\f3nd Lecture What's cause production performance go south? VARIABILITY ASSESSMENT & ITS IMPACT 1 Books for this class 2 From previous lecture We learn about a method to evaluate the production system performance called \"Internal benchmarking\" If TH(system) < TH(pwc) Bad If CT(system) > CT(pwc) Bad But it is better to plot Graphs to see how bad? 3 Best Case Performance W0 rbT0 Minimum WIP level that provides maximum production rate at minimum flow time Best Case Law: The minimum cycle time (CTbest) for a given WIP level, w, is given by CTbest if w W0 T0 , w / rb , otherwise. And the maximum throughput (THbest) for a given WIP level, w is given by, w / T0 , if w W0 THbest rb , otherwise 4 Worst Case Performance Worst Case Law: The worst case cycle time for a given WIP level, w, is given by, CTworst = w T0 The worst case throughput for a given WIP level, w, is given by, THworst = 1 / T0 Practical Worst Case Performance Practical Worst Case Definition: The practical worst case (PWC) cycle time for a given WIP level, w, is given by, CTPWC w 1 T0 rb The PWC throughput for a given WIP level, w, is given by, TH PWC w rb , W0 w 1 where W0 is the critical WIP. HAL Internal Benchmarking Outcome Throughput (panels/hour) 120.0 \"Lean" Region 100.0 Current TH = 71.8 W IP = 47,600 80.0 60.0 \"Fat" Region 40.0 20.0 0.0 0 10,000 20,000 30,000 40,000 50,000 W IP Best Worst PWC Example: An Order Entry System Six distinct steps Capacities and processing times are given Capacity need not be the inverse of its average process time. An Order Entry System Which step is the bottleneck? Engineering Design What is the bottleneck rate (r0)? 2 orders per hour What is the raw processing time (T0)? The sum of the process times or 10.73 hrs. What is critical WIP (W0)? W0 = r0 x T0 = 2 x 10.73 = 21.46 jobs Variability Makes a Difference! Little's Law: TH = WIP/CT, so same throughput can be obtained with large WIP, long CT or small WIP, short CT. The difference? Variability! Penny Fab One: achieves full TH (0.5 j/hr) at WIP=W0=4 jobs if it behaves like Best Case, but requires WIP=27 jobs to achieve 95% of capacity if it behaves like the Practical Worst Case. Why? Variability! Tortise and Hare Example Two machines: subject to same workload: 69 jobs/day (2.875 jobs/hr) subject to unpredictable outages (availability = 75%) Hare X19: long, but infrequent outages Tortoise 2000: short, but more frequent outages Performance: Hare X19 is substantially worse on all measures than Tortoise 2000. Why? Variability! Variability Views Variability: Any departure from uniformity Random versus controllable variation Randomness: Essential reality? Artifact of incomplete knowledge? Management implications: robustness is key Probabilistic Intuition Uses of Intuition: driving a car throwing a ball mastering the stock market First Moment Effects: g Throughput increases with machine speed Throughput increases with availability Inventory increases with lot size Our intuition is good for first moments Probabilistic Intuition (cont.) Second Moment Effects: Which is more variable - processing times of parts or batches? Which are more disruptive - long, infrequent failures or short frequent ones? Our intuition is less secure for second moments Misinterpretation - e.g., regression to the mean Variability Definition: Variability is anything that causes the system to depart from regular, predictable behavior. Sources of Variability: setups machine failures materials shortages yield loss rework operator unavailability workspace variation differential skill levels engineering change orders customer orders product differentiation material handling Measuring Process Variability te mean process time of a job e standard deviation of process time ce e te coefficient of variation, CV Note: we often use the \"squared coefficient of variation\" (SCV), ce2 Variability Classes in Factory Physics Low variability Moderate variability High variability (LV) (MV) (HV) 0 0.75 1.33 ce Effective Process Times: Actual process times are generally LV Effective process times include setups, failure outages, etc. HV, LV, and MV are all possible in effective process times Relation to Performance Cases: For balanced systems MV - Practical Worst Case LV - between Best Case and Practical Worst Case HV - between Practical Worst Case and Worst Case Measuring Process Variability - Example Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 te se ce Class Machine 1 22 25 23 26 24 28 21 30 24 28 27 25 24 23 22 25.1 2.5 0.1 LV Machine 2 5 6 5 35 7 45 6 6 5 4 7 50 6 6 5 13.2 15.9 1.2 MV Machine 3 5 6 5 35 7 45 6 6 5 4 7 500 6 6 5 43.2 127.0 2.9 HV LV vs MV Avg processing time = 20 mins CV = 0.32 Avg processing time = 20 mins CV = 0.75 19 LV vs HV Avg processing time = 20 mins CV = 2.5 20 Natural Variability Definition: Sources: variability without explicitly analyzed cause operator pace material fluctuations product type (if not explicitly considered) product quality Observation: LV category. natural process variability is usually in the Down Time - Mean Effects Definitions: t 0 base process time c 0 base process time coefficien t of variabili ty r0 1 base capacity (rate, e.g., parts/hr) t0 m f mean time to failure m r mean time to repair c r coefficent of variabili ty of repair tim es ( r / m r ) Down Time - Mean Effects (cont.) Availability: Fraction of time machine is up A mf m f mr Effective Processing Time and Rate: re Ar0 te t0 / A Totoise and Hare - Availability Hare X19: Tortoise: t0 = 15 min t0 = 15 min 0 = 3.35 min c0 = 0 /t0 = 3.35/15 = 0.05 mf = 12.4 hrs (744 min) mr = 4.133 hrs (248 min) cr = 1.0 0 = 3.35 min c0 = 0 /t0 = 3.35/15 = 0.05 mf = 1.9 hrs (114 min) mr = 0.633 hrs (38 min) cr = 1.0 Availability: mf A =mf mr 744 0.75 744 248 mf A= m f mr 114 0.75 114 38 No difference between machines in terms of availability. Down Time - Variability Effects Effective Variability: te t0 / A 2 2 2 ( m r )(1 A)t 0 e2 0 r Amr A Conclusions: c 2 e e2 te2 c02 (1 cr2 ) A(1 A) Variability depends on repair times in addition to availability mr t0 Failures inflate mean, variance, and CV of effective process time Mean (te) increases proportionally with 1/A SCV (ce2) increases proportionally with mr SCV (ce2) increases proportionally in cr2 For constant availability (A), long infrequent outages increase SCV more than short frequent ones Tortoise and Hare - Variability Tortoise 2000 Hare X19: t e = ce2 t0 15 20 min A 0.75 2 2 = c 0 (1 c r ) A(1 A) te mr t0 t0 15 20 min = A 0.75 ce2 = c 02 (1 c r2 ) A(1 A) 248 0.05 (1 1)0.75(1 0.75) 15 6.25 high variability mr t0 0.05 (1 1)0.75(1 0.75) 38 15 1.0 moderate variability Hare X19 is much more variable than Tortoise 2000! Setups - Mean and Variability Effects Analysis: N s average no. jobs between setups t s average setup duration s std. dev. of setup time s cs ts ts te t0 Ns s2 Ns 1 2 ts 2 Ns Ns 2 e ce2 2 0 e2 te2 Setups - Mean and Variability Effects (cont.) Observations: Setups increase mean and variance of processing times. Variability reduction is one benefit of flexible machines. However, the interaction is complex. Setup - Example Data: Fast, inflexible machine - 2 hr setup every 10 jobs t 1 hr 0 N s 10 jobs/setup t s 2 hrs te t0 t s / N s 1 2 / 10 1.2 hrs re 1 / te 1 /(1 2 / 10) 0.8333 jobs/hr Slower, flexible machine - no setups t0 1.2 hrs re 1 / t0 1 / 1.2 0.833 jobs/hr Traditional Analysis? No difference! Setup - Example (cont.) Factory Physics Approach: Compare mean and variance Fast, inflexible machine - 2 hr setup every 10 jobs t 0 1 hr c 02 0 . 0625 N s 10 jobs/setup t s 2 hrs c s2 0 . 0625 t e t 0 t s / N s 1 2 / 10 1 . 2 hrs re 1 / t e 1 /( 1 2 / 10 ) 0 . 8333 jobs/hr c s2 Ns 1 0 . 4475 t 2 Ns Ns c e2 0 . 31 2 e 2 0 2 s Setup - Example (cont.) Slower, flexible machine - no setups t0 1.2 hrs c02 0.25 re 1 / t0 1 / 1.2 0.833 jobs/hr ce2 c02 0.25 Conclusion: Flexibility can reduce variability. Setup - Example (cont.) New Machine: Consider a third machine same as previous machine with setups, but with shorter, more frequent setups N s 5 jobs/setup t s 1 hr Analysis: re 1 / te 1 /(1 1 / 5) 0.833 jobs/hr 2 c Ns 1 2 2 2 s 0.2350 e 0 t s 2 Ns Ns ce2 0.16 Conclusion: Shorter, more frequent setups induce less variability. Other Process Variability Inflators Sources: operator unavailability recycle batching material unavailability et cetera, et cetera, et cetera Effects: inflate te inflate ce Consequences: Effective process variability can be LV, MV,or HV. Illustrating Flow Variability Low variability arrivals t smooth! High variability arrivals t bursty! Measuring Flow Variability t a mean time between arrivals 1 ra arrival rate ta a standard deviation of time between arrivals ca a ta coefficient of variation of interarrival times Propagation of Variability ca2(i) ce2(i) i cd2(i) = ca2(i+1) i+1 Single Machine Station: cd2 u 2 ce2 (1 u 2 )ca2 where u is the station utilization given by u = rate Multi-Machine Station: departure var depends on arrival var and process var 2 u (ce2 1) cd2 1 (1 u 2 )(ca2 1) m where m is the number of (identical) machines and u ra te m Propagation of Variability - High Utilization Station LV HV HV HV HV HV LV LV LV HV LV LV Conclusion: flow variability out of a high utilization station is determined primarily by process variability at that station. Propagation of Variability - Low Utilization Station LV HV LV HV HV HV LV LV LV HV LV HV Conclusion: flow variability out of a low utilization station is determined primarily by flow variability into that station. Variability Interactions Importance of Queueing: Manufacturing plants are queueing networks Queueing and waiting time comprise majority of cycle time System Characteristics: Arrival process Service process Number of servers Maximum queue size (blocking) Service discipline (FCFS, LCFS, EDD, SPT, etc.) Balking Routing Many more Queueing Theory Definition: \"The study of waiting line phenomena\" Trivia: \"Queueing\" - the only word in the English language we know with 5 consecutive vowels! Kendall's Classification A/B/C A: arrival process B: service process C: number of machines B A Queue M: exponential (Markovian) distribution G: completely general distribution D: constant (deterministic) distribution. Server C Entities queue up behind processes, so cycle time = waiting time + process time How Arrival and Process Variability Lead to Queueing Arrivals Sources of Variability customer decisions scheduling transportation delays quality problems upstream processing Queue Process Sources of Variability entity variety operator speed failures setups quality problems Lack of Coordination Between Arrivals and Processing Due to Variability Causes Queueing Principle (Queueing) At a single station with no limit on the number of entities that can queue up, the waiting time (WT) due to queuing is given by: WT = V U T V = a variability factor U = a utilization factor T = average effective process time for an entity at the station The G/G/1 Queue Formula: CTq V U t ca2 ce2 2 u 1 u t e Observations: Useful model of single machine workstations Separate terms for variability, utilization, process time. CTq (and other measures) increase with ca2 and ce2 Flow variability, process variability, or both can combine to inflate queue time. Variability causes congestion! \"V\" An increasing function of both the CV of interarrival times and the CV of effective process times. \"U\" An increasing factor of utilization which grows to infinity as utilization approaches 100%. VUT Equation CT = WT + T = VUT + T Variability and utilization interact. Variability hits high utilization stations the hardest. To Reduce Queues... 1. Lower utilization 2. Reduce variability The Utilization Factor - \"U\" Proportional to: 1/(1-u) Where u is the station utilization Variability Factor - \"V\" 24 Depends on arrival and 22 20 process Waiting Time (hrs) variability. Proportional to the squared coefficient of variations of both interarrival and process times. 18 16 14 12 10 High Variability (V=2) 8 6 Low Variability (V=0.5) 4 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Utilization Impact of Utilization on Station Delay Intermediate Conclusions Reductions in utilization tend to have a much greater impact on waiting time than do reductions in variability. However, since capacity is usually costly, high utilization is desirable. Variability reduction is often the key to achieving high efficiency operations systems. Limits on Capacity The first fundamental principle of capacity: Principle (Capacity): The output of a system cannot equal or exceed its capacity. \"We are running at 120% of capacity!\" What does it mean? One shift, no overtime Normal staffing levels A historical average How about, \"We are at 100% of capacity\"? Also impossible due to variability. An Example What happens when we release materials to our hypothetical system at 100% of capacity? 700 600 500 WIP 400 300 200 100 0 0 5 10 15 20 25 Day 30 35 40 45 Actual Capacity 120 120 100 100 80 80 WIP WIP How about releasing materials at the exactly the capacity of the system? 60 60 40 40 20 20 0 0 0 10 20 30 Day 40 50 60 0 10 20 30 40 50 Day Figure 1.3: Two Outcomes of WIP versus Time at with Releases at 100% Capacity 60 What Casinos are Counting On Over the long run, we will eventually be unlucky. 120 120 100 100 80 80 WIP WIP Release Rate < Capacity 60 60 40 40 20 20 0 0 0 10 20 30 Day 40 50 60 0 10 20 30 40 50 60 Day Figure 1.4: Two Outcomes from Releasing at 82% of Capacity Impact on Utilization The second key principle of capacity: Principle (Utilization): Cycle time increases with utilization and does so sharply as utilization approaches 100%. The Relationship Between WIP and Cycle Time. WIP is a buffer between the arrival process and the production process. What's a buffer? Stating WIP in Units of Time Each entity that arrives at the process represents a certain amount of process time. \"That is 10 minutes each for 40 units, or 400 minutes of work you just brought me.\" Big Ticket WIP Starving a process What happens if you finish before the next entity arrives? So You Increase Your Buffer Adds WIP (more work in the system) Utilization gets closer to 100%. More entities will have to wait. Example: Suppose you have 10 minutes of WIP in your system. What does that mean? How about 11 minutes of WIP? Nonlinear Relationship of Cycle Time to Utilization 50 Cycle Time (hrs) 40 30 20 10 Capacity 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Release Rate (entities/hr) 0.9 1 1.1 1.2 The Highway Overtime Vicious Circle The Cycle 50 Management overloads the system. CT without Overtime Cycle Time (hrs) 40 Overtime changes capacity! 30 Management vows \"...not to let that happen again\". 20 10 Original Capacity CT with Overtime Overtime is discontinued. Capacity with Overtime 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Release Rate (entities/hr) 1.1 1.2 1.3 1.4 1.5 Cycle repeats. Figure 1.6: Mechanics Underlying Overtime Vicious Cycle Restaurant Examples: Fast Food V? U? T? Restaurant Example: Fancy Restaurant V? U? T? Example - Ambulances V? U? T? Example - Bottling Process V? U? T? Queueing Parameters ra = the rate of arrivals in customers (jobs) per unit time (ta = 1/ra = the average time between arrivals). ca = the CV of inter-arrival times. m = the number of machines. re = the rate of the station in jobs per unit time = m/te. ce = the CV of effective process times. u = utilization of station = ra/re Note: a station can be described with 5 parameters. Queueing Measures Measures: CTq = the expected waiting time spent in queue CT = the expected time spent at the process center, i.e., queue time plus process time. WIP = the average WIP level (in jobs) at the station WIPq = the expected WIP (in jobs) in queue Relationships: CT = CTq + te WIP = ra CT WIPq = ra CTq Result: If we know CTq, we can compute WIP, WIPq, CT The G/G/1 Queue Formula: CTq V U t ca2 ce2 2 u 1 u t e Observations: Useful model of single machine workstations Separate terms for variability, utilization, process time. CTq (and other measures) increase with ca2 and ce2 Flow variability, process variability, or both can combine to inflate queue time. Variability causes congestion! The G/G/m Queue Formula: CT V U t q ca2 ce2 u 2 ( m 1) 1 te 2 m(1 u ) Observations: Useful model of multi-machine workstations Extremely general. Fast and accurate. Easily implemented in a spreadsheet (or packages like MPX). setups failures basic data VUT Spreadsheet MEASURE: Arrival Rate (parts/hr) ra Arrival CV Natural Process Time (hr) ca t0 Natural Process SCV Number of Machines MTTF (hr) MTTR (hr) Availability Effective Process Time (failures only) Eff Process SCV (failures only) Batch Size Setup Time (hr) Setup Time SCV Arrival Rate of Batches Eff Batch Process Time (failures+setups) Eff Batch Process Time Var (failures+setups) yield Eff Process SCV (failures+setups) Utilization measures STATION: 1 10.000 2 9.800 3 9.310 4 8.845 5 7.960 2 1.000 0.090 0.181 0.090 0.031 0.095 0.061 0.090 0.035 0.090 c0 m mf mr A te' 2 0.500 1 200 2 0.990 0.091 0.500 1 200 2 0.990 0.091 0.500 1 200 8 0.962 0.099 0.500 1 200 4 0.980 0.092 0.500 1 200 4 0.980 0.092 ce ' k ts 2 0.936 100 0.000 0.936 100 0.500 6.729 100 0.500 2.209 100 0.000 2.209 100 0.000 2 1.000 0.100 9.090 1.000 0.098 9.590 1.000 0.093 10.380 1.000 0.088 9.180 1.000 0.080 9.180 0.773 1.023 6.818 1.861 1.861 0.009 0.909 0.011 0.940 0.063 0.966 0.022 0.812 0.022 0.731 cs ra/k te = kt0/A+ts 2 2 2 k*0 /A + 2mr(1-A)kt0/A+s 2 ce u 2 Departure SCV Yield Final Departure Rate cd y ra*y 0.181 0.980 9.800 0.031 0.950 9.310 0.061 0.950 8.845 0.035 0.900 7.960 0.028 0.950 7.562 Final Departure SCV ycd +(1-y) 2 0.198 0.079 0.108 0.132 0.077 0.909 9.800 45.825 54.915 54.915 458.249 549.149 549.149 0.940 9.310 14.421 24.011 78.925 141.321 235.303 784.452 0.966 8.845 14.065 24.445 103.371 130.948 227.586 1012.038 0.812 7.960 1.649 10.829 114.200 14.587 95.780 1107.818 0.731 7.562 0.716 9.896 124.096 5.700 78.773 1186.591 Utilization Throughput Queue Time (hr) Cycle Time (hr) Cumulative Cycle Time (hr) WIP in Queue (jobs) WIP (jobs) Cumulative WIP (jobs) u TH CTq CTq+te (CT i q(i)+te(i)) raCTq raCT i(ra(i)CT(i)) Effects of Blocking VUT Equation: characterizes stations with infinite space for queueing useful for seeing what will happen to WIP, CT without restrictions But real world systems often constrain WIP: physical constraints (e.g., space or spoilage) logical constraints (e.g., kanbans) Blocking Models: estimate WIP and TH for given set of rates, buffer sizes much more complex than non-blocking (open) models, often require simulation to evaluate realistic systems The M/M/1/b Queue 2 1 Infinite raw materials B buffer spaces Note: there is room for b=B+2 jobs in system, B in the buffer and one at each station. Model of Station 2 (b 1)u b 1 u WIP( M / M / 1 / b) 1 u 1 u b 1 Goes to u/(1-u) as b Always less than WIP(M/M/1) 1 ub TH ( M / M / 1 / b) r b 1 a 1 u Goes to ra as b Always less than TH(M/M/1) CT ( M / M / 1 / b) WIP( M / M / 1 / b) TH ( M / M / 1 / b) where u t e (2) / t e (1) Little's law Note: u>1 is possible; formulas valid for u1 Blocking Example te(1)=21 te(2)=20 B=2 M/M/1/b system has less WIP and less TH than M/M/1 system u t e (2) / t e (1) 20 / 21 0.9524 WIP( M / M / 1) u 20 jobs 1 u TH ( M / M / 1) ra 1 / t e (1) 1 / 21 0.0476 job/min 1-u b 1 0.9524 4 TH(M/M/ 1/b) ra 1-u b 1 1 0.9524 5 1 0.039 job/min 21 18% less TH (b 1)u b 1 5(0.9524 5 ) u WIP( M / M / 1 / b) 20 1.8954 jobs 90% less WIP 1 u 1 u b 1 1 0.9524 5 Conclusion: Seeking Out Variability General Strategies: look for long queues (Little's law) look for blocking focus on high utilization resources consider both flow and process variability ask \"why\" five times Specific Targets: equipment failures setups rework operator pacing anything that prevents regular arrivals and process times Improving Performance of Process Flows We have studied PWC formula that can only tell us how efficient a line is given the parameters rb and T0. Other Routes for Enhancing Performance 1. Improve system parameters 2. Improve performance given parameters How to Improve System Parameters Increase the bottleneck rate (rb) or Decrease the raw process time (T0). Work Faster! How to Increase the BNR? Add capacity (new, faster machine) Improve reliability Improve yield Staffing Improve Quality Increasing BNR Increasing rb from 0.5 to 0.67 in Penny Fab and Dime Fab. Decreasing T0 Reducing the process times at two of the stations from 2 minutes to 1.5 minutes and one of the stations from 2 minutes to 1 minute so that RPT = 6 while the BNR remains unchanged at 0.5. Which has a Greater Effect? Increase BNR Speeding up BNR adds capacity! Decreasing RPT does not. Decrease RPT However, faster nonbottlenecks feed bottlenecks better. Improve Performance Given Parameters 1. Reduce batching delays at or between processes Setup reduction Better scheduling More efficient material handling 2. Reduce delays caused by variability Changes in products Changes in processes Changes in operators and management Improving Efficiency Given System Parameters The effect of reducing the variability at all stations in the Dime Fab such that CV is reduced from 1 to 0.25. Capacity remains unchanged. Stations starve less often. Higher TH for given WIP. Conclusion The specific steps required to achieve these improvements depend on the details of the operations system. Balance of performance measures (TH, CT, WIP, service, flexibility, cost) depends on the business strategy. Lecture#4 How to reduce variability? Managing of variability in production system 1 Influence of Variability Variability Law: Increasing variability always degrades the performance of a production system Examples: Process time variability pushes best case toward worst case Higher demand variability requires more safety stock for same level of customer service Higher cycle time variability requires longer lead time quotes to attain same level of on-time delivery Variability Buffering Buffering Law: Systems with variability must be buffered by some combination of: 1. inventory 2. capacity 3. time Interpretation: If you cannot pay to reduce variability, you will pay in terms of high WIP, under-utilized capacity, or reduced customer service (i.e., lost sales, long lead times, and/or late deliveries). Variability Buffering Examples Ballpoint Pens: can't buffer with time (who will backorder a cheap pen?) can't buffer with capacity (too expensive, and slow) must buffer with inventory Ambulance Service: can't buffer with inventory (stock of emergency services?) can't buffer with time (violates strategic objectives) must buffer with capacity Organ Transplants: can't buffer with WIP (perishable) can't buffer with capacity (ethically anyway) must buffer with time Simulation Studies ra arrival rate ca CV of interarrival times te (i ) effective process time at station i ce (i ) effective CV at station i B(i ) buffer size in front of station i Variability in Push Systems Case 1 2 3 4 Comments te(i), te(3) c(i), i = 1-4 TH CT WIP CT i = 1, 2, 4 (min) (unitless) (j/min) (min) (jobs) (min) (min) 1 1.2 0 0.8 4.2 3.4 0.0 best case 1 1.2 1 0.8 44.6 35.7 26.8 WIP buffer 1 1.0 1 0.8 20.0 16.0 10.3 capacity buffer 1 1.2 0.3 0.8 7.8 6.2 3.3 reduced variability *Result from simulation Notes: ra = 0.8, ca = ce (i) in all cases B (i)= , i = 1-4 in all cases Observations: TH is set by release rate in a push system. Increasing capacity (rb) reduces need for WIP buffering. Reducing process variability reduces WIP, CT, and CT variability for a given throughput level. Variability in Pull Systems Case 1 2 3 4 5 6 te(i), te(3) c(i), i = 1-4 B(3) TH CT WIP CT i = (min) (unitless) (jobs) (j/min) (min) (jobs) (min) 1,2,4 (min) 1 1.2 0 0 0.83 4.6 3.8 0.0 1 1.2 1 0 0.48 6.4 3.1 2.4 1 1.2 1 1 0.53 7.2 3.8 2.6 1 1.2 0.3 0 0.72 5.0 3.6 0.6 1 1.2 0.3 1 0.76 6.0 4.5 0.8 1 1.2 0.3 0 0.73 6.3 4.6 0.7 Comments best case plain JIT inv buffer var reduction inv buffer + var reduction non-bottleneck buffer *Result from simulation Notes: Station 1 pulls in job whenever it becomes empty. B (i) = 0, i = 1, 2, 4 in all cases, except case 6, which has B (2) = 1. Variability in Pull Systems (cont.) Observations: Capping WIP without reducing variability reduces TH WIP cap limits effect of process variability on WIP/CT Reducing process variability increases TH, given same buffers Adding buffer space at bottleneck increases TH Magnitude of impact of adding buffers depends on variability Buffering less helpful at non-bottlenecks Reducing process variability reduces CT variability Conclusion: Consequences of variability are different in push and pull systems, but in either case the buffering law implies that you will pay for variability somehow Example - Discrete Parts Flowline process buffer process buffer process Inventory Buffers: Raw materials, WIP between processes, FGI Capacity Buffers: Overtime, equipment capacity, staffing Time Buffers: Frozen zone, time fences, lead time quotes Variability Reduction: Smaller WIP & FGI , shorter CT Example - Batch Chemical Process reactor column tank reactor column tank reactor column Inventory Buffers: Raw materials, WIP in tanks, FGI Capacity Buffers: Idle time at reactors Time Buffers: Lead times in supply chain Variability Reduction: WIP is tightly constrained, so target is primarily throughput improvement, and maybe FGI reduction Example - Moving Assembly Line in-line buffer fabrication lines final assembly line Inventory Buffers: Components, in-line buffers Capacity Buffers: Overtime, rework loops, warranty repairs Time Buffers: Lead time quotes Variability Reduction: Initially directed at WIP reduction, but later to achieve better use of capacity (e.g., more throughput) Buffer Flexibility Buffer Flexibility Corollary: Flexibility reduces the amount of variability buffering required in a production system Examples: Flexible Capacity: cross-trained workers Flexible Inventory: generic stock (e.g., assemble to order) Flexible Time: variable lead time quotes Finding the Right Mix Depends on physical characteristics and business strategy. THIS is the critical management challenge! Example - Newspapers Demand is variable Can the vendor print more copies? Are customers willing to wait? Example - Emergency Fire Service Demand is highly variable - Can the provider of a service use inventory? - Are customers willing to wait? Example - Organ Transplant Supply and demand are variable Inventory of organs impossible due to perishability. Capacity cannot be augmented ethically. The Role of Strategy Consider McDonalds and Burger King circa 1970. Similar menus Similar production processes Unpredictable demand How Did McDonald's Respond? Stocking finished goods under a heating lamp, i.e., inventory. How Did Burger King Respond? \"Customize your order!\" (variety) Assemble to order. We can't use inventory so... We need more capacity and time to deal with variability. Insight #1 Design of the physical production environment is an important management policy. Layout Material handling Process reliability Automation Insight #2 Different operations systems can be used for different products 1980 Mickey D's stocking Big Macs but not Filet-o-Fish sandwiches. Insight #3 The appropriate operations system for a given application will change over time. Have you ever gone to a fast food restaurant late at night and the food hasn't seemed so fresh? Could be they are using the wrong buffer strategy! Mickey D's switches to \"make to order\" during the slow evening hours so the food is fresh. Buffer Flexibility Variability buffering involves more than selecting a mix of buffer types. The nature of buffers can be influenced by management policy too. Principle (Buffer Flexibility) \"Flexibility reduces the amount of buffering required in a production or supply chain system.\" Example - Flexible Inventory Undyed sweaters at Benetton are \"dyed-toorder\" to fill demand for any color. Example - Flexible Inventory Centralized stocking of spare parts at Bell & Howell. Example - Flexible Inventory Summary: Lower quantities of a generic stock (undyed sweaters or centralized parts) is required to achieve the same service achieved with specialized stock (dyed sweaters or localized parts). Example - Flexible Capacity Capacity that can be shifted from one process to another. One operator who has been cross-trained. Flexible manufacturing systems Remember the flight attendant that flew and safely landed the plane in Airport 1975? Talk about cross training! Example - Flexible Capacity Example - Flexible Capacity Conclusion: Flexible capacity can be more highly utilized than fixed capacity and therefore achieve a given level of performance with less total capacity. Example - Flexible Time Time that can be allocated to more than a single entity. Example - Flexible Time A production system that quotes fixed lead times (10 weeks) vs. a system that quotes dynamic lead times based on work backlog at the time of the quote. Weeks of lead time are thus shifted between customers Costly All buffers are costly Minimizing them is key to efficient operation of production and supply chain systems. The essence of \"Lean Production\" Buffer Location What are the two most useless things in the world to a aircraft pilot? 1. Runway behind you 2. Altitude above you Lesson: Location of the buffer matters! Bottlenecks Bottlenecks influence throughput, cycle time, and WIP. Therefore, a buffer that impacts a bottleneck has a larger effect on performance than one that impacts a nonbottleneck. Example Given a flow with: Fixed arrival rate of entities What goes in must come out! Principle (Buffer Position) For a flow with a fixed arrival rate, identical nonbottleneck processes, and equal sized WIP buffers in front of all processes: The maximum decrease in WIP and cycle time from a unit increase in nonbottleneck capacity will come from adding capacity to the process directly before or after the bottleneck. The maximum decrease in WIP and cycle time from a unit increase in WIP buffer space will come from adding buffer space to the process directly before or after the bottleneck. Example All stations have moderate variability (CV=1). Zero buffers A station is \"blocked\" if it finishes before the downstream station is empty. Q - What is the effect of adding WIP or capacity buffers at various stations? Question What two phenomena can cause the bottleneck in the previous example to cease producing? 1. Murphy upstream causing Starvation 2. Murphy downstream causing Blocking Relative Impact of Adding WIP Buffer Spaces at Different Stations Buffer added before the bottleneck Lesson: WIP buffering is most effective when used at or near the bottleneck Observations for This Example Q - Which will happen more frequently, starvation or blocking? A - Starvation due to the number of stations before vs. the number after. Protect the Bottleneck! More capacity less downstream WIP buffering. More variability more downstream WIP buffering Diminishing Returns to Additional Buffer Spaces In Front of the BN Adding buffer space in front of the BN prevents starving the BN. But what about blocking? Lesson: Diminishing returns on increasing the buffer in front of the BN. Add buffer space elsewhere. Station 4 - throughput will increase 0.498. Station 3 or 5 - throughput will increase to 0.512, a 4.6% improvement. Capacity Buffers Q - In front of which nonbottleneck resource would you put an additional unit of capacity buffer in the example flow? A - In front of the resource immediately upstream of the BN to prevent starving. Example: opening additional check-out lanes at the store. Capacity Laws Capacity Law: In steady state, all plants will release work at an average rate that is strictly less than average capacity Utilization Law: ra < re If a station increases utilization without making any other change, average WIP and cycle time will increase in a highly nonlinear fashion Notes: Cannot run at full capacity (including overtime, etc.) Failure to recognize this leads to \"fire fighting\" Cycle Time vs. Utilization 24 22 20 Cycle Time (hrs) 18 16 14 12 High Variability 10 8 6 Low Variability 4 Capacity 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Release Rate (entities/hr) 0.9 1 1.1 1.2 47 What Really Happens: System with Insufficient Capacity 700 ra > re 600 500 WIP 400 300 200 100 0 0 5 10 15 20 25 Day 30 35 40 45 120 120 100 100 80 80 WIP WIP What Really Happens: Two Cases with Releases at 100% of Capacity 60 60 40 40 20 20 0 0 0 10 20 30 Day 40 50 60 0 10 20 30 Day 40 50 60 What Really Happens: Two Cases with Releases at 82% of Capacity 120 120 100 100 80 80 WIP WIP ra 0.05(90) = 4.5 k ra t minimum batch size required for stability of system... Parallel Batching (cont.) Average wait-for-batch time: WT k 1 1 10 1 1 90 2 ra 2 0.05 batch size affects both wait-for-batch time and queue time Average queue plus process time at station: ca2 / k c02 CT 2 u 0.1 1 0.45 1 u t t 2 1 0.45 90 90 130.5 Total cycle time: CT WT 90 130.5 220.5 Cycle Time vs. Batch Size in a Parallel Operation 1400.00 queue time due to utilization wait for batch time Total Cycle Time 1200.00 1000.00 800.00 600.00 400.00 200.00 0.00 0 10 20 Optimum Batch Size 30 40 50 60 Nb 70 80 90 100 B 110 Variable Batch Sizes Observation: Waiting for full batch in parallel batch operation may not make sense. Could just process whatever is there when operation becomes available. Example: Furnace has space for 120 wrenches Heat treat requires 1 hour Demand averages 100 wrenches/hr Induction coil can heat treat 1 wrench in 30 sec. What is difference between performance of furnace and coil? Variable Batch Sizes (cont.) Furnace: Ignoring queueing due to variability Process starts every hour 100 100 wrenches in furnace 50 50 wrenches waiting on average 150 total wrenches in WIP CT = WIP/TH = 150/100 = 3/2 hr = 90 min Induction Coil: Capacity same as furnace (120 wrenches/hr), but CT = 0.5 min = 0.0083 hr WIP = TH CT = 100 0.0083 = 0.83 wrenches Conclusion: Dramatic reduction in WIP and CT due to small batchesindependent of variability or other factors. Move Batching Move Batching Law: Cycle times over a segment of a routing are roughly proportional to the transfer batch sizes used over that segment, provided there is no waiting for the conveyance device. Insights: Basic Batching Tradeoff: WIP vs. move frequency Queueing for conveyance device can offset CT reduction from reduced move batch size Move batching intimately related to material handling and layout decisions Move Batching Problem: Two machines in series First machine receives individual parts at rate ra with CV of ca(1) and puts out batches of size k. First machine has mean process time of te(1) for one part with CV of ce(1). Second machine receives batches of k and put out individual parts. How does cycle time depend on the batch size k? Move Batching Calculations Time at First Station: Average time before batching is: ca2 (1) ce2 (1) u (1) te (1) te (1) 2 1 u (1) regular VUT equation... Average time forming the batch is: k 1 1 k 1 te (1) 2 ra 2u (1) first part waits (k-1)(1/ra), last part doesn't wait, so average is (k-1)(1/ra)/2 Average time spent at the first station is: ca2 (1) ce2 (1) u (1) k 1 te (1) te (1) te (1) CT (1) 2 1 u (1) 2u (1) k 1 CT(1, no batching) te (1) 2u (1) Move Batching Calculations (cont.) Output of First Station: Time between output of individual parts into the batch is ta. Time between output of batches of size k is kta. Variance of interoutput times of parts is cd2(1)ta2, where c (1) (1 u (1) )c (1) u (1) c (1) 2 d 2 2 a 2 2 e Variance of batches of size k is kcd2(1)ta2. SCV of batch arrivals to station 2 is: 2 2 ( 1 ) kc t ca2 (2) d 2 2 a k ta cd2 (1) k because cd2(1)=d2/ta2 by def of CV because departures are independent, so variances add variance divided by mean squared... Move Batching Calculations (cont.) independent process times... Time at Second Station: Time to process a batch of size k is kte(2). Variance of time to process a batch of size k is kce2(2)te2(2). SCV for a batch of size k is: kce2 (2)t e2 (2) ce2 (2) 2 2 e k t ( 2) k Mean time spent in partial batch of size k is: first part doesn't wait, k 1 t e (2) last part waits (k-1)te(2), 2 so average is (k-1)te(2)/2 So, average time spent at the second station is: cd2 (1) / k ce2 (2) / k u (2) k 1 CT (2) kt e (2) t e ( 2) t e ( 2) 2 2 1 u ( 2) VUT equation to k 1 CT(2, no batching ) t e ( 2) compute queue time 2 of batches... Move Batching Calculations (cont.) Total Cycle Time: CT (batching) CT(no batching) k 1 k 1 te (1) t e ( 2) 2u (1) 2 k 1 te (1) CT(no batching) te (2) 2 u (1) Insight: inflation factor due to move batching Cycle time increases with k. Inflation term does not involve CV's Congestion from batching is more bad control than randomness Assembly Operations Assembly Operations Law: The performance of an assembly station is degraded by increasing any of the following: 1. Number of components being assembled. 2. Variability of component arrivals. 3. Lack of coordination between component arrivals. Observations: This law can be viewed as special instance of variability law. Number of components affected by product/process design. Arrival variability affected by process variability and production control. Coordination affected by scheduling and shop floor control. Attacking Variability Objectives reduce cycle time increase throughput improve customer service Levers reduce variability directly buffer using inventory buffer using capacity buffer using time increase buffer flexibility Cycle Time Definition (Station Cycle Time): The average cycle time at a station is made up of the following components: cycle time = move time + queue time + setup time + process time + wait-to-batch time + wait-in-batch time + wait-to-match time Definition (Line Cycle Time): delay times typically make up 90% of CT The average cycle time in a line is equal to the sum of the cycle times at the individual stations less any time that overlaps two or more stations. Reducing Queue Delay CTq = V U t ca2 ce2 2 Reduce Variability failures setups uneven arrivals, etc. u 1 u Reduce Utilization arrival rate (yield, rework, etc.) process rate (speed, time, availability, etc) 78 Reducing Batching Delay CTbatch = delay at stations + delay between stations Reduce Process Batching Reduce Move Batching Optimize batch sizes Reduce setups - Stations where capacity is expensive - Capacity vs. WIP/CT tradeoff Move more frequently Layout to support material handling (e.g., cells) Reducing Matching Delay CTbatch = delay due to lack of synchronization Reduce Variability on high utilization fabrication lines usual variability reduction methods Improve Coordination Reduce Number of Components scheduling product redesign pull mechanisms kitting modular designs 80 Increasing Throughput TH = P(bottleneck is busy) bottleneck rate Reduce Blocking/Starving buffer with inventory (near bottleneck) reduce system \"desire to queue\" CTq = V U t Reduce Variability Increase Capacity add equipment increase operating time (e.g. spell breaks) increase reliability reduce yield loss/rework Reduce Utilization Note: if WIP is limited, then system degrades via TH loss rather than WIP/CT inflation Customer Service Elements of Customer Service: lead time fill rate (% of orders delivered on-time) Quality Law (Lead Time): The manufacturing lead time for a routing that yields a given service level is an increasing function of both the mean and standard deviation of the cycle time of the routing. Improving Customer Service LT = CT + z CT Reduce CT Visible to Customer delayed differentiation assemble to order stock components Reduce Average CT queue time batch time match time Reduce CT Variability generally same as methods for reducing average CT: improve reliability improve maintainability reduce labor variability improve quality improve scheduling, etc. Cycle Time and Lead Time 0.18 CT = 10 CT = 3 0.16 0.14 Lead Time = 14 days Densities 0.12 0.1 0.08 CT = 10 CT = 6 Lead Time = 27 days 0.06 0.04 0.02 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 Cycle Time in Days Diagnostics Using Factory Physics Situation: Two machines in series; machine 2 is bottleneck ca2 = 1 t0 19 min Machine 1: c02 0.25 MTTF 48 hr, MTTR 8 hr Machine 2: t0 22 min c02 1 MTTF 3.3 hr, MTTR 10 min Space at machine 2 for 20 jobs of WIP Desired throughput 2.4 jobs/hr, not being met Diagnostic Example (cont.) Proposal: Install second machine at station 2 Expensive Very little space Analysis Tools: Analysis: ca2 ce2 u CTq te 2 1 u cd2 u 2 ce2 (1 u 2 )ca2 VUT equation Propogation equation Ask why five times... Step 1: At 2.4 job/hr CTq at first station is 645 minutes, average WIP is 25.8 jobs. CTq at second station is 892 minutes, average WIP is 35.7 jobs. Space requirements at machine 2 are violated! Diagnostic Example (cont.) Step 2: Why is CTq at machine 2 so big? Break CTq into ca2 ce2 u CTq te (3.16)(12.22)(23.11 min) 2 1 u The 23.11 min term is small. The 12.22 correction term is moderate (u 0.9244) The 3.16 correction is large. Step 3: Why is the correction term so large? Look at components of correction term ce2 = 1.04, ca2 = 5.27. Arrivals to machine are highly variable Diagnostic Example (cont.) Step 4: Why is ca2 to machine 2 so large? Recall that ca2 to machine 2 equals cd2 from machine 1, and cd2 u 2 ce2 (1 u 2 )ca2 (0.887 2 )(6.437) (1 0.887 2 )(1.0) 5.27 ce2 at machine 1 is large. Step 5: Why is ce2 at machine 1 large? Effective CV at machine 1 is affected by failures, mr 2 2 ce c0 2 A(1 A) 0.25 6.18 6.43 t0 The inflation due to failures is large Reducing MTTR at machine 1 would substantially improve performance Procoat Case - Situation Problem: Current WIP around 1500 panels Desired capacity of 3000 panels/day (19.5 hr day with breaks/lunches) Typical output of 1150 panels/day Outside vendor being used to make up slack Proposal: Expose is bottleneck, but in clean room Expansion would be expensive Suggested alternative is to add bake oven for touchups Procoat Case - Layout IN Loader Unloader Clean Coat 1 Coat 2 Unloader Touchup D&I Inspect Develop Loader Bake Manufacturing Inspect Expose Clean Room OUT Procoat Case - Capacity Calculations Process Std Dev or Load Process Conveyor Number Machine Time Time Trip Time of Name (min) (min) (min) Machines MTTF MTTR 0.33 0 15 1 80 4 Clean1 0.33 0 15 1 80 4 Coat1 0.33 0 15 1 80 4 Coat2 103 67 5 300 10 Expose 0.33 0 2.67 1 300 3 Develop 0.5 0.5 2 Inspect 0.33 0 100 1 300 3 Bake 161 64 8 MI 9 0 1 Touchup Avail 0.95 0.95 0.95 0.97 0.99 1.00 0.99 1.00 1.00 Setup Rate Time (p/day) 0 3377 0 3377 0 3377 15 2879 0 3510 0 4680 0 3510 0 3488 0 7800 2879 Time (min) 36.5 36.5 36.5 121.9 22.7 0.5 121.0 161.0 9.0 545.7 rb = 2,879 p/day T0 = 546 min = 0.47 days W0 = rbT0 = 1,343 panels Procoat Case - Benchmarking TH Resulting from PWC with WIP = 1,500: w 1,500 TH rb 2,879 1,520 w W0 1 1,500 1,343 1 Conclusion: Higher than actual TH actual system is significantly worse than PWC. Question: what to do? Procoat Case - Factory Physics Analysis 1) Bottleneck Capacity (Expose) - rate: Operator training, setup reduction - time: Break spelling, shift changes 2) Bottleneck Starving - process variability: operator training - flow variability: coater line - field ready replacements reduces \"desire to queue\" so that clean room buffer is adequate Procoat Case - Outcome 3300 Best Case 3000 TH (panels/day) 2700 After 2400 "Good" Region Practical Worst Case 2100 1800 "Bad" Region 1500 1200 Before 900 600 300 Worst Case 0 -300 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 WIP (panels) Corrupting Influence Takeaways Variance Degrades Performance: many sources of variability planned and unplanned Variability Must be Buffered: inventory capacity time Flexibility Reduces Need for Buffering: still need buffers, but smaller ones Corrupting Influence Takeaways (cont.) Variability and Utilization Interact: congestion effects multiply utilization effects are highly nonlinear importance of bottleneck management Batching is an Important Source of Variability: process and move batching serial and parallel batching wait-to-batch time in addition to variability effects Corrupting Influence Takeaways (cont.) Assembly Operations Magnify Impact of Variability: wait-to-match time caused by lack of synchronization Variability Propagates: flow variability is as disruptive as process variability non-bottlenecks can be major problems The Science of Lean Production A contemporary term for Just-InTime approach popularized by Toyota and other Japanese firms in the 1980's. \"Lean\" = Waste Reduction But What is Waste? Obvious - unnecessary operations Less obvious - inefficiencies Scratch Your Back! Were you efficient? Can you think of a more efficient way to get the job done? Unnecessary Operations Flame from lamp (A) catches on curtain (B) and fire department sends stream of water (C) through window. Old man (D) thinks it is raining and reaches for umbrella (E), pulling string (F) and lifting end of platform (G). Iron ball (H) falls and pulls string (I), causing hammer (J) to hit plate of glass (K). Crash of glass wakes up pup (L) and mother dog (M) rocks him to sleep in cradle (N), causing attached wooden hand (O) to move up and down along your back. Symptoms Example Root cause: Variability caused by a quality issue. Symptoms: Excess inventory on the balance sheet Lower throughput (loss of capacity) Longer lead times Definition (Lean Production) Production of goods or services is lean if it is accomplished with minimal buffering costs. Obvious Waste Excess inventory due to poor scheduling Excess capacity due to unnecessary process steps. Both lead to higher buffering costs! Less Obvious Waste Inefficiency such as those due to the variability caused by: Machine outages Operator inconsistencies Setups Quality problems, etc. Excess Capacity What kind of capacity in your car do you pay for that you don't use? 4WD in Florida where it's flat Capacity to seat 7 when you usually drive alone. Zero to 100 MPH in 6 seconds when you usually drive in bumper to bumper traffic. BTW, Anyone care to guess the world record for mpg? (Super Lean!) 20,384 mpg! See http://www.guinnessworldrecords.com Definition (Lean Production) Production of goods or services is lean if it is accomplished with minimal buffering costs. Hmm...This definition allows us to look beyond inventory. I knew there was more to lean than low WIP! Management Decision Choice of buffering mechanism impacts how lean is implemented. Capacity Time Inventory Simply Lowering Inventory Does Not Necessarily Make a System \"Lean\" Example: Are you in shape? Can you lose the wrong kind of weight? Can a person be too thin? What is optimal? Consider a system with Low WIP operating at 10 % utilization; is this \"lean\"? Lowering Inventory Summary - Phases of Lean Implementation Cycle Eliminate direct waste Phase 0: Substitute capacity for inventory buffers Phase 1: Reduce variability Phase 2: Reduce capacity buffers Phase 3: Summary - Phases of Lean Implementation Cycle Substitute capacity for inventory buffers Eliminate direct waste Phase 0: Phase 1: Reduce variability Phase 2: Direct waste: Redundant operations Outages due to unreliable equipment Delays due to operator errors, etc. Reduce capacity buffers Phase 3