The Study for Product Variety Optimization

1. The Study for Product Variety Optimization 　　　　　課程老師：陳茂生 教授 　　　　　　　　　　阮約翰 教授 　　　　　報告學生：鄭漢中 937802

2. Reference • Karl Ulrich (1995), ” The role of product architecture in the manufacturing firm,” Research Policy, Vol. 24, pp. 419-440. • Kikuo Fujita (2002), ” Product variety optimization under modular architecture,” Computer-Aided Design, Vol. 34, pp. 953-965. • David He, Andrew Kusiak* and Tzu-liang(Bill) Tseng (1998), “Delayed product differentiation：a design and manufacturing perspective,” Computer-Aided Design, Vol. 30, No. 2, pp. 105-113.

3. Agenda • Introduction • Product Architecture • Product variety • Module attribute optimization • Module combinatorial optimization • Part modularity optimization • Conclusion

4. Introduction • 大量客製化的趨勢 • Product Architecture importance • 產品結構的適當與否，不僅決定了產品本身的品質與開發專案績效，也直接影響到後端供應鏈的管理方式 • Product variety design • 同時考量多個產品的設計 • Product variety optimization problem • 產品結構的設計、產品模組選擇、模組屬性的決定、零件模組化最佳、Product differentiation point（push-pull）的決定 ….

5. box protect cargo from weather hitch connect to vehicle fairing minimizeair drag bed support cargo loads springs suspendtrailer structure wheels transfer loadsto road What is Product Architecture chunks functions • The physical elements of a product are the parts, components, and subassemblies that implement the product’s function. • The physical elements of a product are typically organized into several major physical building blocks, referred to as chunks. • The product architecture is the scheme by which the functional elements of the product are arranged into physical chunks and how the chunks interact with each other.

6. Modular vs. Integral • A modular architecture usually has the following properties • Each chunk implement one or a few functional elements • The interactions between chunks are well defined • A integral architecture usually has the following properties • Functional elements are implemented with more than one chunk • A single chunk implements many functional elements • The interactions between chunks are not well defined and may be incidental to the primary functions of the product • A productis rarely strictly modular or integral. Modularity is used to characterize the relative degree of this property.

7. Product Variety • Product variety is a vital element in mass customization. • High variety can be produced by any production system at some cost. • Manufacturing flexibility and product architecture interact to enable high product variety. Differentiate process and assembly flexibility.

8. Problem Focus • Attribute quantification – to develop modules across multiple product by quantifying attributes under acceptable ranges of specifications • Combinatorial selection – to develop multiple products by selecting practical combinations of modules from feasible ones. Class I – to optimize module attributes under fixed module combination Class II – to optimize module combination under pre-defined module candidates Class III – to simultaneously optimize both module attributes and module combination

9. Tradeoffs needs optimization • Cost depended on production volume – the commonalization of modules for different products causes excess cost per unit due to over-specification • Cost depended on the number of product and module kinds

10. Attribute optimization under Stretch-based Design

11. Stretch-based Aircraft Design

12. Stretch-based Aircraft Design • The stretch-based enlargement of fuselage is directly effective for the increase of seats of less expense, while it has some side effects on other features through mutual functional couplings. • The compromises on the underlying tradeoffs is essential for achieving the optimal design, since these stretches and replacements have side effects beside their primary effects. • The coupled attributes of different modules must be simultaneously optimized toward product variety optimality. Class I problem: constrained real-number non-linear mathematical programming

13. Example The design is aimed at the same seat number and the increased different cruise range

14. Implications • The optimal module combination varies with the range of product variety. (three optimal designs along the x-axis) • Other similar designs are worse than the two chosen designs. • The totally independent design is the worst in most parts. • The product variety optimization with an abstracted mathematical basis is important for rationally planning multiple products under complicated conditions.

15. Module combinatorial optimization Class II problem: integer, constrained non-linear mathematical programming, a combinatorial problem.

16. Example

17. Result - I

18. Result - II

19. Result - III

20. Implications • There is a cost reduction (2.6%) by the optimization. • The cost incurred by the module types is decreased due to the reduction of the number of different modules. • The cost is also increased by the over-specification due to module diversion. • The optimal solution depends on the production volume.

21. Problem Focus • 利用設計產品結構的手法，將產品零件(Integral component) 拆解設計成標準零件或模組化零件

22. The part classification scheme

23. 假設 • 所有標準品均已確定，設計者主要目的在於將integral Design設計成包含標準品之differential designs，且一次只考慮一種設計，不同時考慮兩種設計的情況 • 組裝系統沒有buffer存在且很流蝪 • Job 單方向移動無迴流情況產生 • 每個工作站一次只處理一件Job，Job的處理時間為該站總工作組裝時間 • 假設給定目標生產率為q且生產線平衡 • 直線型組裝線

24. 基本法則 • 避免當assembly level h<H時，將元件設計成包含半組裝件之差異設計 • 避免差異設計設計的組裝時間大於組裝系統的cycle time的情況發生 • 避免superimposed assembly graph產生cycle的情況發生

25. The example for Rule 1. • The reason for rule 1 is： a. A complex digraph b. assembly time is eliminated

26. The example for Rule 3.

27. The integer programming formulation Notation is defined： • K = set of parts • Nk = set of differential designs for part k • N = , set of all differential designs • A = set of connections from the set Nv to set Nw, and v !=w • d ij = part count differentiation cost for designs i and j defined in eqn (5) • u = unit manufacturing cost • ri = u△Cmax (i) = manufacturing cost change due to differential design i • xi =1 , if differential design i is selected =0 , otherwise • yij=1, if differential design i and j is selected =0 , otherwise

29. The impact of differential designs on manufacturing cycle time Notation is defined： • t(*) = processing (machining or assembly ) time of a part or subassembly • h = assembly level index • Q(h) = the set of parts at assembly level h • Ah = subassembly at level h • H = the maximum assembly level of a digraph • Pj = part j of differential design of part P • SP(P) = the set of parts in the differential design of part P • A(P) = subassembly of the differential design of part P • Cmax (i) = the makespan of aggregate schedule when part P ( corresponding to integral design i ) is integral • C’max (i) = the makespan of aggregate schedule when part P is designed as differential design i. • △Cmax (i) = C’max (i) - Cmax (i) = the change in the makespan due to the differential design i .

30. The impact of differential designs on manufacturing cycle time • If differential design i of part P of class A contains no subassembly: • If differential design i of part P of class A contains a subassembly A(P):

31. For differential design i of part P of class B • For differential design i of part P of class C

32. The part count differentiation cost • ei=[ei1,… eim, … eiM] Where eim =1 ,if differential design i uses part type m =0 ,otherwise • Part count differentiation cost: for all i and j Where q(eim, ejm)=1 , if eim!= ejm =0,otherwise Wm=the most cost efficient of part type m

33. Illustrative example

34. Illustrative example(2)-step1

35. Illustrative example(3)-step2 • D2 violates rule2 and • D6 violates rule1

36. Illustrative example(4)-step3 Let Wm=1 & u=1

37. The optimal designs D1,D3,and D5 are selected

38. Conclusion • Product variety optimization should be considered in the planning phase, which contain many parameters involved in optimization models that are difficult to determine with enough accuracy and reliability → robustness for product variety optimization. • Computational methods (OR approach) have rational bases to find the optimal design. • The optimization methodology only can be used in a single factory and only a single design was considered