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Graduate Seminar - Deadlock Avoidance in FMS, June 2002    Deadlock Avoidance Methodsin Flexible Manufacturing Systems    ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002   Introduction: Flexible Manufacturing Systems    An automatic, pr...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Introduction: Flexible Manufacturing SystemsComponents of the Syst...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Introduction: Flexible Manufacturing Systems                       ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Introduction: Flexible Manufacturing Systems                       ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Deadlock-free operation is crucial  to the operation of an FMSResea...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Deadlock - background  Parts in FMS compete for a finite number of ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Necessary conditions for deadlocks Mutual exclusion: resources can ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Part Flow Deadlock Machine M1                       Machine M2     ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Methods for handling Deadlocks  Detection/Recovery (Wysk et al., 19...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002   (Capacity-Designated Graph (CDG                         Mi      ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002   (Capacity-Designated Graph (CDG                                 ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Loops in a Capacity-Designated Graph                               ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Loops in a Capacity-Designated Graph                               ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Necessary Condition for a DeadlockThere is a loop S isuch that :  ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Impending (Policy-Induced) Deadlocks                              ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Cycle reduction in a CDG graph                                    ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Objective- Deadlock Avoidance Policies  To propose various control ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002 DAP properties   Correctness   Guarantees always a deadlock-free o...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002The Deadlock Avoidance Method  Request for movement        Compute ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Part Flow Management      Operation on part completed...           ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Four Different Deadlock Avoidance Policies   Static (SDAP)         ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Static Strategy   Off-line                                        M...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002                                            R1 : M1→M2→M3          ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Setup CENTRAL                                         ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002System Structure   BP    Static Deadlock           Dynamic Deadlock...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental DesignFour Different Deadlock Avoidance Policies      ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Experimental Design – 2 cell types   part types machines, 4 : Cell...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Design(Part Selection Rules (PSR   PSR1 – priority to ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental DesignRII – Routing Intensity Index                   ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Design   High Routing Intensity                    Low...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Design – Product Mix    Unbalanced mix             Bal...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : C(CB)=0, C(IB)={0}                                       ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : C(CB)=M, C(IB)={0}                                       ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : C(CB)=0, C(IB)={1}                                       ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : SDDAP performance for different buffer sizes             ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : SDDAP performance for different buffer sizes             ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : SDDAP performance for different buffer sizes. #Config    ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Incorporating a Central Buffer Operation on a part completed: if th...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Conclusions - Efficiency: The static policies are inefficient and g...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002  Conclusions - Computational Complexity   The computational comple...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Potential Implementation: Cluster Tools                  NEXUS 600 ...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Questions?                                             Dr. Jacob Ru...
Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : Part Selection Rules                                     ...
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Deadlock avoid

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Deadlock Avoidance Methods in FMS
Seminar in Univ. of Minho in 2002

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  1. 1. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Deadlock Avoidance Methodsin Flexible Manufacturing Systems Jacob Rubinovitz Technion - Israel Institute of Technology Faculty of Industrial Engineering & Mgmt. Dr. Jacob Rubinovitz
  2. 2. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Introduction: Flexible Manufacturing Systems An automatic, programmable manufacturing systemVolume Transfer Lines Dedicated CIM Systems Flexible Systems Automated Cells Job Shops Variety Dr. Jacob Rubinovitz
  3. 3. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Introduction: Flexible Manufacturing SystemsComponents of the System•Programmable machines (CNC, Robots)•Flexible tools and fixtures• Flexible MH systems (AGV’s, Robots)•Automated Storage and Retrieval System•Computer control Dr. Jacob Rubinovitz
  4. 4. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Introduction: Flexible Manufacturing Systems Dr. Jacob Rubinovitz
  5. 5. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Introduction: Flexible Manufacturing Systems Dr. Jacob Rubinovitz
  6. 6. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Deadlock-free operation is crucial to the operation of an FMSResearch of Deadlock Avoidance Methods:• Evaluation of different policies.• Integration of avoidance policies into the control software of Flexible Manufacturing Cells.• A joint work with Jean-David Salama. Dr. Jacob Rubinovitz
  7. 7. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Deadlock - background Parts in FMS compete for a finite number of resources (like robots, tools, pallets, fixtures, etc), and share buffers or queues having limited capacities. A deadlock state occurs when each process in a set of processes is blocked indefinitely from access to resources held by other processes within the set. A good FMS control method must resolve or avoid all the potential deadlocks during operation, without seriously degrading the system performance Dr. Jacob Rubinovitz
  8. 8. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Necessary conditions for deadlocks Mutual exclusion: resources can be allocated to only one process at a time. No preemption: resources held by one process cannot be allocated to another process until they are released by the process holding them. Hold and wait: processes hold their resources when waiting for the next required resources. Circular wait: closed chain of processes, where each process waits for a resource held by the next process in the chain. Dr. Jacob Rubinovitz
  9. 9. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Part Flow Deadlock Machine M1 Machine M2 P1: M1→M2(No Buffer ) (No Buffer ) P2: M2→M1Part P1 Part P2 M1 M2 )‫ טובורובוט‬MHD( M2 M1 M2 P1: M1→M2 M1 P2: M2→M3 P3: M3→M1 M3 P1: M1→M2 M3 P2: M2→M3 P3: M3→M1 Dr. Jacob Rubinovitz
  10. 10. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Methods for handling Deadlocks Detection/Recovery (Wysk et al., 1994)Prevention – System design, such thatdeadlocks are impossible (Epzeleta et al., 1995;Minoura and Ding, 1991; Viswanadham et al., 1990)Avoidance – a control policy thatexamines each request for resourceallocation prior to its execution (Banaszak and Krogh,1990; Ferrarini and Maroni,1998; Hsieh and Chang,1994; Lee and Lin, 1995; Revelotis and Ferreira,1996; Xing et al.,1996;Yim et al.,1990) Dr. Jacob Rubinovitz
  11. 11. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 (Capacity-Designated Graph (CDG Mi Ni 3 IBi A machine and its CDG node.Yim, D.S., Kim, J.I. and Woo, H.S. (1997) Avoidance of deadlocksin flexible manufacturing systems using a capacity-designateddirected graph. International Journal of Production Research, 35(9), 2459-2475. Dr. Jacob Rubinovitz
  12. 12. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 (Capacity-Designated Graph (CDG N2 |N|=4, N1 A12=A21=A24=A43=A32=A14=A41=1 2 2 A42=A13=A31=A34=A23=0 N4 X={1,2,0,1} N3 C={2,2,1,3} 3 1 Fully detailed CDG graph G=(N,A,X,C).Yim, D.S., Kim, J.I. and Woo, H.S. (1997) Avoidance of deadlocksin flexible manufacturing systems using a capacity-designateddirected graph. International Journal of Production Research, 35(9), 2459-2475. Dr. Jacob Rubinovitz
  13. 13. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Loops in a Capacity-Designated Graph N2 N1 Cycle S1: N1→N2→N1 N1 N2 N3 Cycle S2: N1→N2→N4→N1 Cycle S3: N2→N4→N3→N2 A4CDG G=(N,A) Cycle S : N →N →N N N3 containing 57 cycles. 4 1 4 1 Cycle S : N1→N →N3→N2→N1 A CDG G=(N,A) containingN5 cycles. 4 5 5 N4 N N! Smax = [Σ i =1 (N -i) !·i ] -N Dr. Jacob Rubinovitz
  14. 14. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Loops in a Capacity-Designated Graph N2 N1 N3 A CDG G=(N,A) containing 57 cycles. N5 N4 Routing Intensity Index N N ΣΣA i = 1 j =1,j = i ij RII = ; 0<RII<1 N (N - ) 1 Dr. Jacob Rubinovitz
  15. 15. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Necessary Condition for a DeadlockThere is a loop S isuch that : ΣX(N ) = ΣC(N ) Nj ∈ Sj j Nj ∈ Sj j Macro N1 N2 S1: N1→N2→N1 Nodes S2: N2→N3→N2 S3: N1→N3→N1 MN1={N1,N2} MN2={N2,N3} S4: N1→N2→N3→N1 MN3={N1,N3} N3 S5: N1→N3→N2→N1 MN4={N1,N2,N3} A CDG G=(N,A) with 5 cycles and 4 macro nodes.DeadlockAvoidance Policy: C(MNi ) < Σ C(Nj)-1 Nj ∈ Si Dr. Jacob Rubinovitz
  16. 16. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Impending (Policy-Induced) Deadlocks N2 MN1={N1,N2,N4,N5} N1 N3 MN2={N2,N3,N4} 1 2 constraints: 1 1 X(MN1) ≤ 3 X(MN2) ≤ 2 N5 1 N4 1In order to avoid the impending deadlocks,CDG graph (cycle) reduction is needed Dr. Jacob Rubinovitz
  17. 17. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Cycle reduction in a CDG graph Cycle Reduction Algorithm output N2 N1 N3 Macro Node elements Macro node capacityLevel 0 1 node 1 1 N5 MN1 {N1,N2,N4,N5} C(MN1)=C(N1)+C(N2) 1 N4 1 G1 +C(N4)+C(N5)-1=3Level 1 N N11 MN2 2 MN MN1 N3 MN2 {N2,N3,N4} C(MN2)=C(N2)+C(N3) 1 +C(N4)-1=2 1 2 2 3 1 N5 5 11 G2 G3 {MN1,N3}= C(MN3)=C(MN1) MN3 {N1,N2,N3,N4,N5} +C(N3)-1=3 MN3 MN4 Level 2 G4 3 3 G5 MN4 {MN2,N1,N5}= C(MN4)=C(MN2) {N1,N2,N3,N4,N5} +C(N1)+C(N5)-1=3 Dr. Jacob Rubinovitz
  18. 18. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Objective- Deadlock Avoidance Policies To propose various control solutions for part flow regulation in FMCs, all structured around four different deadlock avoidance policies (DAPs). The DAPs will be evaluated by their properties of:  correctness,  scalability,  configurability,  efficiency. Dr. Jacob Rubinovitz
  19. 19. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 DAP properties Correctness Guarantees always a deadlock-free operation Scalability Computational complexity for the control system is independent of the FMC complexity Configurability Can be applied to various FMC configurations Efficiency FMC operation is not restricted by policies that degrade its performance Dr. Jacob Rubinovitz
  20. 20. Graduate Seminar - Deadlock Avoidance in FMS, June 2002The Deadlock Avoidance Method Request for movement Compute the current number of parts in of a part to a node in a each relevant macro node assuming that given CDG graph G the requesting part was transported Yes Condition No Allow the X(RMNi)≤C(RMNi) Refuse the movement satisfied for all i ? movement Dr. Jacob Rubinovitz
  21. 21. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Part Flow Management Operation on part completed... The robot completed a delivery...Is the robot idle and is there some open space in the downstream station ? Checking if the transfer of each waiting part is unfeasible, No Yes feasible but refused, or feasible and accepted Transfer Transfer feasible: 2 or unfeasible: DAP applied to morePart waiting for allow or refuse the A part Numberfuture transfer transfer selection of accepted 0 transfers ? rule is Transfer Transfer 1 used to refused: allowed: Parts requesting pick a part Part waiting for Part actually movement The requesting future transfer moved by the remain at their part picked by robot locations. the robot Dr. Jacob Rubinovitz
  22. 22. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Four Different Deadlock Avoidance Policies Static (SDAP) M1 M2 Dynamic (DDAP) FIFO Loading Discipline M3 applied to parts in the Entry Buffer Input Buffer Selective Static (SSDAP) Selective Dynamic (SDDAP) Step-by-step M1 M2 Selection from all the backward search different part types waiting M3 in the input buffer Entry Buffer Dr. Jacob Rubinovitz
  23. 23. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Static Strategy Off-line Movement of a waiting On-line Create a CDG from the static part feasible information on machines, machine capacities and complete part type Determine the resulting number of parts routes in each relevant macro node X(RMN) Compute the relevant macro nodes RMNs and their capacities C(RMNs) Apply the deadlock avoidance methodDynamic Strategy On-line Movement of a waiting part feasible Create a CDG considering remaining machine sequences of each part in the system, and assuming that the requesting part was transported. Determine the current number of parts Compute the relevant macro in each relevant macro node X(RMN) nodes RMNs and their assuming that the requesting part was capacities C(RMNs). transported. Apply the deadlock avoidance method Dr. Jacob Rubinovitz
  24. 24. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 R1 : M1→M2→M3 M1 M2 M3Illustrative R2 : M3→M2→M1 |N|=3Example A12=A23=A21=A32=1 Entry Buffer C={1,1,1} Gantt chart, schedule under a static strategy - SDAP or SSDAP M1 M2 M3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 WIP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time Gantt chart, schedule under a dynamic strategy - DDAP M1 M2 M3 1 2 3 2 1 1 2 2 1 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 WIP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time Gantt chart, schedule under a dynamic strategy - SDDAP M1 M2 M3 1 2 3 3 2 1 2 2 3 3 2 1 1 2 2 1 1 1 1 1 1 1 1 1 WIP 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Time Dr. Jacob Rubinovitz
  25. 25. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Setup CENTRAL STATION 2 # Processed Parts WAREHOUSE Initial State 0 EXIT STATION 0 0 STARVED STATION 1 STATION 3 CENTRAL BUFFER IDLE STARVED 0 STARVED 0 0 0 STATION 4 STATION 5 INSPECTION ENTRY STATION # Parts in System 0 Replication Number 0 STARVED Current Time 0 STARVED 08:00:00 0 Dr. Jacob Rubinovitz
  26. 26. Graduate Seminar - Deadlock Avoidance in FMS, June 2002System Structure BP Static Deadlock Dynamic Deadlock External Avoidance Module Avoidance Module Module SBP SDAP SSDAP DDAP SDDAP Deadlock Cycle Reduction Algorithm Detection Module Part Flow Cycle Search Control Module Part Selection Rules Module Algorithm PSR1 PSR2 PSR3 PSR4 FMC Simulation Model (Arena) Dr. Jacob Rubinovitz
  27. 27. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental DesignFour Different Deadlock Avoidance Policies M1 M2 Static (SDAP) Dynamic (DDAP) M3 Entry BufferFIFO Loading Discipline applied to parts in the Input Buffer M1 M2 Selective Static (SSDAP) Step-by-step backward search M3 Selective Dynamic (SDDAP) Entry Buffer Selection from all the different part types waiting in the input buffer Dr. Jacob Rubinovitz
  28. 28. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Experimental Design – 2 cell types part types machines, 4 : Cell A 3 part types machines, 5 : Cell B 6Buffer Capacities Cell A Cell B 1 C(CB)=0, C(IB)={0}, CBS=4 C(CB)=0, C(IB)={0}, CBS=5 2 C(CB)=4, C(IB)={0}, CBS=8 C(CB)=5, C(IB)={0}, CBS=10 3 C(CB)=0, C(IB)={1}, CBS=8 C(CB)=0, C(IB)={1}, CBS=10 4 C(CB)=4, C(IB)={1}, CBS=12 C(CB)=5, C(IB)={1}, CBS=15 5 C(CB)=0, C(IB)={2}, CBS=12 C(CB)=0, C(IB)={2}, CBS=15 Dr. Jacob Rubinovitz
  29. 29. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Design(Part Selection Rules (PSR PSR1 – priority to parts with minimum remaining processes PSR2 – priority to parts with maximum remaining processes PSR3 – priority based on part type PSR4 – priority based on resource (machine) type Dr. Jacob Rubinovitz
  30. 30. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental DesignRII – Routing Intensity Index High RII Low RII Cell A RII = 1 RII = 2/3 Cell B RII = 0.9 RII = 0.6 Dr. Jacob Rubinovitz
  31. 31. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Design High Routing Intensity Low Routing IntensityR1: M4→ M2→ M1→ M4→ M3→ M1 R1: M1→ M2→ M4→ M3 CellR2: M1→ M2→ M3→ M4 R2: M4→ M1→ M3→ M2R3: M3→ M2→ M4→ M1→ M3 N 1 N2 R3: M3→ M4→ M2 N1 N2 A N4 N3 N4 N3R1: M1→ M5→ M3→ M4→ M2 R1: M1→ M2→ M3→ M4 CellR2: M2→ M3→ M1 R2: M2→ M1→ M4R3: M4→ M5→ M2→ M4 R3: M4→ M5→ M1 BR4: M1→ M4→ M3→ M5 R4: M5→ M4→ M2→ M1R5: M5→ M4→ M3→ M2→ M1 N2 R5: M3→ M4→ M1 N2 N1 NR6: M4→ M1→ M2→ M5 1 N3 R6: M4→ M3→ M1 N3 N5 N5 N4 N4 Dr. Jacob Rubinovitz
  32. 32. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Experimental Design – Product Mix Unbalanced mix Balanced mix P1=0.65 P1=P2=P3=0.333 Cell P2=0.25 A P3=0.10 P1=0.55 P1=P2=P3=P4=P5=P6= 0. 1666 Cell P2=0.20 B P3=0.10 P4=0.5 P5=0.5 P6=0.5 4 * 2 * 5 * 2 * 2 = 160 Dr. Jacob Rubinovitz
  33. 33. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : C(CB)=0, C(IB)={0} Dr. Jacob Rubinovitz
  34. 34. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : C(CB)=M, C(IB)={0} Dr. Jacob Rubinovitz
  35. 35. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : C(CB)=0, C(IB)={1} Dr. Jacob Rubinovitz
  36. 36. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : SDDAP performance for different buffer sizes Dr. Jacob Rubinovitz
  37. 37. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : SDDAP performance for different buffer sizes Dr. Jacob Rubinovitz
  38. 38. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : SDDAP performance for different buffer sizes. #Config Cell A Cell B 1 [87.8%,67.3%] [79.4%,69.7%] 2 [90.6%,82.3%] [92.4%,78.9%] 3 [92.4%,84.1%] [98.5%,80.9%] 4 [99.5%,92.2%] [98.7%,88.3%] 5 [96.2%,82.4%] [99.8%,81.8%] Dr. Jacob Rubinovitz
  39. 39. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Incorporating a Central Buffer Operation on a part completed: if the transfer is unfeasible or refused by the DAP, the part is moved to the central buffer CB, provided that there is some open space in it . The robot completed a delivery: the control system checks first all the parts currently in the CB. Priority is given to these parts in order to reduce the amount of average WIP in the CB. Dr. Jacob Rubinovitz
  40. 40. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Conclusions - Efficiency: The static policies are inefficient and generate low throughput rates in single capacity cells (SCCs(, even after incorporating a central buffer. For this system configuration, SDDAP is the most appropriate operating policy. The DAPs have similar performance for double capacity cells (DCCs( with no central buffer; Throughput is slightly higher with SDDAP. The use of SDDAP is recommended for a high routing intensity level. High throughput rate is achieved for manufacturing cells of | M| machines with attached input buffers of single capacity and a |M| capacity central buffer. The superiority in terms of throughput of a selective policy (such as SSDAP or SDDAP( over a standard one (like SDAP or DDAP( is, as expected, more apparent when the part mix is balanced. Dr. Jacob Rubinovitz
  41. 41. Graduate Seminar - Deadlock Avoidance in FMS, June 2002 Conclusions - Computational Complexity The computational complexity becomes higher in the following order of DAPs application: SDAP, SSDAP, DDAP, and SDDAP. SDDAP is computationally more intensive when applied respectively to Single, Double and Triple Capacity Cells. As a result, a static strategy may represent the best alternative for operating a system including machines with buffers of capacity two or more. Under such conditions, a static policy is not less efficient than a dynamic one, generates less WIP, and is computationally much less complex. Dr. Jacob Rubinovitz
  42. 42. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Potential Implementation: Cluster Tools NEXUS 600 Six-port cluster tool that will accommodate four process modules and dual load-locks and integrated wafer handler. NEXUS 600 NEXUS 800 Eight-port cluster tool that will accommodate six process modules and dual load-locks and integrated wafer handler. NEXUS 800 Dr. Jacob Rubinovitz
  43. 43. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Questions? Dr. Jacob Rubinovitz
  44. 44. Graduate Seminar - Deadlock Avoidance in FMS, June 2002Results : Part Selection Rules Dr. Jacob Rubinovitz
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