Post on 18-Dec-2015
transcript
Due Date Planning for Complex Product Systems
with Uncertain Processing Times
By: Dongping Song
Supervisor: Dr. C.Hicks and Dr. C.F.Earl
Dept. of MMM Eng.
Univ. of Newcastle upon Tyne
April, 1999
Overview
1. Introduction
2. Literature review
3. Leadtime distribution estimation
4. Due date planning
5. Industrial case study
6. Discussion and conclusion
7. Further work
Introduction
Production planning
Upper level
MIddle level
Lower level
Product due date planning
Stage due date planning
Scheduling
Sequencing
Uncertainty in processing• disrupt the timing of material receipt
• result in deviation of completion time from due date
2
3
1
+ =
Introduction• Complex product system
– Assembly and product structure– Uncertain processing times– Cumulative and interacting
• Problem : setting due date in complex product systems with uncertain processing times
Literature ReviewTwo principal research streams
[Cheng(1989), Lawrence(1995)]
• Empirical method: based on job characteristics and
shop status. Such as: TWK, SLK, NOP, JIQ, JIS
Due date(DD) = k1TWK + k2
• Analytic method: queuing networks, mathematical
programming etc. by minimising a cost function
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
Appr. procedure for product DDAnalytical / numerical
method
Moments of two-stageleadtime
Approximate leadtimedistribution
Product due dateplanning
Appr. procedure for stage DD
Analytical / numericalmethod
Moments of two-stageleadtime
Approximate leadtimedistribution
Stage due dateplanning
Planned start time S1, S1i
component 11
component 12
component 1n
assembly proc. time
assembly proc. time
component 1n
S 1S 11
S 12
S 1n
... ...
• Holding cost at subsequent stage• Resource capacity limitation• Reduce variability
Minimum processing time M1
Prob. density func.(PDF) Cumul. distr. func.(CDF) • Big variance may result in negative operation times
Analytical Result• CDF of leadtime 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
Leadtime Distribution EstimationComplex product structure approximate method
Assumptions normally distributed processing times approximate leadtime by truncated normal distribution
(Soroush, 1999)
Leadtime 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 leadtime 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
Due Date Planning
• Mean absolute lateness (MAL)
DD* = median
• Standard deviation lateness (SDL)
DD* = mean
• Asymmetric earliness and tardiness cost
DD* by root finding method
Industrial Case Study• Product structure
17 components 17 components
Stage 1
Stage 2
Stage 3
Stage 4
Stage 5
Stage 6 … … … …
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
• backward scheduling based on mean data• planned start time: 0 for 32 components and 3.5 for
other two.
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
Stage Due Dates
Stage 6 5 4 3 2 1
Due Date 8 40 72 104 135 167
Prob.achievedin simul.
90.6%
88.3%
90.8%
89.9%
91.8%
89.9%
• Simulation verification for stage due dates to achieve 90% probability
Conclusion
• Complex product systems with uncertainty
• A procedure to estimate leadtime distribution
• Approximate method to set due dates
• Used to design planned start times