ROBUST CAPACITY PLANNING IN A MAKE-TO-ORDER JOB-SHOP

Prof. Dr. José Antonio Heredia Álvaro

Industrial System Engineering and Design Department

Universitat Jaume I

Castellón - Spain

MAKE-TO-ORDER PLANNING

• It is fundamentally a capacity planning problem

• A trade-off between cost and quality of service:

+capacity +manufacturing cost

+capacity -WIP

+capacity quality of service

Lead-time

Reliability

Case example

Product family: Sprinkler clampWorkstation: Press 160 and Press 200Customer : HiltiDemand 2013: 2,5 million units

Stock level: 220.000 unitsService level: 96%Lead time: 5 days

Cycle time distribution

• A very complex problem using traditional approaches

• With traditional queuing theory researchers doesn´t find the solution ->

approximations for the mean (and variance in some cases)

• Embedded Markov chains at departure epochs allows to obtain the exact

density function in some simple cases (Neuts, Bertsimas)

• The approach that I´m developing solve this problem with a different paradigm

Example of PH-distribution

l l

p0

1-p0

phase-type distribution as a network of exponential processes among which with certain probability transitions may occur

Example: workstation with 2 machines

l

m1

m2

0,0 1,0 2,0

0,1 1,1 2,1

l

m1

m2

m1

m2

l

l

2,b

l

m1 +m2

m1

m1

m2l l

Cycle time distribution

PH-distribution modelling

1TH

TH

PH-characterization

=( ,0, 1- )a D D

p1=1-p0

Function relating Lead-Time and Capacity

1

2

3

4

5

6

7

8

9

0,5 0,6 0,7 0,8 0,9 1 1,1 1,2 1,3 1,4 1,5

Lead Time

Capacity

service level95%

90 %

85 %

1

1,5

2

2,5

3

3,5

4

4,5

5

5,5

6

1 3 5 7 9 11

Lead Time

Buffer size

95%

90%

85%

Conclusions

•The new approach allows modeling more realistic cases that previous

•For simple cases the approach is accurate

•Provides valuable insights to understand the system behavior

•It is a pedagogical tool to master the art of simulation modeling