The Effects of Process Variability 35E00100 Service Operations and Strategy #3 Fall 2015

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 2 Topics on Variability  Variability basics Measure of variability Process variability Flow variability Key points  The corrupting influence of variability Factory physics “laws” Batching Serial system Parallel system Transfer batching Ways to improve operations Key points  Useful material: Hopp, W. & Spearman, M. (2000), Factory Physics, Chapters 8, 9 and 15.3

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 3 Basics - The Concept of Variability  Variability Any departure from uniformity (regular, predictable behavior) Sources and causes Compared to randomness?  Use of intuition  Measuring variability Coefficient of variation (CV) Classification based on the values of CV:  Natural process times have generally low variability (LV)  Effective process times can be LV, MV, or HV 0.75 High variability (HV) Moderate variability (MV)Low variability (LV) cece Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 4 Measuring Variability Illustrative example What is the variability of each machine?

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 5 Natural Variability  Variability without explicitly analyzed cause(s)  Sources in process Operator pace Material fluctuations Product type (if not explicitly considered) Product quality  Observation Natural process variability is usually in the low variability category Hopp and Spearman 2000, 255

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 6 Hopp and Spearman 2000, 256 Mean Effects of Breakdowns  Definitions  Availability A is the fraction of time machine is up:  Effective process time t e and rate r e can be calculated as follows:

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 7 Which machine is better?  Two machines, Tortoise 2000 and Hare X19, are subject to the same average workload: 69 jobs per day operate 24 hours per day  jobs per hour have unpredictable breakdowns  Tortoise 2000 has long, infrequent breakdowns  Hare X19 has short, more frequent breakdowns  How would you compare? Example 1

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 8 Calculating Machine Availability Tortoise 2000 t 0 = 15 min  0 = 3.35 min c 0 2 =  0 2 /t 0 2 = 3.352/152 = 0.05 m f = 12.4 hrs (744 min) m r = hrs (248 min) c r = 1.0 Availability of the machine Hare X19 t 0 = 15 min  0 = 3.35 min c 0 2 =  0 2 /t 0 2 = /15 2 = 0.05 m f = 1.9 hrs (114 min) m r = hrs (38 min) c r = 1.0  Availability of the machine Hopp and Spearman 2000, 256 Example 1 No difference between the machines in terms of availability.

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 9  Assumptions Times between failures are exponentially distributed Time to repair follows some probability distribution  Effective variability  Conclusions Failures inflate mean, variance, and CV of effective process time Mean t e increases proportionally with 1/A For constant availability A, long infrequent breakdowns increase SCV more than short frequent ones Variability Effects of Downtime Variability depends on repair times in addition to availability Hopp and Spearman 2000, 257

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 10 Estimating Variability Tortoise 2000 Hare X19  High variability  Moderate variability Example 1

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 11 Mean and Variability Effects of Setups  Analysis  Observations Setups increase the mean and variance of processing times Variability reduction is one benefit of flexible machines Interaction is complex Hopp and Spearman 2000, 259

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 12 Mean Effects of Setups  Two machines Fast, inflexible machine: 2 hour setup every 10 jobs Slower, flexible machine: no setups Hopp and Spearman 2000, 260 Example 2 In traditional analysis there is no difference between the machines.

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 13 Slower, flexible machine no setups Variability Effects of Setups Flexibility can reduce variability. Fast, inflexible machine 2 hour setup every 10 job Example 2

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 14 Example 2 Variability Effects of Setups Third Machine  New machine Otherwise same than the fast machine but more frequent setups  Analysis  Conclusion Shorter, more frequent setups induce less variability Hopp and Spearman 2000, 260

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 15 Inflators of Process Variability  Sources e.g. Operator unavailability Batching Material unavailability Recycle  Effects of process variability Inflate the mean processing time t e Inflate the CV of t e  Effective process variability can be LV, MV, or HV

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 16 Flow Variability t Low variability arrivals t High variability arrivals

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 17 Propagation of Variability i Departure variance depends on arrival variance and process variance re(i)re(i) ra(i)ra(i) Hopp and Spearman 2000, 262 r d (i) = r a (i+1) c d 2 (i) = c a 2 (i+1) ce2(i)ce2(i) ca2(i)ca2(i) i+1 r e (i+1) c e 2 (i+1) where station utilization u is given by u = r a t e  Departure SCV in single machine station  Departure SCV in multi-machine station

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 18 Propagation of Variability Low Utilization Stations High process Var Low flow Var High process Var High flow Var Low process Var Low flow Var Low process Var High flow Var

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 19 Propagation of Variability High Utilization Stations High process Var Low flow VarHigh flow Var High process Var High flow Var Low process Var Low flow Var Low process Var High flow VarLow flow Var

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 20 Variability Pooling  Basic idea CV of a sum of independent random variables decreases with the number of random variables  Time to process a batch of parts Hopp and Spearman 2000, 280

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 21 Key Points  Variability Cannot be eliminated Causes congestion Propagates Interacts with utilization  Components of process variability Failures, setups and many others deflate capacity and inflate variability Long infrequent disruptions are worse than short frequent ones  Measure of variability: coefficient of variation (CV)  Pooled variability is less destructive than individual variability

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 22

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 23 Notation  c a 2 = SCV of the inter-arrival time  c e 2 = SCV of the effective process time  c r 2 = SCV of the repair times  c 0 2 = SCV of the base process time  m f = mean time to failure  m r = mean time to repair  n = number of jobs or parts in a batch  N s = number of jobs or parts between setups  r a = arrival rate  r e = service rate  r d = departure rate  r 0 = base capacity rate  t a = inter-arrival time  t e  = process time  t s  = setup time  t 0 = base process time

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 24 Abbreviations Used  CV= coefficient of variation  HV= high variability  LV= low variability  MTTF= mean time to failure  MTTR= mean time to repair  MV= moderate variability  SCV= squared coefficient of variation

The Corrupting Influence of Variability

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 26 Factory Physics “Laws”  Law 1: Variability Law Increasing variability degrades the performance of a production system.  Law 2: Variability Buffering Law Systems w/ variability must be buffered by some combination of inventory, capacity and time.  Law 3: Product Flows Law In a stable system, over the long run, the rate out of a system will equal to the rate in, less any yield loss, plus any parts production within the system.  Law 4: Capacity Law In steady state, all plants will release work at an average rate that is strictly less than the average capacity.  Law 5: Utilization Law If a station increases utilization without making any other changes, average WIP and cycle time will increase in a highly nonlinear fashion.  Law 6: Process Batching Law In stations with batch operations or significant changeover times minimum process batch size yielding a stable system may be over 1, cycle time at the station will be minimized for some process batch size (may be greater than one), and as process batch size becomes large, average cycle time grows proportionally with batch size.  Law 7: Move Batching Law Cycle times over a segment of a routing are roughly proportional to transfer batch sizes used over that segment, provided there is no waiting for the conveyance device.  Law 8: Assembly Operations Law The performance of an assembly station is degraded by increasing any of the following: the number of components being assembled, variability of component arrivals, or lack of coordination between component arrivals. Hopp and Spearman 2000

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 27 Variability Law Increasing variability degrades the performance of a production system.   For example: Higher demand variability requires more safety stock for same level of customer service. Higher cycle time variability requires longer lead time quotes to attain the same level of on-time delivery. ”Law 1” Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 28 Variability Buffering Law Systems with variability must be buffered by some combination of inventory, capacity, and time. Is variability always harmful? ”Law 2” Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 29 Variability Buffering Law Systems with variability must be buffered by some combination of inventory, capacity, and time. ”Law 2” Inventory Capacity Time Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 30 Material Flow Laws  Product flows In a stable system, over the long run, the rate out of a system will equal to the rate in, less any yield loss, plus any parts production within the system.  Capacity In steady state, all plants will release work at an average rate that is strictly less than the average capacity.  Utilization If a station increases utilization without making any other changes, average WIP and cycle time will increase in a highly nonlinear fashion. ”Laws 3-5” Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 31 Cycle Time versus Utilization

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 32 Process Batching Law  In stations with batch operations or significant changeover times The minimum process batch size that yields a stable system may be greater than one. Cycle time at the station will be minimized for some process batch size, which may be greater than one. As process batch size becomes large, average cycle time grows proportionally with batch size. ”Law 6” Hopp and Spearman 2000, 306

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 33 Recap: Forms of Batching  Serial batching Processes with sequence-dependent setups Batch size is the number of jobs between setups Reduces loss of capacity from setups  Parallel batching True batch operations Batch size is the number of jobs run together Increases the effective rate of process  Transfer batching Batch size is the number of parts that accumulate before being transferred to the next station (not necessarily equal to the process batch  lot splitting) Less material handling

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 34 Process Batch Versus Move Batch Case “Batch Size in a Dedicated Assembly Line”  Process batch Depends on the length of setup. The longer the setup, the larger the lot size required for the same capacity.  Move (transfer) batch: Why should it equal process batch? The smaller the move batch, the shorter the cycle time. The smaller the move batch, the more material handling.  Lot splitting: Move batch can be different from process batch. 1. Establish smallest economical move batch. 2. Group batches of like families together at bottleneck to avoid setups. 3. Implement using a “backlog”.

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 35 Batching and Process Performance  Impact of batching Flow variability Waiting inventory  Impact of lot splitting

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 36 Serial Batching  Parameters  Effective process time  Arrival of batches  Utilization  For stability (u < 1) t tsts racaraca Queue of batches Setup k Forming batch Minimum batch size required for stability of system Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 37 Serial Batching  Average queue time at station  Average cycle time depends on move batch size Move batch = process batch Move batch = 1 Splitting move batches reduces wait-in-batch time Arrival CV of batches is assumed c a regardless of batch size. Hopp and Spearman 2000,

Effect of Batch Size on Average Total CT An analysis of a Series System 38

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 39 Cycle Time versus Batch Size Optimum batch size

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 40 Optimal Serial Process Batch Sizes One Product  Assumptions Identical product families in terms of process and setup times Poisson arrivals  Effective process time  Utilization  Good approximation of the serial batch size minimizing cycle time at a station is given by CT is minimized through finding the optimal station utilization. Good approximation: Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 41 Optimal Serial Process Batch Sizes Multiple Products  Assumptions Multiple products Poisson arrivals  Eff. process time  Utilization  Good approximation of the serial batch size minimizing cycle time at a station is given by Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 42 Parallel Batching  Parameters  Wait-to-batch time  Time to process a batch  Arrival rate of batches  Utilization t0t0 k Queue of batches Forming batch racaraca Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 43 Parallel Batching  Minimum batch size required for system stability (u<1)  Average queue + process time at station = CT q + t  Total cycle time Batch size affects both WTBT and CT q.

Effect of Batch Size on Average Total CT Analysis of a Parallel System 44

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 45 Cycle Time versus Batch Size Parallel System Queue time due to too high utilization Wait for batch time B Optimum Batch Size

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 46 Move Batching Law  Cycle times over a segment of a routing are roughly proportional to transfer batch sizes used over that segment, provided there is no waiting for the conveyance device.  Insights Queuing for conveyance device can offset cycle time reduction from reduced move batch size. Move batching intimately related to material handling and layout decisions. ”Law 7” Hopp and Spearman 2000, 312

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 47 Effects of Transfer Batching  Two machines in series Machine 1  Receives individual parts at rate r a with CV of c a (1)  Mean process time of t e (1) for one part with CV of c e (1)  Puts out batches of size k Machine 2  Receives batches of k  Mean process time of t e (2) for one part with CV of c e (2)  Puts out individual parts How does cycle time depend on the batch size k? single job batch Machine 1Machine 2 k r a c a (1) t e (1) c e (1) t e (2) c e (2) Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 48 Average time forming the batch: Average time after batching: Average total time spent at the 1 st station: Time between output of individual parts into the batch: t a Time between output of batches of size k: kt a Variance of inter-output times of parts is c d 2 (1)t a 2, where Variance of batches of size k: Transfer Batching – Machine 1 1 st part waits (k-1)(1/r a ), last part does not wait. By definition CV c d 2 (1)=  d 2 /t a 2 Departures are independent  variances add Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 49 Transfer Batching - Machine 2 SCV of batch arrivals: Time to process a batch of size k: Variance of time to process a batch of size k: SCV for a batch of size k: Mean time spent in partial batch of size k: Average time spent at the 2 nd station: 1 st part doesn’t wait, last part waits (k-1)t e (2) Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 50 Transfer Batching – Total System Hopp and Spearman 2000, Inflation factor due to transfer batching

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 51 Assembly Operations Law  The performance of an assembly station is degraded by increasing any of the following The number of components being assembled Variability of component arrivals Lack of coordination between component arrivals ”Law 8” Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 52 Ways to Improve Operations 1.Increase throughput 2.Reduce queue time 3.Reduce batching delay 4.Reduce matching delay 5.Improve customer service Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics Increase Throughput Throughput = P(bottleneck is busy)  bottleneck rate CT q = VUT Reduce variability Reduce utilization Increase capacity Add equipment Increase operating time Increase reliability Reduce yield loss Quality improvements Reduce blocking/starving Buffer with inventory (near bottleneck) Reduce system “desire to queue” Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics Reduce Queue Delay Reduce variability Process variability -Repair times, setups Arrival variability -Decrease process variability in upstream -Pull system -Eliminate batch releases Reduce utilization Increase bottleneck rate -Decrease time to repair -Cross-training Reduce flow into bottleneck -Improve yield -Reduce rework, etc Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics Reduce Batching Delay CT batch = delay at stations + delay between stations Reduce process batching Optimize batch sizes Reduce setups -Stations where capacity is expensive -Capacity versus WIP tradeoff Reduce move batching Move more frequently Layout to support material handling -E.g. cell manufacturing Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics Reduce Matching Delay CT match = delay due to lack of synchronization Reduce variability Improve coordination Scheduling Pull mechanisms Modular designs Reduce number of components E.g. product redesign Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics Improve Customer Service  LT = CT + z  CT Reduce CT variability (Generally same methods as for CT reduction) Improve reliability Improve maintainability Reduce labor variability Improve quality Improve scheduling, etc. Reduce avg CT Queue time Batch time Match time Reduce quoted LT Assembly to order Stock components Delayed differentiation Safety lead time Hopp and Spearman 2000,

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 58 Variability Influences Cycle Times and Lead Times CT = 10  CT = 3 CT = 10  CT = 6

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 59 Key Points  Factory physics laws!  Variability Decreases performance Buffering through inventory, capacity, and time Interacts with utilization  Congestion effects multiply  Nonlinear effects of utilization on cycle time  Batching In serial and parallel batching minimum feasible batch size may be greater than one Cycle time increases proportionally with batch size  Without wait-for-batch time, cycle time decreases in batch size  Lot splitting can reduce the effects of batching Batching delay is essentially separate from a variability delay.

35E00100 Service Operations and Strategy #3Aalto/BIZ Logistics 60 Notation  c e 2 = SCV of the effective process time (parts and setups)  c d 2 = SCV of the departure times  CT= cycle time  D/d = demand  k = serial batch size  LT= lead time quoted to customer  n = number of products (i=index for products, i=1,…,n)  N s = number of jobs or parts between setups  r a = arrival rate  r b = bottleneck rate  r e = service rate  r d = departure rate  t s  = setup time  t 0 = time to process a part  u 0 = utilization without setups  WTBT= wait to batch time  WIBT= wait in batch time