mn(0, k d) where k s the processng tme of a job n L(J) wth mn. If d and some J of L( J ) suchthatts p ( d ) then the startng tme of the optmal schedule s t = 0 and a job of L(J) wth max moves to the set E(J) and straddlng job occurs. If d and f at least one job of L(J) wth p ( d ) then the startng tme of the optmal schedule s t=0 and the completon tme of such job n L(J) concdes wth the common due date d. If d and some J of E( J ) suchthatts p d then t=0 and the completon tme of the last job of E(J) s after the due date and straddlng job occurs.

11 38 If d and some J of E( J ) suchthatts p d then t=0 and the job moves to L(J). Also a job of E(J) concdes wth the common due date d. If d and J E( J ) suchthat p d then two or more jobs of E(J) moves to L(J) accordng to untl d. If some J wth 1 then a newset S( J ) J / 1. And f If d then the job wth max of S(J) moves to the set E(J), the process repeats untl tme gap (d-) 0 and the remanng jobs of S(J) moves to L(J). d then all the jobs of S(J) moves to L(J). The proposed algorthm was appled to benchmark problems of job sze n=10 for the above test nstances. Based on proposed algorthm t s presented wth some of the propertes of the jobs whose completon tme concdes wth the common due date and the nstances n whch early jobs moves after the due date and the late jobs before the due date. The proposed algorthm outperforms n many nstances of the test cases. v. Robust Heurstc Algorthm Robust Heurstc Algorthm was dscussed and appled to problems rangng from job sze 10 to The heurstc strategy conssts of partton of two sets, E( J ) J / 1 & L( J ) J / 1 and determnng each set accordng to the rato of processng tme of the job to ts dfference p between the penaltes. Also, for each problem nstance, the dfferent n common due date d s gven by the formula d h p 1, where h s called the restrctve factor n the nterval (0,1).

12 39 To measure the effectveness of the algorthm, the proposed RHA was tested on benchmark problems wth dfferent job szes (n=10, 20, 50, 100, 200, 500, 1000) and restrctve factors (h=0.2 and 0.4). The results are compared wth benchmark solutons and the percentage dfference between obtaned soluton and the benchmark soluton s computed. The percentage dfferences of the proposed algorthm are compared wth the algorthms proposed by Celso et al 2005,.e. Tabu Search, Genetc Algorthm and Hybrd Metaheurstcs (HTG and HGT). Among the fve algorthms, the percentage dfference obtaned from Robust Heurstc Algorthm acheved better mean value. For the restrctve factor h=0.2, out of 70 problems, 64 problems have better result than benchmark values, whch gves a success percentage of 90%. For h=0.4, 60 out of 70 problems have better result than benchmark values, whch gves 85.7% success. RHA outperforms the other algorthms proposed by Celso M. Hno et al (2005). The Genetc Algorthm proved to be better but ts computatonal tme s more. The Robust Heurstc Algorthm sorts the lst n O(log n) tme. The proposed algorthm s also sutable for unrestrcted problems aganst a sngle machne, whch can also be further extended to m machnes. The proposed algorthm gves better results n a sgnfcantly lower computatonal tme. v. Set-based Partcle Swarm Optmzaton Many dfferent approaches have been appled to JSP and a rch harvest has been obtaned. However, some JSP, even wth moderate sze, cannot be solved to guarantee optmalty. The standard Partcle Swarm Optmzaton algorthm s generally used to solve contnuous optmzaton problems, and s used rarely to solve dscrete problems such as job schedulng problem. We-Neng Chen et al (2010) proposed a novel Set-based PSO to solve dscrete optmzaton problems and the algorthm was tested on travelng salesman problem and multdmensonal knapsack problem. Magnus

13 40 Erk et al (2010) tuned the PSO parameters used for velocty updaton accordng to the problem dmenson of the PSO varants to decrease the tme complexty of the algorthm. In chapter 7, a Set-based Partcle Swarm Optmzaton (SPSO) method s proposed to solve the sngle-machne job schedulng problem. The proposed SPSO defnes the poston and velocty usng the concept of set and possblty to solve dscrete space problems. Ths algorthm developed n dscrete space, converges faster under certan condtons on the parameters. 2.4 DATA COLLECTION The data was collected from LMW CNC Dvson Combatore and respectvely for Mult machne Input data and Sngle machne Input data, to examne the proposed algorthms Mult Machne Input Data To llustrate the effectveness and performance of the proposed algorthm n mult machne job schedulng, the algorthm s appled to dfferent cases of analyss based on practcal data. The requred data about components and the resource detals have been collected from LMW CNC Dvson Combatore. Based on the practcal data selected to compute, the effcency of the algorthm was made by comparson wth the exstng benchmark values. The due date crtera analyzed through DMGS s clearly adequate for solvng large scale complex problems. The mplementaton of DMGS for the three dfferent cases outperformed the benchmark tardness. The DMPSO schedules usng a prorty rule n whch the prortes are defned by the dspatchng rule. Through experments we can clearly get that the DMPSO s better than the exstng technques for job schedulng to mnmze makespan. Among the dscussed fve dspatchng rules, the crtcal rato rule has the hgh performance n obtanng smaller upper bound of makespan.

14 Sngle Machne Input Data The URL html s referred to get all possble nputs to the sngle machne schedulng problem. The proposed RSA, RHA and SPSO for the restrcted snglemachne common due date problem can be stated as follows: A set of n jobs wth determnstc processng tmes p and a common due date d are gven. The jobs have to be processed on one machne. For each of the jobs an ndvdual earlness and tardness penalty s gven, whch s ncurred, f a job s fnshed before or after the common due date d, respectvely. The goal s to fnd a schedule for the n jobs whch jontly mnmzes the sum of earlness and tardness penaltes. 2.5 SIMULATION AND OUTPUT Java s a modern, object-orented language based on open, publc standards. Java s much more standardzed and has a rcher collecton of core functons than any other general-purpose computer language. Java code can be wrtten usng technques such as abstract classes and the class. Core java API s very rch and ncludes standard packages for seral I/O, Ethernet and nternet access, securty, graphcs, sound and other typcal functons. Java has very robust, mature securty model whch has been pounded on by a huge communty. But not n the case of Vendor X s custom C-language TCP/IP stack and securty provsons. Java has bult-n excepton handlng, whch C lacks completely. It s possble to crcumvent Java s good ntentons. Java programs are potentally much more relable. Java code can be tested and debugged on a platform, then moved wth lttle or no changes to an embedded system Java Features

15 42 1 Java Vrtual Machne (JVM). 2 An magnary machne that s mplemented by emulatng software on a real machne. 3 Provdes the hardware platform specfcatons to whch we comple all Java technology code. 4 Garbage collecton thread. 5 Responsble for freeng any memory that can be freed. Ths happens automatcally durng the lfetme of the Java program. 6 Programmer s freed from the burden of havng to deallocate that memory themselves. 7 Code securty s attaned n Java through the mplementaton of ts Java Runtme Envronment (JRE). Table 2.1 gves the phases of the java program such as 1. Wrte the program wth Text Edtor Tool. 2. Save fle wth.java Extenson. 3. Input n the form of.class Extenson wth Text Edtor Tool. 4. Comple the program wth Java compler. 5. Run the Program wth Java nterpreter. Table 2.1 Phases of a Java Program Task Tool to use Output Wrte the program Any Text edtor Fle wth.java Extenson Comple the program Java compler Fle wth.class extenson (Java byte codes) Run the program Java nterpreter Program output

16 43 Consderng these advantages of Java programmng, the program code was wrtten n java DMGS Output After enterng the nputs to Job Scheduler, t creates an nput fle and smulaton run takes place. Also, an output fle s created and stored as output. job. The output fle can drectly takes that stored data to MS-Excel for analyss of results and plottng graphs. Fgure 2.1 depcts the job machne Gantt chart wth ten jobs, three machnes and ts allocaton. Each block stands for a job gven wth job ID. The length of a block mples ts processng tme. C max s the total tme requred to complete all the jobs n the schedule. Fgure 2.1Gantt chart wth 10 jobs Creatng Gantt chart s an added advantage of the Job Scheduler. Gantt chart s a powerful management tool nvented by Gantt n the early 20 th century for plannng operatons and controllng jobs. In Fgure 2.1, a tme scale s placed on the horzontal axs. On the vertcal axs producton facltes to accomplsh requred jobs or jobs to be performed are represented. A planned tme schedule for the progress of jobs to be performed on the correspondng producton facltes s depcted by the horzontal bar.

17 44 Performance of the actual work may be montored n comparson wth the plan and wherever qute a large devaton between them occurs approprate acton may be taken to mprove the managng effcency of productve work DMPSO Output For smulaton, program s developed n java platform and DMPSO s performed wth varous Dspatchng Rules under dfferent number of machnes for sxteen jobs. The smulaton based Job producton analyzer s based on modern java and database technology and can be used for: Research on future producton concepts. Operatve producton plannng and control. Input for smulaton s gven n notepad. The nputs requred are the number of jobs to be scheduled, number of machnes avalable, processng tme, early and late penalty and the due date of each job. The output s stored after smulaton as a text fle (.txt) wth the specfed name. We can drectly take that stored data to MS-Excel for analyss of results and plottng graphs.

18 45 Fgure 2.2 DMPSO Output of Machne Wse allocaton n notepad Fgure 2.2 shows the allotted machne of each job. At the end of each teraton the penalty for the sequence s shown. Ths optmzaton s performed under varous teratons and partcles. Accordng to number of jobs, teraton can be performed. At the end of all teraton, global best soluton and machne wse allocaton are shown usng Gantt chart RSA Output Sngle machne schedulng problem was tested on problems of job sze 10 gven n secton 2.4 wth fve dfferent test nstances. The resultng schedules are plotted n column chart. The horzontal axs represents the optmal sequence of the job, where J0 represents the dle tme of the machne. In the optmal sequence there cannot be an dle tme between any consecutve jobs. The dle tme s nserted only n the begnnng of the schedule. The vertcal axs represents the processng tme. Length of each bar s the processng tme of the job wth penalty of the correspondng job on the top of the bar. Also the common due date s ndcated by the lne perpendcular to the horzontal axs RHA Output To valdate the proposed Robust Heurstc Algorthm, t was appled to 140 benchmark problems, whch yelds encouragng results when compared wth benchmark solutons. The comparson of the results are gven n table from job sze n=10 to n=1000. For 70 problem nstances, wth two common due dates were presented. The percentage dfference between the obtaned soluton and the benchmark soluton was calculated and compared wth the percentage dfferences gven by Celso (2005) for hybrd searches. The proposed RHA algorthm acheved better result wth less tme complexty. A comparson chart s gven for the tme complextes of dfferent methods.

19 SPSO Output A Set-based PSO s proposed to solve sngle machne schedulng problem n dscrete space. The orgnal PSO takes random ntal velocty, whereas the proposed SPSO ntalze the velocty accordng to ts processng tme and penalty of the jobs. In SPSO global best soluton and partcle s best soluton s updated n each teraton upto the best ftness. To analyze the performance, the SPSO algorthm was expermented wth the benchmark problems of job sze n = 5, 8, 10 and the results are tabulated.