1. Due Date Planning for Complex Product Systems with Uncertain Processing Times By: D.P. Song, C.Hicks and C.F.Earl Dept. of MMM Eng. Univ. of Newcastle upon Tyne 2nd Int. Conf. on the Control of Ind. Process, March, 30-31, 1999

2. Overview 1. Introduction 2. Literature Review 3. Simple Two Stage System 4. Leadtime Distribution Estimation 5. Due Date Planning 6. Industrial Case Study 7. Discussion and Further Work

3. Introduction Delivery performance Uncertainties Complex product system –Assembly –Product structure Problem : setting due date in complex product systems with uncertain processing times

4. Literature Review Two principal research streams [Cheng(1989), Lawrence(1995), Philipoom(1997)] Empirical method: based on job characteristics and shop status. Such as: TWK, SLK, NOP, JIQ, JIS Analytic method: queuing networks, mathematical programming etc. by minimising a cost function Limitation of above research Both focus on job shop situations Empirical -- time consuming in stochastic systems Analytic -- limited to “small” problems

5. Our approximate procedure Using analytical/numerical method  moments of two stage leadtime  approximate distribution  decompose into two stages  approximate total leadtime  set due date

6. Product structure Fig. 1 A two stage assembly system Simple Two Stage System

7. Analytical Result Cumul. Distr. Func.(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 M 1  minimum assembly time S 1  planned assembly start time 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

8. Leadtime Distribution Estimation Assumptions  normally distributed processing times  approximate leadtime by normal distr.(Soroush,1999) Approximating leadtime distribution  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 normal distribution: N(  W,  W 2 ), t  M 1 + S 1.

9. Due Date Planning Mean absolute lateness  d* = median Standard deviation lateness  d* = mean Asymmetric earliness and tardiness cost  d* by root finding method Achieve a service target  d* by N(0, 1)

10. Industrial Case Study Product structure 17 components Fig. 2 An practical product structure

11. 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.

12. Leadtime distribution comparison Fig. 3 Approximation PDF and Simulation histogram of total leadtime

13. Due date results comparison Table. Due dates to achieve service targets by simulation and approximation methods

14. Discussion & Further Work Production plan/Minimum processing times Skewed distributed processing times More general distribution to approximate, like -type distribution Resource constraint systems