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

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

Introduction• Delivery performance

• Uncertainties

• Complex product system– Assembly– Product structure

• Problem : setting due date in complex product systems with uncertain processing times

Literature ReviewTwo 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

Our approximate procedure

• Using analytical/numerical method

moments of two stage leadtime

approximate distribution

decompose into two stages

approximate total leadtime

set due date

• Product structure

Fig. 1 A two stage assembly system

Simple Two Stage System

ComponentManufacturing

Assembly

11 12 1n

1

Analytical Result• Cumul. Distr. Func.(CDF) of leadtime W is:

FW(t) = 0, t<M1+S1;

FW(t) = F1(M1) FZ(t-M1) + F1FZ, t M1 + S1.where

M1 minimum assembly time

S1 planned assembly start time

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

Leadtime Distribution EstimationAssumptions 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, Z2 and Q, Q

2

Obtain mean and variance of leadtime W(=Z+Q):

W = Q+Z, W2 = Q

2+Z2

Approximate W by normal distribution:

N(W, W2), t M1+ S1.

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)

Industrial Case Study• Product structure

17 components 17 components

Fig. 2 An practical product structure

Stage 1

Stage 2

Stage 3

Stage 4

Stage 5

Stage 6 … … … …

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.

Leadtime distribution comparison

Fig. 3 Approximation PDF and Simulation histogram

of total leadtime

Due date results comparison

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

Table. Due dates to achieve service targetsby simulation and approximation methods

Discussion & Further Work

• Production plan/Minimum processing times

• Skewed distributed processing times

• More general distribution to approximate, like

-type distribution

• Resource constraint systems