ThroughputFlowTimeAndLittlesLaw v3 4xgs (1)

ThroughputFlowTimeAndLittlesLaw v3 4xgs (1) - Overview •...

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Unformatted text preview: Overview • Throughput Concepts Throughput Concepts, Flow Time, and Little’s Law • What is it Worth to Increase Throughput? • Flow time and Lead time Peter L. Jackson Professor School of O.R. and I.E. 1/29/2012 Industrial Data and Systems Analysis • Little’s Law • What is it Worth to Reduce Flow Time? 1/29/2012 1 What is Throughput? is Throughput? Definition of ‘cycle time’ is not consistent: even within the same company! • Takt time • Inverse of throughput rate • Units of time per unit of output • Time between successive outputs • Toyota System • Measure of interest: throughput rate • Flights per hour, out-patients per day, per hour out per day gallons per second, messages per hour, etc. Industrial Data and Systems Analysis 2 What is ‘Cycle Time’? is Cycle Time • Activity of a repetitive process of repetitive process • Output = input (∴ throughput), unless... 1/29/2012 Industrial Data and Systems Analysis 3 1/29/2012 • Flow time • Time spent in spent in system by single unit (includes queue time) Industrial Data and Systems Analysis 4 Throughput Detractors Throughput Detractors The M.F.D. THRUPUT Game M.F.D. THRUPUT Game • Unscheduled time • Starved / blocked by production control system • Speed loss • Quality loss • Scrap, rework • Breakdowns • Setup time • Planned downtime • partial shifts • maintenance • meetings, training training 1/29/2012 Industrial Data and Systems Analysis 5 1/29/2012 Industrial Data and Systems Analysis Throughput Targets Targets Will the Process Achieve the Target? • DGR (daily going rate): units per day required to (daily going rate): units per day required to 6 • Begin with throughput rate achievable with throughput rate achievable support final assembly schedule (level schedule) under ideal operating conditions • Adjust for breakdowns, setups, quality for breakdowns setups quality loss, speed loss • Cycle time (Takt time): time allowed between successive units of output to achieve DGR • Ex. Adjust for speed loss: Adjust for speed loss: • Equipment runs at 100y% speed • Throughput rate adjusted for efficiency = • Takt time = effective daily operating time / DGR unadjusted rate * y • Stated as requirement: process must be • Adjust for planned downtime designed and operated to achieve these targets 1/29/2012 Industrial Data and Systems Analysis 7 1/29/2012 Industrial Data and Systems Analysis 8 Adjust for Repair Cycles Adjust for Repair Cycles operational repair Adjust for Setup Cycles for Setup Cycles setup repair Setup time TTF TTR Industrial Data and Systems Analysis 100(1-x)% Run time rate • Setup cycle length = Setup time + run time cycle length Setup time run time • Fraction of time equipment is running = Run time / (Setup cycle length) • Throughput rate adjusted for setups = unadjusted rate * run time / cycle length 9 Adjust for Scrap for Scrap I setup • Run time = average lot size / production ti MTTF: mean time to fail (when running) MTTR: mean time to repair Mean repair cycle length = MTTR+MTTF Fraction of time equipment is operational = MTTF / (MTTR+MTTF) MTTF (MTTR+MTTF) • Throughput rate adjusted for repair = Unadjusted rate MTTF (MTTR Unadjusted rate * MTTF / (MTTR+MTTF) • • • • 1/29/2012 run 1/29/2012 Industrial Data and Systems Analysis 10 Adjust for Rework Cycles for Rework Cycles I O 100x% 100(1-x)% O 100x% • Output rate is 100(1-x)% of input rate • Throughput rate adjusted for scrap = • Suppose reject rate applies to reworked parts as well unadjusted throughput rate * (1-x) • Expected number of work and rework cycles per ∞ part part = x=1/(1-x) 1/(1 n n=0 • Throughput rate adjusted for rework = unadjusted rate * (1-x) 1/29/2012 Industrial Data and Systems Analysis 11 1/29/2012 Industrial Data and Systems Analysis 12 Aside: Rework analysis Aside: Rework analysis Aside: Rework Analysis (cont’d) Rework Analysis (cont • Let N= number of work + rework cycles • Unadjusted time per piece = 1/unadjusted time per piece 1/unadjusted ∞ E[ N ] = P{N > n} since N is nonnegative r.v. n =0 P{N > 0} = 1 since every part has at least one cycle P{N > n} = x n , n ≥ 1 i.e. part must fail n times in a row ∞ E[ N ] = 1 + x + x + x + = x n = 2 3 n =0 1/29/2012 1 1− x Industrial Data and Systems Analysis 13 Adjust for Planned Downtime for Planned Downtime throughput rate • Adjusted time per piece = E[N]/unadjusted throughput rate • Adjusted throughput rate = 1/adjusted time per piece = unadjusted throughput rate / E[N] • Adjusted throughput rate = unadjusted throughput rate * (1-x) 1/29/2012 Multi-Stage Throughput Throughput • Begin with 24 hour clock • Subtract planned downtime to get 1 available hours • Multiply throughput per hour by available hours to get achievable throughput per day (nominal day (nominal t’put) • Compare to DGR Blocked operation Bottleneck operation 3 Starved operation with the lowest throughput rate determines the throughput rate of the system as a whole inadequate • Downstream operations will be starved • Upstream operations will be blocked operations will be blocked • If DGR < nominal t’put then process will be idle (unscheduled time) (unscheduled time) Industrial Data and Systems Analysis 2 • In a series of operations, the operation series of operations the operation • If DGR > nominal t’put then design is DGR nominal then design is 1/29/2012 14 Industrial Data and Systems Analysis 15 1/29/2012 Industrial Data and Systems Analysis 16 Sample Problem Sample Problem 1 • • • • • • Speed and Quality Losses and Quality Losses • What is effective throughput rate of the is effective throughput rate of the The engineering specifications indicate that an automated lathe can turn a certain metal part at a rate of 100 pieces per hour. However, in practice the lathe is run at only 95% of that speed. The scrap rate from the machine is only about 1 part in 10,000. Rework occurs at about the same rate. On average the machine is out of service for repairs 30 minutes for every 20 hours of operation. Furthermore, jobs arrive in batches of 250 units and there is a setup time required of 15 minutes for each job. 1/29/2012 lathe considering speed loss, scrap, and rework? (pieces per hour) • Assume rework % expressed in terms of non- scrapped units • i.e. apply rework adjustment after scrap adjustment 17 Industrial Data and Systems Analysis Breakdown Losses Losses 1/29/2012 In service In service 18 Transitions (Setups) (Setups) Down for repairs In service Industrial Data and Systems Analysis In service In service … • What fraction of time in service is spent in fraction of time in service is spent in In service In service production (rather than in setup)? • What fraction of potential operational time is the equipment available for service? 1/29/2012 Industrial Data and Systems Analysis 19 1/29/2012 Industrial Data and Systems Analysis 20 Net Effect Net Effect Sample Problem 2 Problem • What is the effective throughput rate of is the effective throughput rate of • • • • the lathe considering all effects of speed, quality, reliability, and transition? • • • • Automobile assembly plant Production rate: 40 jobs per hour Sales rate per week: 3,040 vehicles Plant operates 5 days per week, two shifts per day + overtime Daily going rate: 608 vehicles Hours per shift: 8 Planned downtime per shift: 20 minutes Compute: • Operating hours per day: 15.333 • Takt time: 1.513 minutes per vehicle 1/29/2012 Industrial Data and Systems Analysis 21 1/29/2012 Industrial Data and Systems Analysis 22 Actual Performance Performance Performance Against Target Against Target • There are quality problems if we run the are quality problems if we run the • Effective throughput: 34.1 vehicles per hour • Takt time: 1.513 minutes per vehicle • Effective cycle time: 1.759 minutes per • • • • • line too fast We have slowed the line speed by 10% There are lots of little interruptions on the line that cause it to slow down Duration of interruption: 20 seconds Frequency of interruption: 10 per hour of interruption: 10 per hour Uninterrupted hours per hour of operation: 0.947 1/29/2012 Industrial Data and Systems Analysis vehicle • “Measure” : a quantity describing performance (ex. effective cycle time) ti • “Metric”: a measure used as a standard (ex. takt time) takt time) • Our cycle times in the plant are 16% too high, compared to our metric 23 1/29/2012 Industrial Data and Systems Analysis 24 What is it Worth to Increase Th Throughput? What Does Overtime Cost? Does Overtime Cost? • Approach: pp • assume production target is fixed • As throughput rate increases, time required decreases • Time is money: compute wages saved • Available regular time hours per week: ti 76.67 • Available regular time production per week: regular time production per week: 2614.7 • Overtime hours required: 12.47 hours required: 12 1/29/2012 Industrial Data and Systems Analysis 25 What is it Worth to Increase Th Throughput? • • • • • • • • Workers per line per shift: 50 per line per shift: 50 Salaries+benefits per year: $70,000 Weeks per year: 50 per year: 50 Salary+benefits per worker-week: $1,400 Benefit rate: 25% rate: 25% Salary per hour: $28 Overtime per hour: $42 (no benefits) per hour: $42 (no benefits) Total cost per overtime hour: $2,100 1/29/2012 Industrial Data and Systems Analysis 26 What are Other Ways to Measure Benefit of Increasing Throughput? Th • Current predicted overtime cost: $26,185 predicted overtime cost: $26,185 per week • Annualized cost: $1,309,259 • What is impact of cutting speed loss in half (without hurting quality)? $492,593 per year • What is impact of cutting interruption frequency (or duration) in half? $246,296 per year 1/29/2012 Industrial Data and Systems Analysis 27 1/29/2012 Industrial Data and Systems Analysis 28 How Can You Increase Th Throughput? Overview • Continuous improvement improvement • Measure, Analyze, Act • Observe factory, interview workers and staff, • Throughput Concepts • What is it Worth to Increase Throughput? collect data on problems • Brainstorm solutions, implement and test • Flow time and Lead time • Recitation this week • Use SQL to analyze instances of throughput • Little’s Law problems problems 1/29/2012 • What is it Worth to Reduce Flow Time? Industrial Data and Systems Analysis 29 What is Flow Time? is Flow Time? 1/29/2012 Industrial Data and Systems Analysis 30 Accounting for Lead Time for Lead Time • Lead time: the time time: the time • Cycle time • Inverse of throughput rate throughput rate • Ex. Oven cycle time: 32 min. • Two trays of 8 trays of cookies per cycle • Cookie cycle time: 2 min./cookie 1/29/2012 from when you trigger an action until you see the result • Typically, lead time is duration of time between order placement and order placement and order fulfillment (delivery) • Flow time • Time spent in spent in system by single unit (includes queue time) • Cookie flow time: flow time: 32 min. + queue time Industrial Data and Systems Analysis 31 1/29/2012 Industrial Data and Systems Analysis 32 Lead Time Analysis Lead Time Analysis Order Sent Sent Credit Approved Schedule Released Queue Factor Factor Long Haul Haul Transport Drop Shipments Consolidated Material Picked / Produced • Order lead time is flow time of order through the entire system (order processing, factory scheduling, production, packing, shipping, and receiving) • Distinguish between value-added time and nonvalue added time Material Received / Inspected / Order Verified Order Lead Time Order Scheduled Order Received Material Packed / Shipped • Value-added time: material transformation + transport to time: material transformation transport to Short Haul Haul Delivery customer Production Lead Time Pick Materials Operation 1 Operation 2 • Non-value-added time: queue time+internal transport time Operation 3 • Queue factor: (time in queue+value added time) / factor: (time in queue+value added time) value added time Operation Lead Time Production Transport Queue Queue 1/29/2012 Setup Run • If measured rigorously, queue time is many orders Transport Queue Queue Industrial Data and Systems Analysis of magnitude larger than value of magnitude larger than value-added time time 33 1/29/2012 Industrial Data and Systems Analysis How to Reduce Lead Times to Reduce Lead Times Overview • Continuous improvement 34 • Throughput Concepts • Measure, Analyze, Act • What is it Worth to Increase Throughput? • How to reduce value-added time: • Flow time and Lead time • Increase speed of operations • How to reduce queue time • Little’s Law • Increase frequency of operations • Reduce variability 1/29/2012 Industrial Data and Systems Analysis • What is it Worth to Reduce Flow Time? 35 1/29/2012 Industrial Data and Systems Analysis 36 Unit Flowing Through a System 0 a unit enters the system 1/29/2012 Unit Spending Time in a System Time 0 a unit leaves the system W, time spent in the system (flow time lead time time, lead time, waiting time,…) 37 Industrial Data and Systems Analysis Units Flowing Through a System 0 next unit enters the system Time 1/29/2012 38 Industrial Data and Systems Analysis Units Arriving (and Leaving) at Some Rat te Time 0 next unit leaves the system 1 Time 1 unit of time λ, input rate ( = output rate = throughput rate) 1/29/2012 Industrial Data and Systems Analysis 39 1/29/2012 Industrial Data and Systems Analysis 40 In Steady State, How Many Units Are in the System? th Average Units in System Units in System W • Average Units in System = Throughput Units in System Throughput λ 1 L, average number of units in the system rate * Unit Flow Time • Little’s Law: L = λW • Applicable in wide variety of systems in wide variety of systems • When is it not applicable? 1/29/2012 Industrial Data and Systems Analysis 41 1/29/2012 Industrial Data and Systems Analysis 42 Little’s Law Law How Much Money is Tied Up in Inventory? • 600 students admitted annually to four- • Automotive example continued: • Sales: 3,040 vehicles per week • Production and transport time per vehicle: 8 year degree program • 2400 students in program, on average • • • • • • 15 days for ship to cross Pacific Ocean, 700 vehicles per ship, one ship per week • 1500 vehicles in oceanic transit, on average 1/29/2012 Industrial Data and Systems Analysis 43 days Pipeline inventory: 3,474.3 vehicles Vehicle cost: $12,000 Pipeline inventory investment: $41,691,429 Interest rate to finance investment: 12% fi 12% Annual pipeline inventory interest charge: $5 $5,002,971 1/29/2012 Industrial Data and Systems Analysis 44 What is it Worth to Reduce Fl Flow Time? Ti What are Other Benefits of Reducing Fl Flow Times and Lead Times? Ti Ti • Reducing material flow time reduces inventory (“pipeline inventory”) • Reducing production and transportation flow time by 1 day would reduce pipeline inventory by 12 inventory by 12.5 % • Interest savings per year: $625,371 1/29/2012 Industrial Data and Systems Analysis 45 Overview • Throughput Concepts • What is it Worth to Increase Throughput? • Flow time and Lead time • Little’s Law • What is it Worth to Reduce Flow Time? 1/29/2012 Industrial Data and Systems Analysis 47 1/29/2012 Industrial Data and Systems Analysis 46 ...
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This note was uploaded on 02/09/2012 for the course ORIE 3120 taught by Professor Jackson during the Spring '09 term at Cornell University (Engineering School).

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