PROJECT DESCRIPTION by N6Tc7ce

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            IE 368: FACILITY DESIGN AND
             OPERATIONS MANAGEMENT

                                Lecture Notes #4

                        Production System Design
                                 Part #3


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                      Outline of this Module
                                               2


      Generalizations of queuing model
      Generalizations of utilization formula
      Multiple linked workstations
      Automated systems
      Batched arrivals and departures




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
           Queuing Model Generalizations
                                               3


  Workstations with multiple machines
    Assume machines are identical

                                              WS
                                                    1

                                                    2

               Jobs                                 3
                                               .
                                               .
                                               .
                                                    m




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT       WINTER 2012
     Queuing Model Generalizations                                          (cont.)
                                               4



                                 CVa2  CVe2  u 2 ( m 1) 1 
                          TIQ  
                                             
                                               m(1  u ) 
                                                                t e
                                      2                      

                         CVa2  CVe2  u 2 ( m 1) 1 
                  TIS  
                                                     
                                       m(1  u ) t e  t e  TIQ  t e
                              2                      

  m = number of machines
  Reduces to the prior TIQ/TIS formulas when m =1




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                              WINTER 2012
                            In-class Exercise
                                               5

  In the prior example where option 2 was selected, the demand has
   tripled. Jobs now arrive at 3*2.875 JPH = 8.625 JPH. Three option 2
   machines will be purchased.
  Compare the following two configurations with respect to average TIQ
   and WIP in queue. Assume CVa = 1 and the data for a single option 2
   machine is unchanged.

       Option 1 (Separate queues)                   Option 2 (Single queue)


                                      1                               1
                          1/3
              Jobs                                   Jobs
                          1/3         2                               2

                          1/3         3                               3




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                         WINTER 2012
                      In-class Exercise (cont.)
                                               6




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                      In-class Exercise (cont.)
                                               7




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                        Machines in Parallel
                                               8


  In the original example
    Arrival rate = 2.875 JPH (ta =.3478 hrs)
    CVa = 1
  With a single option 2 machine
    te = 1/3 hr
    CVe=1.0
    Average TIS = 8.03 hrs
  What happens if you increase te but also increase m
    so that utilization is constant (more machines in
    parallel are added?)

IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                  Machines in Parallel (cont.)
                                               9



                          Arrival rate=    2.875
                          te =             0.33
                          ta =          0.34782609


                  m            TIQ            te      TIS    Utilization
                   1           7.67          0.33     8.00    0.9583
                   2           7.52          0.67     8.19    0.9583
                   3           7.40          1.00     8.40    0.9583
                   4           7.30          1.33     8.63    0.9583
                   5           7.20          1.67     8.87    0.9583
                   6           7.12          2.00     9.12    0.9583
                   7           7.04          2.33     9.37    0.9583
                   8           6.97          2.67     9.64    0.9583
                   9           6.90          3.00     9.90    0.9583
                  10           6.84          3.33    10.17    0.9583


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                          WINTER 2012
                Summary Handout On Web
                                               10


  Word document with all formulas and most of the
    examples we covered so far




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                     Utilization Calculations
                                               11


  If each machine in the workstation always has work,
    utilization for a workstation is the ratio of:
     The average time between job departures (if each machine in
      the workstation always has work), and average time between
      job arrivals
     The average rate of job arrivals, and the average rate of job
      departures (if each machine in the workstation always has
      work)

                                  te
         u = Utilization =
                                 m * ta
           = The percent of time machines in a workstation are busy


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                 WINTER 2012
              Utilization Calculations (cont.)
                                               12


  A more general formula for utilization is:

                       Arrival rate of " work" to a WS
              u
                 Maximum processing rate of " work" by the WS

  In the prior formulas the unit of “work” is
    __________




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT               WINTER 2012
              Utilization Calculations (cont.)
                                               13

 1
     Arrival rate of jobs
 ta


 1
     Maximum processing rate of jobs by a single machine
 te


 m
     Maximum processing rate of jobs by a workstation with m identical machines
 te




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                      WINTER 2012
              Utilization Calculations (cont.)
                                               14

  Situation 1 – There are multiple non-identical machines at a
    WS, and a single job type



                                                    te1 = 12   min/job
           ta = 6   min/job

                                                    te2 = 10   min/job




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                        WINTER 2012
                 Utilization Calculations (cont.)
                                               15


  Situation 2 – There are two different job types
    and multiple identical machines at a WS


                                                    teA = 5 min. for both machines
           taA   = 6 min.
                                                    teB = 10 min. for both machines
           taB   = 12 min.




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                              WINTER 2012
              Utilization Calculations (cont.)
                                               16




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
              Utilization Calculations (cont.)
                                               17


  Situation 3 – Multiple job types and multiple non-
    identical machines.
     No simple way to calculate utilization – schedule dependent




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT            WINTER 2012
                      Multiple Workstations
                                               18


  Single workstations with single and multiple
   machines can be analyzed
  Extend methods to systems of workstations
  Attention will be restricted to workstations in series
   (production lines, Batch/group technology lines)
     Analysis of systems with more complicated flows is possible
      but much more involved.
     See Whitt (1983), Bell System Technical Journal, Vol. 62. No.
      9.




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT             WINTER 2012
               Multiple Workstations (cont.)
                                               19


  Linking workstations
    The output from workstation i is the input for workstation
     (i+1)
    In the prior formulas for the analysis of a single workstation,
     the CV of the interarrival times was needed (CVa)
    An estimate is needed for the CV of the interdeparture times
     from WS i = CV of the interarrival times to WS (i+1)




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT              WINTER 2012
               Multiple Workstations (cont.)
                                               20


  Interdeparture times from a workstation with a
    single machine

      Let CVd  Interdeparture time coefficient of variation for a
                 workstation.

      CVd2  u 2CVe2  (1  u 2 )CVa2




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT            WINTER 2012
                 Multiple Workstations (cont.)
                                               21


  Intuition of the formula

                                       WS
           CVa              WIP
                                                    CVd
                          Storage



            Let CVd  Interdeparture time coefficient of variation for a
                         workstation.


            CVd2  u 2CVe2  (1  u 2 )CVa2



IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                          WINTER 2012
               Multiple Workstations (cont.)
                                               22

  Interdeparture times from a workstation with
    multiple machines
           Let CVd  Interdeparture time coefficient of variation for a
                      workstation.

                                      u2
          CV  1  (1  u )(CV  1) 
              d
               2             2
                                    a
                                     2
                                         (CVe2  1)
                                       m
  Reduces to the prior formula when m=1
    No direct intuitive interpretation




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                         WINTER 2012
                                           Example
                                               23


  Objective –         Calculate the TIQ before each workstation
                                                      WS2
                               WS1                                  WS3
                TP = 3 JPH
                 CVa = 1.0
                             te = 15 min                          te = 18 min
                              CVe = 1.5             te = 38 min    CVe = 1.0
                                                     CVe = 2.0




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                               WINTER 2012
                               Example (cont.)
                                               24




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                               Example (cont.)
                                               25




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
   In-class Exercise – Estimate total TIQ and WIPQ at each WS
                        WS 1
                                         WS 2
                                                            WS 3
              -->               -->                -->                -->
                                                            26

           Interarrival Times          Process Time Samples (Minutes)
           (Minutes)            WS 1               WS 2               WS 3
    1         0.9                3.5               1.8                1.6
    2         3.2                3.6               5.7                3.9
    3         3.0                4.5               1.1                4.5
    4         2.5                3.9               3.9                0.3
    5         5.7                3.1               7.3                0.2
    6         0.2                3.2               21.8               2.6
    7         3.6                4.1               0.5                1.6
    8         1.5                3.8               17.5               12.5         WS2
    9         0.7                4.5               1.2                17.4
   10         0.7                4.9               8.2                5.5    WS1          WS3
   11         13.8               4.2               26.0               1.2
   12         4.0                4.3               4.5                1.8
   13         6.4                4.8               0.5                2.2
   14         4.8                3.3               9.5                1.0
   15         27.0               3.2               14.2               12.9
   16         0.3                4.1               5.8                6.8
   17         3.2                3.4               17.2               3.5
   18         4.1                4.8               1.4                0.3
   19         3.0                4.0               15.2               0.4
   20         0.7                4.0               11.1               3.3
   21         19.4               3.8               2.9                0.8
   22         4.2                3.2               11.0               0.5
   23         8.8                5.0               3.8                2.1
   24         11.2               3.3               2.7                7.8
   25         3.2                3.2               24.7               0.8
  Avg.        5.4               3.9                8.8                3.8
 StdDev.      6.4               0.6                7.8                4.5

IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                                        WINTER 2012
   In-class Exercise – Estimate total TIQ and WIPQ at each WS
                                               27




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT      WINTER 2012
   In-class Exercise – Estimate total TIQ and WIPQ at each WS
                                               28




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT      WINTER 2012
                        Automated Systems
                                               29


  We have assumed that we can observe/collect data
   on interarrivals, effective process times, and then
   estimate ta, CVa, te, CVe
  If the machines at a workstation are automated with
   relatively infrequent failures, collecting effective
   process time data may not be practical or data on
   machine reliability may be collected (MTBF, MTTR)




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                  Automated Systems                 (cont.)
                                               30


  Assume you have data on
    C = actual process time (move + process time)
    MTBF = Mean time between failures
    MTTR = Mean time to repair
  How can you apply prior queuing formulas?
    Approach – find te and CVe from the prior data




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT             WINTER 2012
                  Automated Systems                       (cont.)
                                               31
            ( MTBF  MTTR)
 te  c *
                MTBF
 Let Te  Effective process time random variable ( E[Te ]  te ).

           2 * MTTR2 * c
Var(Te ) 
               MTBF
                                                      2
         2 * MTTR2 * c       MTBF          
  CVe                 ( MTBF  MTTR) * c 
                      *                    
             MTBF                          

                2 * MTTR2 * MTBF
            
              ( MTBF  MTTR) 2 * c


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                   WINTER 2012
                                       Example
                                                     32

  Calculate TIQ for the automated system shown below
                                                   WS1
                                  ta = 1.7 min
                                   CVa = 1.0
                                                   C = 1 min
                                                 MTBF = 50 min
                                                 MTTR = 30 min




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                WINTER 2012
                            In-class Exercise
                                                  33

  An automated machine has an MTBF = 50 min, MTTR = 50 min, and c=
    1 min.
     Plot te as a function of reduced MTTR (0,10,20,30,40). Do the
      same for increased MTBF (0,10,20,30,40)
     Repeat similar plots for CVe
     What conclusions can you make?
                                           MTTR                     MTBF
           Reduction/
            Increase
              (min)      MTTR         te          CVe   MTBF   te          CVe
                0         50                             50
                10        40                             60
                20        30                             70
                30        20                             80
                40        10                             90

IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                                WINTER 2012
                                In-class Exercise – te Plot
                                                               34


                                   te vs. Reduction (increase) in MTTR and MTBF

                      2.5


                      2.0


                      1.5
           te (min)




                      1.0


                      0.5


                      0.0
                            0          10                 20              30   40
                                            Reduction (increase) in minutes




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                                   WINTER 2012
                     In-class Exercise – CVe Plot
                                                    35


                         CVe vs. Reduction (increase) in MTTR and MTBF

                 6


                 5


                 4
           CVe




                 3


                 2


                 1


                 0
                     0      10                20               30   40
                                 Reduction (increase) in minutes




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                        WINTER 2012
                               MTTR vs. MTBF
                                               36
            ( MTBF  MTTR)
 te  c *
                MTBF
 Let Te  Effective process time random variable ( E[Te ]  te ).

           2 * MTTR2 * c
Var(Te ) 
               MTBF
                                                      2
         2 * MTTR * c     2
                             MTBF          
  CVe                ( MTBF  MTTR) * c 
                     *                    
             MTBF                         

                2 * MTTR2 * MTBF
            
              ( MTBF  MTTR) 2 * c


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                   WINTER 2012
          Batched Arrivals and Departures
                                               37


  Output is sometimes batched for delivery
  Batching is often done due to practical packaging or
    material handling reasons
     Large sheet metal parts (e.g., car doors) are stored in racks for
      part protection
     There may be 20 doors held in each rack
  From a        flow perspective (rate, variability of job flow),
    what does batching do?




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT              WINTER 2012
      Batch Arrivals and Departures (cont.)
                                               38


  Intuition – Rental car example
    Arriving to rent a car
    Returning to the terminal




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                                      Example
                                               39


  Batches of 16 jobs arrive to a workstation every 8
    hours
     The flow of batches has no variability
     What about the flow of parts?




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                               Example (cont.)
                                               40




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
                            In-class Exercise
                                               41


  Batches of 20 jobs arrive every 20 minutes to a
    workstation with a single machine
     te = 0.9 min, CVe = 1.0
  Estimate TIQ and WIPQ for a job




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT    WINTER 2012
                      In-class Exercise (cont.)
                                               42




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
  Production Systems with Limited WIP Space
                                               43


  Production systems with limited WIP space occur
    (are common)
     Production lines - Automated




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
 Prod. Systems with Limited WIP Space (cont.)
                                               44


  Kanban system
    Inventory between workstations is limited by using production
     authorization cards or kanbans
  Limited WIP space can cause delays (due to
    downtimes, variability, etc.) to propagate to other
    workstations
     This reduces the capacity or throughput of the system




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT             WINTER 2012
 Prod. Systems with Limited WIP Space (cont.)
                                               45


  The WIP space is a buffer between the workstations
    It reduces the impact of variability and downtimes
  What allows a system to run with high throughput
    and no buffer/WIP space?




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
 Prod. Systems with Limited WIP Space (cont.)
                                               46


  Finite WIP space reduces throughput by allowing
    workstations to block each other
     Blocking
        • The workstation is able to work but is prevented by the job just
          finished since there is no WIP space
     Starving
        • The workstation is able to work but is prevented by the lack of
          jobs
  For systems of this type more extensive evaluation is
    needed
     More than queuing or equipment fraction calculations


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                    WINTER 2012
             Just-In-Time Production Systems
                                               47

  Just-In-Time or JIT is a catch all term that encompasses a
   manufacturing/production philosophy of continuous small
   improvements and variability reduction
  Japanese in origin, many US companies have adopted parts
   or all of the techniques employed in JIT
  US companies have coined their own names for the
   fundamental JIT production/operation methods




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT       WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               48


  Examples
     Lean production/manufacturing – many companies
      • Recent focus may have extended and changed
          Lean
     Synchronous Mfg. – GM
     Materials As Needed – Harley Davidson
     Continuous Flow Mfg. - IBM




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               49


  JIT focuses on controlling certain aspects of the
   production environment
  We will examine a few of these
    Production scheduling
    Setups
    Cross-training
    Kanban system




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
        Just-In-Time Production Systems (cont.)
                                               50

  Production scheduling
    Objective is production smoothing
  Example of how to smooth aggregate production
    requirements
       Monthly production = 10,000 Units
       Daily production (@20 days/month) = 500 units
       Shift production (2 shifts) = 250 units
       Hourly production = 31.25 units
       Production time = 1.92 minutes per unit




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT       WINTER 2012
        Just-In-Time Production Systems (cont.)
                                               51

  Once the aggregate requirements of the MPS have been
   translated to daily rates, we must translate the product-
   specific requirements to a production sequence
  Example
     If three products A, B, C are produced and no setup is required
      between products, try to produce the same amount of each in the
      same sequence
     e.g., vehicle assembly (sedans, coupes, hatchbacks)




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               52

  What is production smoothing doing that is explainable with
    the queuing models studied?




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT      WINTER 2012
          Just-In-Time Production Systems (cont.)
                                               53


  Setups
    Suppose multiple products are produced on a workstation and
     that a setup is required whenever a different product is
     produced.
          • Changing dies in sheet metal stamping
          • Changing molds in an injection molding machine
  Consider the output side of the workstation and plot
    times when jobs are completed

      X    X   X   X   X   X           X   X   X    X   X   X   Time




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT               WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               54


  What is a setup doing to the effective process times?




  JIT has focused on setup reduction
    Conduct as much staging as possible
        • Execute all activities related to setup that may be done
          concurrently with production
     Develop methods (tools, jigs, testing fixtures, etc.) for faster
      adjustments to get the workstation running as quickly as
      possible


IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT                    WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               55


  Cross-Training
     Train the work force to be multi-skilled
     What does this accomplish?




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               56


  Kanban system
    Kanban means card
    Inventory and production control system between workstations
    The number of kanbans used is a function of
        •   Demand
        •   Container size
        •   Variability, and
        •   Desired time-in-system




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT         WINTER 2012
                              Kanban System
                                               57




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT   WINTER 2012
       Just-In-Time Production Systems (cont.)
                                               58


  Kanbans reduce throughput if utilized incorrectly
    High system variability – Use many kanbans
    As variability is reduced lower the number of kanbans
    Reduced variability allows low inventory (low # of kanbans)
    Low inventory/WIP forced on a system results in poor
     performance
    Low inventory is a result not a cause




IE 368. FACILITY DESIGN AND OPERATIONS MANAGEMENT           WINTER 2012

								
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