Due Date Planning for Complex Product Systems
with Uncertain Processing Times
By: Dongping SongSupervisor: Dr. C.Hicks and Dr. C.F.EarlDept. of MMM Eng.Univ. of Newcastle upon TyneApril, 1999
Overview1. Introduction2. Literature review3. Leadtime distribution estimation4. Due date planning5. Industrial case study6. Discussion and conclusion7. Further work
IntroductionProduction 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
Uncertainty in complex products
1
3
4 5
6 7
2
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 DDAnalytical / numerical
method
Moments of two-stageleadtime
Approximate leadtimedistribution
Stage due dateplanning
• Product structure
Simple Two Stage System
ComponentManufacturing
Assembly
11 12 1n
1
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 EstimationNormal 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, W
2 = Q2+Z
2
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• Achieve a specified probability
DD* by N(0, 1)
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.
Simulation histogram & Appr. PDF
Simulation histogram & Appr. PDF
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
Discussion
• Minimum processing time
• Production plan
• Stage due date
Conclusion
• Complex product systems with uncertainty
• A procedure to estimate leadtime distribution
• Approximate method to set due dates• Used to design planned start times
Further Work
• Skewed processing times
• Using more general distribution to
approximate, like -type distribution
• Resource constraint systems