IMPROVEMENTS IN THE OPTIMIZATION OF FLEXIBLE MANUFACTURING CELLS MODELLED WITH DISCRETE EVENT DYNAMICS SYSTEMS: APPLICATION TO A REAL FACTORY PROBLEM

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1 IMPROVEMENTS IN THE OPTIMIZATION OF FLEXIBLE MANUFACTURING CELLS MODELLED WITH DISCRETE EVENT DYNAMICS SYSTEMS: APPLICATION TO A REAL FACTORY PROBLEM Dieg R. Rdríguez (a), Mercedes Pérez (b) Juan Manuel Blanc (b) (a) Ikerlan, Pase J. M. Arizmendiarrieta, 2, Arrasate-Mndragón, Guipuzca, Spain (b) University f La Rija. Industrial Engineering Technical Schl. Department f Mechanical Engineering. Lgrñ, Spain (c) University f La Rija. Industrial Engineering Technical Schl. Department f Electrical Engineering. Lgrñ, Spain (a) drdriguez@ikerlan.es, (b) mercedes.perez@unirija.es, (c) juan-manuel.blanc@unirija.es ABSTRACT Mdeling f Flexible Manufacturing Systems has been ne f the main research tpics dealt with by researchers in the last decades. The mdeling paradigm chsen can be in many cases a key decisin that can imprve r give an added value t the example mdeling task. Here, the mdeling tasks are represented by ne f the mstly used ne in the academia, the Petri Net paradigm, and in particular the Stchastic Petri Net mdels. These mdels cnstructed will be used t ptimize the perfrmance measures that culd be interesting fr the prductin systems. The prductin indicatrs used here are related with the prductivity f the systems and its efficiency in the prductin. We have added here and extra element t the ptimizatin prblem that is related with the energy cnsumptin during the prductive prcess. This will add an extra value t the actual scenari, intrducing energy efficiency terms and infrmatin int the mdels and int the ptimizatin prcess. These prductivity and energy cnsumptin measures culd be included int an ptimizatin prcess by changing a certain number f parameters int the mdel. A tw phase ptimizatin prcess has been applied t the real example we have cnsidered and an imprvement f this tw phase methdlgy has been applied, cmparing these results with the riginal tw phase methd t check whether which apprach is mre apprpriate. Previus results btained fr this systems are imprved by this new piece f research. Keywrds: Stchastic Petri nets, flexible manufacturing, simulatin, perfrmance measures, energy cnsumptin. 1. INTRODUCTION Flexible Manufacturing Systems and their representatin in an adequate mdel that expresses their behavir the mre accurately is a typical tpic treated by many researchers. Here, a cmparisn between tw ptimizatin appraches using a nvel representatin f the energy cnsumptin prcess assciated t the mdel is presented. The mdel representatin is dne thrugh stchastic Petri nets. Petri nets have shwn their capacities t represent the behavirs that Flexible Manufacturing Systems pse, and specially cncurrency and resurces representatin that are typical features f Manufacturing Systems. Stchastic Petri nets have been used largely t represent systems where an stchastic behavir is assciated t tasks. This mdeling methd has sme lacks when dealing with cmplex mdels where the state space is clearly untreatable and even simulatin can be a great time cnsuming task. Here we will cnsider nly simulatin appraches due t this cmplexity previusly mentined Here, a particular ptimizatin prblem will be intrduced. This particularity lies n the intrductin f terms related t the energy cnsumptin assciated t the machining prcesses and the inclusin f these data int the ptimizatin prblem and in particular int the gal functin. This will make that the energy cnsumptin infrmatin will be cnsidered as a new term f the ptimizatin functin. In rder t have the best pssible results f this ptimizatin prcess with a cntained cmputatinal effrt a cuple f ptimizatin appraches have been cnsidered. The first ne is a tw phase ptimizatin methd where the secnd phase uses the slutin btained frm the first ne, while the secnd apprach takes advantage f the infrmatin extracted frm the slutins visited during the first phase t reduce the cmplexity f the prblem we are cnsidering here. The rest f the paper is as fllws, in sectin 2 the FMS that will be used alng this paper will be explained and all the elements that will be f interest t be represented in ur mdel will be enumerated. Later n, in sectins 3 Petri net mdel will be depicted. In sectin 4, the ptimizatin will be depicted and the appraches are extensively cmmented. Finally, the results we are 619

2 interested in are represented assciated t the tw appraches in sectin 5 where a cmparisn f the results is shwn. Finally sme cnclusins are presented in sectin DESCRIPTION OF THE FMS The Manufacturing system initially cnsidered is able t perfrm windw frames with the fllwing different features: Feature 1 The first feature t be cnsidered when mdeling the system is the type f windw where the frame will be included: Accessible windw, tilt and turn windw, Slide windw Frames withut any ther element. Feature 2 This feature is related with the presence f a crsspiece that ges hrizntally frm ne extreme t the ther f the windw frame. With crsspiece Withut crsspiece Feature 3 The number f leafs that cmpse the windw is the next differentiatin element. One leaf Tw leafs It was cnsidered a third leaf in the initial mdeling cnstraints but finally it was cnsidered that the third leaf culd be added as a future imprvement f the manufacturing system. Feature 4 The last feature is related with the size f the windw that will change the treatment r steps that must be fllwed in case f cnsidering ne size r the ther. Big size Little size Cnsidering all the features depicted here, there are finally 32 different types f prducts that the manufacturing cell will be able t prduce. Apart frm these types f windws, a set f accessries can be added t the different prducts. These accessries are: Bx and Guide t include int this device the blind that can be integrated int the windw. Drip edge t get all the water that can slide thrugh the windw Initially we will describe the prcesses signing them in bld letters and describing wh the peratrs that perfrm every prcess are: Operatr 1 perfrms the selectin f the materials needed t cmplete satisfactrily the aluminum prfiles depending n the frame t be prduced Operatr 1 als supervises the cutting f the PVC prfiles in the crrespnding machine. Operatr 1 perfrms the peratin f intrductin f the reinfrcement Operatr 1 supervises peratins perfrm inside the Numerical Cntrl Machine. These peratins are 6 different peratins that must be perfrmed. We d nt enter int mre details abut these peratins because is nt the bjective f this thesis. Finally peratr 1 checks the crrectness f the reinfrcement screwing peratin. Operatr 2 perfrms the fllwing peratins Selectin f Material fr the reinfrcement cutting Supervises the reinfrcements cutting in the crrespnding machine Distributes the reinfrcements t the crrespnding prfile Perfrms an extra peratin that is the leaf cutting that crrespnds t the inverse leaf fr the windws that are cmpsed f tw leafs Operatr 3 perfrms the fllwing tasks: Once all the peratins are cmpleted in the Numerical Cntrl Machine, he distributes the cmpleted pieces in the crrespnding carriage. Fr the pieces where the sldering is nt needed this peratr will retest the strip/pst In case the previus parts are frames they shuld be sldered and cleaned passing t peratr 4 Operatr 5 will distribute the pieces after cming frm the previus task. There is ne decisin imprtant in the prductin prcess at this pint that is the presence f a crssbar in the windw. Depending n this the pieces will take a way r anther. Operatr 6 is in charge f inserting the crssbar int the windw frame. After this peratin all the frames (independently f having r nt crssbar) cntinue t the next peratins jintly Nw the system will need t knw if the windw is a tw leafs windw then peratr 6 will fix the inverse leaf Once finished this peratin all the frames will pass t the irnwrk placing. This peratin will be accmplished by peratr 7 Operatr 8 will cntinue being in charge f the fllwing: 620

3 In case the windw is a frame he will place the lcks and the hinges In any case he will hang the windw in a place where the ther peratrs will take it t perfrm the fllwing peratins. After all these prcesses if the windw has a bx in its features there will be 7 pssible cnfiguratins related with the bx placing. All these peratins related with the bx are perfrmed by peratrs 9 and 9 bis. These seven ptins are: 1. Guide Assembly + Bx + Drip Edge + Silicne Insert 2. Guide Assembly + Bx + Silicne Insert 3. Guide Assembly + Drip Edge + Silicne Insert 4. Bx + Drip Edge + Silicne Insert 5. Guide Assembly + Silicne Insert 6. Drip Edge + Silicne Insert 7. Bx + Silicne Insert Once the bx assembly prcess is cmpleted the next phase will be glaze the windw in case is needed. This task is perfrmed t all windws independently f the bx presence. Operatr 10 will cntinue with: Glazing the windw Inserting the reeds int the windw Operatr 11 will: Disassemble the leaf/frame Pack the finished windw There is an extra peratr in the system, peratr 12, that will perfrm ancillary peratins helping peratr 3 with the distributin f wagns Operatr 13 selects and distributes the glass supplying them previus t the peratin f lcks and hinges Finally, peratr 14 perfrms the task f cut and distributin f reeds previus t the peratin related with them. Once the peratins and the initial peratrs that are perfrming the tasks we will cnsider a table with all the peratins and a task numbering that will help us when mdeling this example is presented. The fllwing table presents a descriptin f the different tasks that have t be perfrmed and whm is respnsible f perfrming them. Task Descriptin Perfrmed By the selectin f the Task1 materials Operatr 1 Task2 cutting f the PVC prfiles Operatr 1 Intrductin f the Task3 reinfrcements Operatr 1 Numerical Cntrl Task4 Machine 6 Operatins NCM Reinfrcements material Task5 selectin Operatr 11 Task6 Reinfrcements Cutting Operatr 11 Task7 Reinfrcement distributin Operatr 11 Operatr 1 and Screwing f Machining Task8 reinfrcements Center Task9 Leaf cutting Operatr 2 Task10 Inverse Leafs distributin Operatr 2 Task11 Wagn distributin Operatr 3 Task12 Retest the strip/pst Operatr 3 Task13 Crssbar distributin Operatr 3 Task14 Sldering and cleaning Operatr 4 Task15 Frame distributin Operatr 5 Task16 Crssbar Munting Operatr 6 Task17 Lcks and hinges fixing Operatr 8 Task18 Windw hanging Operatr 8 Task19 Inverse leaf munting Operatr 6 Bx assembly (with all Task20 ptins) Operatr 9 Task21 Glazing Operatr 10 Task22 Insert the reeds Operatr 10 Task23 Glass selectin and distributin Operatr 13 Task24 Reeds cut and distributin Operatr 14 Task25 Disassemble leaf/frame Operatr 11 Task26 Pack finished windw Operatr 11 The flw f parts f the systems under study is represented in figure

4 Figure 1. Flw mdel f the example 3. STOCHASTIC PETRI NET MODEL Here we present the Petri net it has been mdeled using stchastic PNs. The cmplete mdel is represented by the fllwing figure. 1,while T53, T511, T521, T441 and T4111 represent the five peratins that the secnd peratr can perfrm. Finally, the machining tl availability is represented by place Machining_TOOL1 and the peratin is shwn under transitin T421. Figure 3. Petri Net mdel Operatr 1 and 2 and NCM frm example 2. Figure 2. Cmplete Petri Net mdel This cmplete Petri net mdel shwn befre will be mre clearly presented in the next figures where it will be divided in substructures that will help understanding the mdeling issues. Figure 3 presents the peratins where peratrs 1, 2 and the numerical cntrl machine are invlved. Places Oper1 and Oper2 represent the availability f the peratrs when marked. Transitins T45, T412, T32 and T431 represent the 4 peratins that can be perfrmed r supervised by Operatr Figure 4, represents the peratrs 3 and 4 and due t their simplicity, because they are nly perfrming an peratin we have cnsidered that a simple peratr can cver each ne f the tasks assciated. There is n cmpetitin fr the peratr tasks. Figure 4 Petri Net mdel Operatr 3 and 4 frm example

5 The next figure (Figure 5) represents the tasks where peratrs frm 5 t 9 are invlved. This Petri net mdel represents mst f the decisins that must be taken (depending n the type f final prduct that the FMS is generating).after peratr 5 perfrms its task (transitin T611) then the raw parts will take ne way r anther depending n the type f final prduct (windw r frame). If it is a windw will cntinue thrugh transitin windw and then a secnd decisin shuld be taken depending if what has t be built is a leaf f this windw r a frame f it (transitins Leaf r Frame). All these peratins will be supervised by peratr 6. Then peratrs 7 and 8 will perfrm their tasks assciated t them (transitins T15, T151 and T17). Finally, peratr 9 will perfrm its peratin represented by transitin T19 but befre that a decisin shuld be taken regarding the presence f a BOX in the windw structure represented by immediate transitins BOX and NO_BOX. The last Petri net submdel is represented in Figure 6, where peratrs frm 10 t 14 are mdeled. These peratrs generally are perfrming simpler peratins than the previus nes and their mdel representatin is simpler als. 4. TWO PHASE OPTIMIZATION APPROACHES The search space crrespnding t the ptimizatin prblem that it is slved is cmpsed by the fllwing variables: Variable NOper1 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 2. Variable NOper2 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 2. Variable NOper5 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 5. Variable NOper6 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 6. Variable NOper8 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 8. Variable NOper9 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 9. Figure 5.Petri Net mdel Operatrs 5 t 9 frm example 2. Variable NOper10 is an integer variable that represents the number f peratrs that will perfrm the peratins initially assigned t peratr 10. Variable Mach_Delay is a real variable that represents the time that in average takes t the Numerical Cntrl Machine t perfrm the different tasks. Variable PROB_BOX is a real variable that represents the percentage f windws that has a bx inside its structure. Variable PROB_FRAME is a real variable that represents the percentage f windws that will be a fixed frame windw withut any leaf (r with a unique une) Variable PROB_WINDOW is a real variable that represents the percentage f prducts that will have a windw structure instead f a frame ne. Figure 6.Petri Net mdel Operatrs 11 t14 frm example 2. The search space cnsidered fr this example will be the ne shwn in the fllwing text bx Parameter definitins: # name type minimum maximum initial delta temp 0 NOper1 INT NOper2 INT NOper5 INT NOper6 INT NOper8 INT NOper9 INT NOper10 INT Mach_Delay REAL PROB_BOX REAL PROB_FRAME REAL PROB_WINDOW REAL

6 The ptimizatin functin will include the perfrmance measures we are interested in and are mainly related with the thrughput f the system and the prfit fr a 8 hur shift, cmbined with the csts assciated with the presence f mre peratrs in the different psitins f the FMC. The manner hw is represented this utilizatin in a PN mdel is by the frmula represented belw that will be explained later n. MEASURE Prfit P{#P37>0}* (P{#P34>0}+P{#P26>0}+ P{#P12>0})*2880*0.3)- 40*(NOper1+NOper2+NOper5+NOper8+NOper9+NOper_ 10)-20000*Mach_Delay; The first expressin f this frmula (P{#P37>0}) represents the thrughput f the whle system given that place P37 is the place psitined just befre being perfrmed the last task (dne by peratr 11). This expressin will represent the prbability that there is mre than zer tkens in place P37, and this is exactly the meaning f the thrughput (cnsidering that the maximal number f tkens in place P37 is 1 because there is a P-invariant that cntains this place and als places P37 and Oper11). The amunt f crrespnds t the gain that the cmpany is having cnsidering a mean selling price fr all the windws prduced f 25 Eurs per unit prduced and cnsidering that there is a shift f 8 hurs (28800 secnds). The next term (E{#P34}+E{#P26}+ E{#P12})*30*8*0.1) crrespnds t the energy cnsumptin term that is assciated with the use f the different machines that are invlved in the prcess. In this particular case there are three peratin machines that are represented in places P34, P26 and P12. Cmputing the utilizatin f these machines during a shift f eight hurs and cnsidering the mean cst f the energy equal t30 kwh and cnsidering a cst f energy equal t 0.1 /kwh The next part crrespnds t the cst assciated with the utilizatin f the different peratrs that has been estimated in 40 Eurs fr each wrker and fr and 8 hur shift. Finally, the last part crrespnds t the cst assciated t the inclusin int the system f a quicker Numerical Machine Center that will increase the price accrding t the mean peratinal speed (20000 /secnd) 5. RESULTS AND COMPARISON The results we are interested t cmpare between the tw appraches previusly shwn are related with prductivity measures. It will be cnsidered the number f pieces prduced per time unit fr each type f prduct (32 different types can be prduced in the FMS). Anther perfrmance measure we will cnsider will be the utilizatin f the different peratrs that are present int the system Anther imprtant cmparisn measure will be hw efficient is the cnvergence prcess fr the tw mdels and the accuracy they can reach. Als the cmputatinal time that the cmputer will be calculating the measures will be anther measure f hw gd the simulatin prcess is with respect t the clred and the stchastic mdels. Als given the cmplexity f the mdel is imprtant t cnsider the quality f the slutin btained cmbined with mre qualitative measures mre related with the cmputatinal effrt and the number f iteratins dne during the ptimizatin prcess. In rder t present all this infrmatin, the fllwing tables are presented. There are 5 experiments r ptimizatin methds we have applied. Experiments EXP1: Tw Phase Apprach: Temp_anneal_scale parameter 100 EXP2: Tw Phase Apprach: Temp_anneal_scale parameter 50 EXP3: Tw Phase Apprach: Temp_anneal_scale parameter 20 EXP4: Tw phase Apprach with Reductin f Search Space in the secnd Phase EXP5: Tw phase Apprach with Temperature Parameter in variables in secnd Phase Experiment Time (Minutes) Simulatins Prfit EXP EXP EXP EXP EXP Experiment QUALITY Timing Simulatins EXP % % % EXP % 39.43% 51.41% EXP % 21.32% 20.17% EXP % 50.12% 67.08% EXP % 10.46% 5.25% 6. CONCLUSIONS AND FUTURE RESEARCH Here we have presented a set f appraches that have been applied t a real Flexible Manufacturing System where a first apprach t the intrductin f energy cnsumptin infrmatin is intrduced int the ptimizatin prblem adding an extra value t the ptimizatin prcess and giving anther slutin t the cmpanies in rder t reduce the expenses assciated with this energy cnsumptin. Sme pssible future research tpics will be related with the intrductin f mre energy related infrmatin int the mdels s that the ptimizatin prcess will be mre cncentrated int this tpic. REFERENCES Aarts, E., Krst, J. Simulated Annealing and Blzmann Machines, Wiley (1989) Ajmne Marsan, M., Balb, G., Cnte, G., D-natelli, S., Francheschinis, G. Mdelling with Generalized Stchastic Petri Nets, Wiley (1995) Balb, G., Silva, M.(ed.), Perfrmance Mdels fr Discrete Events Systems with Synchrnisatins: 624

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