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

Uncertainty in processing Latest component completion time distribution Component Manufacture Assembly process distribution Lead time distribution

Uncertainty in complex products Uncertainty is cumulative Product due date Stage due dates Stage due dates

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) = k 1  TWK + k 2 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

Planned start time S 1, S 1i Holding cost at subsequent stage Resource capacity limitation Reduce variability

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 Probability density function (PDF) Cumulative distribution function ( CDF) M 1 = Minimum processing time

Lead-time distribution for 2 stage system Cumulative distribution function (CDF) of lead- time W is: F W (t) = 0, t<M 1 +S 1 ; F W (t) = F 1 (M 1 ) F Z (t-M 1 ) + F 1  F Z, t  M 1 + S 1. where F 1  CDF of assembly processing time; F Z  CDF of actual assembly start time; F Z (t)=  1 n F 1i (t-S 1i )   convolution operator in [M 1, t - S 1 ]; F 1  F Z =   F 1 (x) F Z (x-t)dx

Lead-time Distribution Estimation Complex 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,  Z 2 and  Q,  Q 2  Obtain mean and variance of lead-time W(=Z+Q):  W =  Q +  Z,  W 2 =  Q 2 +  Z 2  Approximate W by truncated normal distribution: N(  W,  W 2 ), t  M 1 + S 1. More moments are needed if using general distribution to approximate

Approximation procedure for setting stage due date

Approximation procedure for setting product due date

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 (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 Product 1. Good agreement with simulation. 2. Skewed distribution, due dates based upon means achieved with lower probability

Product due date 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 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