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

3. Two stage model

4. Lead-time distribution estimation

5. Due date planning

6. Industrial case study

7. Conclusions and further work

Typical product

Introduction

Production planning

Upper level

Middle level

Lower level

Product due date planning

Stage due date planning

Scheduling

Sequencing

Uncertainty in processing

2

3

1

+ =

Latest component completion time distribution

Component Manufacture

Assembly process distribution

Lead time distribution

Uncertainty in complex products

1

3

4 5

6 7

2

Uncertainty is cumulativeProduct due date

Stage due dates

Stage due dates

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

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

• Product structure

Two Stage Model

ComponentManufacturing

Assembly

11 12 1n

1

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

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.

Truncated distribution

Probability density function (PDF)

Cumulative distribution function ( CDF)

M1 = Minimum processing time

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

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

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

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

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

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)

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

Industrial Case Study• Product structure

17 components 17 components

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6 … … … …

(Data from Parsons)

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.

Simulation histogram & Approximation PDF

Components

Product1. Good agreement with simulation. 2. Skewed distribution, due dates based upon means achieved with lower probability

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

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%

Stage due date setting with safety due dates

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

Further Work

• Skewed processing times

• Using more general distribution to

approximate, like -type distribution

• Resource constrained systems