Due date planning for complex product systems with uncertain processing times
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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. Overview. 1. Introduction 2. Literature review

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Due date planning for complex product systems with uncertain processing times

Due Date Planning for Complex Product Systemswith 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


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

Uncertainty in processing
Uncertainty in processing

Lead time distribution



Assembly process distribution

Latest component completion

time distribution

Uncertainty in complex products
Uncertainty in complex products

Uncertainty is cumulative

Product due date


due dates


due dates

Literature review
Literature Review

Two 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) = k1×TWK + k2

  • Analytic methods: queuing networks, mathematical programming e.g. minimising a cost function

Literature review1
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

Two stage model
Two Stage Model

  • Product structure

Planned start time s 1 s 1 i
Planned start time S1, S1i

  • Holding cost at subsequent stage

  • Resource capacity limitation

  • Reduce variability

Minimum processing time
Minimum processing time

Many 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
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) + F1¢ÄFZ, t ³ M1 + S1.

  • where

  • F1 ¾ CDF of assembly processing time;

  • FZ¾ CDF of actual assembly start time;

  • FZ(t)= P1n F1i(t-S1i)

  • ľ convolution operator in [M1, t - S1];

  • F1¢ÄFZ= òF1¢(x) FZ(x-t)dx

Lead time distribution estimation
Lead-time Distribution Estimation

Complex product structure

  • approximation method based upon two stage model


  • normally distributed processing times

  • approximate lead-time by truncated normal distribution

Lead time distribution estimation1
Lead-time Distribution Estimation

Normal distribution approximation

  • Compute mean and variance of assembly start time Z and assembly process time Q : mZ, sZ2andmQ, sQ2

  • Obtain mean and variance of lead-time W(=Z+Q):

    mW = mQ+mZ, sW2 = sQ2+sZ2

  • Approximate W by truncated normal distribution:

    N(mW, sW2), t ³ M1+ S1.

    More moments are needed if using general distribution to approximate

Due date planning objectives
Due date planning objectives

  • Achieve completion by due date with a specified probability (service target)

  • Very important when large penalties for lateness apply

    ÞDD* by N(0, 1)

Other possible objectives
Other possible objectives

  • Mean absolute lateness (MAL)

    ÞDD* = median

  • Standard deviation lateness (SDL)

    ÞDD* = mean

  • Asymmetric earliness and tardiness cost

    ÞDD* by root finding method

Industrial case study
Industrial Case Study

  • Product structure

    17 components 17 components

(Data from Parsons)

System parameters setting
System parameters setting

  • normal processing times

  • at stage 6: m =7days for 32 components,

    m =3.5 days for the other two.

  • at other stages : m=28 days

  • standard deviation: s= 0.1m

  • backwards scheduling based on mean data

  • planned start time: 0 for 32 components and 3.5 for other two.

Simulation histogram approximation pdf
Simulation histogram & Approximation PDF



1. Good agreement with simulation. 2. Skewed distribution,

due dates based upon means achieved with lower probability

Product due date
Product due date

  • Simulation verification for product due date to achieve specified probability

Days from component start time

Stage due dates
Stage due dates

  • Simulation verification for stage due dates to achieve 90% probability (by settting stage safety due dates)


  • 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
Further Work

  • Skewed processing times

  • Using more general distribution to approximate, like l-type distribution

  • Resource constrained systems