Manufacturing System Flow Analysis Ronald G. Askin Systems & Industrial Engineering The University of Arizona Tucson, AZ 85721 ron@sie.arizona.edu October 12, 2005
How Many IEs Does It Take to Change a Light Bulb?
n? One to Work Sample to Detect Burned out Bulbs One to Flowchart the Process One to Schedule the Maintenance One to Supervise the Maintenance Task One to Implement a Process Improvement Plan/Kaizen Event One to Determine Optimal Lumens for Replacement Bulb One to do an Economic Analysis of Buying Longer Life Bulbs
Overview of Session The Modern (Lean) Factory WIP vs. Flowtime & Throughput (Little s Law) Transfer Batches vs. Process Batches (Lot-streaming) Cross-Training (Balancing and Buckets) Performance Evaluation Open & Closed Cells
1. Factory Flow Thru Cell System Gears Chassis Assembly Shafts Cards Frame
Flow in a Cell J. T. Black, Design of the Factory with a Future, 1991
Cell Independence (Burbidge) Dedicated Team of (Compatible) Workers Dedicated Set of Machines Specified Set of Parts/Products Dedicated Space for Operations Common Goal and Evaluation Independence of Success Ideally 7-10 Members
2. Little s Law: Defining Rule for Flow L = λw (N = XT) WIP = Prod. Rate x Flow Time
Theoretical Profile! Capacity Production Deterministic N = X T Probabilistic (Exponential) WIP
Empirical Profile Little's Law and Chaos 12 10 8 Remember N = XT Throughput 6 4 Deterministic Exponential Empirical 2 0 0 10 20 30 40 50 60 70 80 90 WIP 10 stages, µ = 1
Questions? What happens when we release jobs to a busy shop floor? What happens when we reduce variability?
Typical Scenario: High Utilization, So Jobs are Late, Therefore Release More Jobs Early L=λW (or N=XT) 1. λ high implies λ small; 2. Since L increases, W increases; 3. As W (lead time) increases, tempted to release jobs even earlier 4. Congestion and interference reduce throughput
Reducing Variability General Arrivals (λ) and Service (S) E( ThroughputTime) = E( W ) + E( S) E( W ) q ρ ( 1+ C ) ( ) s Ca + ρ Cs 2 2 2 2 2 1 + ρ C ρ 2 2 s = λ q [ 2 λ(1 ρ) ] E( S) (ρ = X Capacity)
Question: How Far Is the Blue (Random) Line from the Purple (Deterministic) Line? ρ = 0.8, Exponential Arrivals vs. Fixed Interarrivals Random Service vs. Standardized Service What happens if we release jobs at fixed intervals? What happens with reliable processes & standard tasks?
3. Transfer vs. Process Batches Lot-Streaming Dividing the process batch into multiple transfer batches for concurrent processing at successive stages
Simple Illustration Machine 1 Three stages Batch size = 20 2 3 20 80 120 Time Unit proc. times = 1, 3, 2 a. One Transfer Batch No setup Machine 1 2 3 10 40 70 90 Time b. Two Transfer Batches Machine 1 2 3... 0 1 4 20 61 63 Time c. Single Unit Transfer Batches
MH vs Thruput Time Tradeoff MH Loads vs. Cycle Time 25 20 15 MH Loads 10 5 0 0 20 40 60 80 100 120 140 Cycle Time
Basic Rules (L Sublots, Q units) 1. Consistent, equal sublots good (not optimal) (p 2 q i = p 1 q i+1 is optimal for adjacent WSs) 2. Decreasing marginal benefit: 2 sublots50% of max gain Q T Q p p = + b L i b 3. Protect bottleneck (avoid sublot setup loss) i
4. Cross-Training Ensure Redundancy Consider Job Enrichment as Motivator Task Frequency Sufficient for Proficiency Lead Experts for Each Task Cover all Responsibilities Pay per Skill Breadth and Depth Worker Flexibility vs. WIP Safety Stock
a. Dynamic Rebalancing 1 4 min 3 min 6 min 8 min 3 min a. Two Workers Total Time = 24 1 4 min 3 min 6 min 8 min 3 min b. Three Workers Part Flow Worker Flow (Orbit) Workstation
b. Bucket Brigades (TSS) & Variants BB Assumes Task Continuity Ordered Workers Slowest to Fastest Effective in Picking Buffers can be added Champion Strategy (For low machine ρ) Leapfrog Strategy (Less worker movement)
5. Performance Evaluation N = X T Find X & T given N & Capacity Find T and needed N for desired X given Capacity Find T, X Tradeoff
Open System (Receive and Release) Random
Basic Poisson Process Estimate 1. Compute Effective Arrival Rates at Workstations m ' ' j = j + k pkj k = 1 λ λ λ 2. Evaluate Each Workstation (M/M/1) P(0) = 1-ρ 5/day (A) 5 4 4 2 6 L = ρ/(1-ρ) W = L/λ 6/day (B) 5
System & Product Measures 3. Aggregate Across Workstations m = j j= 1 W v W j W B = W +.67W + W
External Demand Closed System (CONWIP)
Basic Performance Evaluation - Closed Consider a Closed System with N Jobs: X = Production rate, T = Throughput time C P M =c j Total Servers or Max Active Jobs j= 1 M =t j Total Job Processing time j= 1 min( C, N) T P so N = XT X P
Performance Evaluation Extension Assume WIP Evenly Spread Out T N 1 1 + P, Exponential Processing Time M = N P, Constant, Synchronous Processing with N M M As Always, N=XT Very Optimistic Model! No Starvation when N M
References and Extensions 1. Askin, R. & J. Goldberg, Design and Analysis of Lean Production Systems, Wiley& Sons, 2002 2. Askin, R. & C. Standridge, Modeling and Analysis of Manufacturing Systems, Wiley & Sons, 1993 3. Black, J. T., Design of the Factory with a Future, McGraw Hill, 1991 4. Harmon, R & L. Peterson, Reinventing the Factory, Free Press, 1989 5. Hopp, W. and M. Spearman, Factory Physics, McGraw Hill, 2000.