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

Uncertainty in processing disrupt the timing of material receipt result in deviation of completion time from due date

Uncertainty in processing Uncertainties in subassemblies reduce the probability of material simultaneously arrivals

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

Literature Review Two 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) = k 1  TWK + k 2 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 DD

Appr. procedure for stage DD

Product structure Simple Two Stage System

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

Minimum processing time M 1 Prob. density func.(PDF) Cumul. distr. func.(CDF) Big variance may result in negative operation times

Analytical Result CDF of leadtime 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

Leadtime Distribution Estimation Complex 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,  Z 2 and  Q,  Q 2  Obtain mean and variance of leadtime 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

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

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 verification

Simulation histogram & Appr. PDF

Product Due Date Simulation verification for product due date to achieve specified probability

Stage Due Dates 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