M. Ogura, M. Kishida, and A. Yassine, “Optimizing product development projects under asynchronous and aperiodic system-local interactions,” in 21st International DSM Conference, 2019, pp. 97-106.

1. Optimizing product development projects under
asynchronous and aperiodic
system-local interactions
Masaki Ogura
Nara Institute of Science and Technology, Japan
Masako Kishida
National Institute of Informatics, Japan
Ali Yassine
American University of Beirut, Lebanon
Full version published in Research in Engineering Design

2. Work Transformation Matrix (WTM)
 WTM = quantitative DSM, focused on works
DSM
A B C D E
A x x
B x
C x x
D x
E x x
WTM
A B C D E
A 0.6 0.6 0.2
B 0.5 0.1
C 0.1 0.4 0.7
D 0.1 0.5
E 0.1 0.9 0.6
From D to E
Within A
transferred to / kept within modules
Fraction of work amounts that is
Smith, Eppinger, “Identifying controlling features of engineering
design iteration,” Management Science, 1997.

3. How WTM works

 𝑥𝑥 𝑘𝑘 + 1 = 𝑊𝑊𝑥𝑥(𝑘𝑘)
A
D
B
C
E
Time
Remaining
work
Vector of remaining work
WTM
A B C D E
A 0.6 0.6 0.2
B 0.5 0.1
C 0.1 0.4 0.7
D 0.1 0.5
E 0.1 0.9 0.6
𝑥𝑥 𝑘𝑘 =
𝑥𝑥𝐴𝐴(𝑘𝑘)
𝑥𝑥𝐵𝐵(𝑘𝑘)
𝑥𝑥𝐶𝐶(𝑘𝑘)
𝑥𝑥𝐷𝐷(𝑘𝑘)
𝑥𝑥𝐸𝐸(𝑘𝑘)

4. Resource allocation for PD process acceleration
 Improvement of WTM
 𝑊𝑊 𝑉𝑉
𝑥𝑥𝑡𝑡+1 = 𝑉𝑉𝑥𝑥𝑡𝑡
𝑥𝑥𝑡𝑡+1 = 𝑊𝑊𝑥𝑥𝑡𝑡
𝑡𝑡
||𝑥𝑥𝑡𝑡||
𝑊𝑊 =
1/2 1
1 1/2
𝑉𝑉 =
𝟎𝟎 1
1 1/2
𝑉𝑉 =
1/2 𝟏𝟏/𝟐𝟐
1 1/2
𝑉𝑉 =
𝟏𝟏/𝟒𝟒 1
1 𝟏𝟏/𝟒𝟒
PD process acceleration
Optimal improvement within budget?
HR management, information
technology, resolving dependency, ...
Several options...

5. System/local structure [Yassine et al., RIED, ‘03]
 Extended WTM structure
System team
Local team
Frequent
information update
𝑘𝑘 = 0, 1, 2, …
Intermittent
system feedback
𝑘𝑘 = 𝜏𝜏0, 𝜏𝜏1, 𝜏𝜏2, …
A B C D E A B C D E
A
B
C
D
E
A
B
C
D
E
Local
System
→ Local
System
Local →
System

6. Time-varying WTM
System team
Local team
System team
Local team
A B C D E A B C D E
A
B
C
D
E
A
B
C
D
E
Local
System
→ Local
System
Local →
System
A B C D E A B C D E
A
B
C
D
E
A
B
C
D
E
Local
System
Local →
System
𝑊𝑊𝑓𝑓 𝑊𝑊
𝑝𝑝

7.  Periodic system feedback [Yassine et al., RIED, 2003]
Coping with uncertainty
𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇
Transition of remaining work
𝑥𝑥 → 𝑊𝑊
𝑝𝑝𝑥𝑥 → 𝑊𝑊
𝑝𝑝
2
𝑥𝑥 → ⋯ → 𝑊𝑊
𝑝𝑝
𝑇𝑇−1
𝑥𝑥 → 𝑊𝑊𝑓𝑓𝑊𝑊
𝑝𝑝
𝑇𝑇−1
𝑥𝑥
Generalized WTM
Determines feasibility
of PD process
Infeasible
Feasible 1
Spectral radius
Spectral radius as a feasibility index

8. System feedback may not necessarily occur regularly
 Periodic system feedback [Yassine et al., RIED, 2003]
 Aperiodic system feedback (this research)
 Assumption: 𝑇𝑇𝑘𝑘’s are independent and identically distributed
random variables
Coping with uncertainty
𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇 𝑇𝑇
𝑇𝑇1 𝑇𝑇2 𝑇𝑇3 𝑇𝑇4 𝑇𝑇5 𝑇𝑇6

9. Theoretical results
 Result 1: Generalized WTM
 𝑀𝑀 = 𝐸𝐸[𝑊𝑊𝑓𝑓𝑊𝑊
𝑝𝑝
𝑇𝑇−1
]
 Spectral radius as a feasibility index
 Process improvement problem
 How should we distribute our managerial resource to minimize the
feasibility index 𝜌𝜌(𝑀𝑀)?
mathematical expectation
𝑇𝑇 = random interval
Infeasible
Feasible 1
Spectral radius

10. Theoretical results
 Result 2:
 Resource allocation problem can be solved via convex
optimization.
 Scales well with respect to the size of PD process
 Very fast solvers available: allows making quick decisions
 Details in the proceeding: geometric programming plays a key
role

11. Automobile appearance design [McDaniel, ‘96]
 Case overview
 Part of automobile PD process
 Process of designing all interior and exterior auto-mobile
surfaces for better appearance, surface quality, and operational
interface.
 Engineering (local) team responsible for the feasibility of
designs
 Styling (system) team responsible for the appearance of the
vehicle
 Tasks: (1) carpet, (2) center console, (3) door trim panel, (4)
garnish trim, (5) overhead system, (6) instrument panel, (7)
luggage trim, (8) package tray, (9) seats, and (10) steering wheel.

12. Automobile appearance design [McDaniel, ‘96]
 Nominal WTMs

13. Problem formulation
 Assumption
 Maximum reduction = 15%
 Reduction cost proportional to reduction amount
 Feedback intervals randomly fluctuated
 Question: Which DSM entry should we invest on?
 Comparison
 Eigenvector-based method assuming constant feedback
intervals [Yassine, RIED, 2003]

14. Results
 Comparison of investment pattern
Proposed Conventional

15. Feasibility index
Proposed
Conventional

16. PD process simulation
Time Project completion time
Remaining
work

17. Conclusion
 Optimal resource allocation for improving PD processes
 Theoretical analysis: Feasibility index
 Based on tools from systems and control engineering
 Decision support tool based on convex optimization
 Improves existing heuristic methodology based on eigenvector
centralities
 Thank you!
Journal version: Ogura, Harada, Kishida, Yassine, “Resource optimization of product development
projects with time-varying dependency structure,” Research in Engineering Design, vol. 30, no. 3,
pp. 435–452, 2019.