due date planning for complex product systems with uncertain processing times
DESCRIPTION
Due Date Planning for Complex Product Systems with Uncertain Processing Times. By : Dongping Song Supervisors : Dr. C.Hicks & Dr. C.F.Earl Department of MMM Engineering University of Newcastle upon Tyne April, 1999. Overview. 1. Introduction 2. Literature review - PowerPoint PPT PresentationTRANSCRIPT
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Due Date Planning for Complex Product Systems
with Uncertain Processing Times
By: Dongping Song
Supervisors: Dr. C.Hicks & Dr. C.F.Earl
Department of MMM Engineering
University of Newcastle upon Tyne
April, 1999
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Overview
1. Introduction
2. Literature review
3. Two stage model
4. Lead-time distribution estimation
5. Due date planning
6. Industrial case study
7. Conclusions and further work
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Typical product
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Introduction
Production planning
Upper level
Middle level
Lower level
Product due date planning
Stage due date planning
Scheduling
Sequencing
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Uncertainty in processing
2
3
1
+ =
Latest component completion time distribution
Component Manufacture
Assembly process distribution
Lead time distribution
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Uncertainty in complex products
1
3
4 5
6 7
2
Uncertainty is cumulativeProduct due date
Stage due dates
Stage due dates
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Literature ReviewTwo principal research streams
[Cheng(1989), Lawrence(1995)]
• Empirical methods: based on job characteristics and
shop status. Such as: TWK, SLK, NOP, JIQ, JIS
e.g. Due date(DD) = k1TWK + k2
• Analytic methods: queuing networks, mathematical
programming e.g. minimising a cost function
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Literature Review
Limitation of above research
• Both focus on job shop situations
• Empirical - rely on simulation, time consuming
in stochastic systems
• Analytic - limited to “small” problems
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• Product structure
Two Stage Model
ComponentManufacturing
Assembly
11 12 1n
1
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Planned start time S1, S1i
• Holding cost at subsequent stage• Resource capacity limitation• Reduce variability
safety time
safety time
safetytime
safetytime
component 11
component 12
component 1n
assembly proc. time
assembly proc. time
component 1n
S 1S 11
S 12
S 1n
... ...
DD
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Minimum processing timeMany research has used normal distribution to model processing time. However, it may have unrealistically short or negative operation times when the variance is large.
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Truncated distribution
Probability density function (PDF)
Cumulative distribution function ( CDF)
M1 = Minimum processing time
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Lead-time distribution for 2 stage system
• Cumulative distribution function (CDF) of lead-time W is:
FW(t) = 0, t<M1+S1;
FW(t) = F1(M1) FZ(t-M1) + F1FZ, t M1 + S1.where
F1 CDF of assembly processing time;
FZ CDF of actual assembly start time;
FZ(t)= 1n F1i(t-S1i)
convolution operator in [M1, t - S1];
F1FZ= F1(x) FZ(x-t)dx
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Lead-time Distribution EstimationComplex product structure approximation method based upon two stage model
Assumptions normally distributed processing times approximate lead-time by truncated normal distribution
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Lead-time Distribution Estimation
Normal distribution approximation Compute mean and variance of assembly start time Z and
assembly process time Q : Z, Z2 and Q, Q
2
Obtain mean and variance of lead-time W(=Z+Q):
W = Q+Z, W2 = Q
2+Z2
Approximate W by truncated normal distribution:
N(W, W2), t M1+ S1.
More moments are needed if using general
distribution to approximate
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Approximation procedure for setting stage due date
Two stage model
Moments of two-stage lead-time
Approximate lead-time distribution
morestages ?
Stage due date planning
End
Begin: bottom of product structure
Yes
No
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Approximation procedure for setting product due date
Two stage model
Moments of two-stage lead-time
Approximate lead-time distribution
morestages ?
Product due date planning
End
Begin: bottom of product structure
Yes
No
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Due date planning objectives• Achieve completion by due date with a specified
probability (service target)• Very important when large penalties for lateness
apply DD* by N(0, 1)
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Other possible objectives
• Mean absolute lateness (MAL)
DD* = median
• Standard deviation lateness (SDL)
DD* = mean
• Asymmetric earliness and tardiness cost
DD* by root finding method
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Industrial Case Study• Product structure
17 components 17 components
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6 … … … …
(Data from Parsons)
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System parameters setting
• normal processing times• at stage 6: =7 days for 32 components,
=3.5 days for the other two.
• at other stages : =28 days
• standard deviation: = 0.1
• backwards scheduling based on mean data• planned start time: 0 for 32 components and 3.5 for
other two.
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Simulation histogram & Approximation PDF
Components
Product1. Good agreement with simulation. 2. Skewed distribution, due dates based upon means achieved with lower probability
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Product due date
Prob. 0.50 0.60 0.70 0.80 0.90
due simu. 150.86 152.11 153.44 155.26 157.46
date appr. 151.66 152.85 154.12 155.61 157.72
• Simulation verification for product due date to achieve specified probability
Days from component start time
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Stage due dates • Simulation verification for stage due dates to achieve 90% probability (by settting stage safety due dates)
Stage 6 5 4 3 2 1
Stage Due Date 8 40 72 104 135 167
Safety Due Date 1 5 9 13 16 20
Prob. achievedin simulation
90.6% 88.3% 90.8% 89.9% 91.8% 89.9%
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Stage due date setting with safety due dates
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Conclusion
• Developed method for product and stage due date setting for complex products.
• Good agreement with simulation
• Plans designed to achieve completion with specified probability
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Further Work
• Skewed processing times
• Using more general distribution to
approximate, like -type distribution
• Resource constrained systems