On Component Commonality for Assemble-to-Order Systems

Transcription

1 On Component Commonality for Assemble-to-Order Systems Hongfeng Liang Advanced Optimization Laboratory McMaster University August 01, 2014 Joint work with Antoine Deza, Kai Huang, Xiao Jiao Wang

2 Outline 1 Introduction Assemble-to-Order(ATO) Literature Review Basic Model 2 Component Commonality Zhang System Remove Component Commonality Λ System 3 Conclusions & Future Work Benefits Future Work Conclusions

3 Outline 1 Introduction Assemble-to-Order(ATO) Literature Review Basic Model

4 ATO What is ATO High demand for the product customizability, fast market respond and short life cycles of products Based on delayed differentiation allowing for assembly of final products within the customer lead time to eliminate stock of final products. Component replenishment lead times are much more significant than product assemble time Main difference between ATO and Build to Stock(BTS): inventory level Classified by review period, optimization problem objectives and decisions made in the optimization problem.

5 Literature Review Related Work Component Commonality is often considered beneficial Focus on common component design Consider service level constraint Often consider a single period case

6 Basic Model Basic Setting Periodic review Independent base stock policy First Come First Served(FCFS) rule for demand satisfaction Random demands of products for each period Deterministic lead time Reward collected when the assembly is within the time window

7 Basic Model Event Sequence Inventory position reviewed New replenishment order of components placed Earlier replenishment order arrived Demand realized Component allocated and product assembled Associated rewards accounted

8 Basic Model Base Stock Policy Base stock policy with deterministic lead times I i,t 1 + A i,t D i,t = I i,t A i,t = D i,t Li 1 I i,t = S i D i [t L i, t] where D i [s, t] = t µ=s D i,µ for s t

9 Basic Model Stochastic Integer Programming 1 ATO inventory management problem formulated as two-stage stochastic integer program 2 Base stock level is decided in the first stage 3 Inventory investment controlled by a given budget B 4 Demand of products as a collection of random variables ξ. 5 Solved by Sample Average Approximation(SAA) method.

10 Basic Model Allocation Formulation where max s.t. k µ=0 j=1 w m j ( ) r jk x jk Alloc(S, ξ) j=1 k=0 L+1 x jk = P j k=0 j = 1,..., m m a ij x jµ Oi k i = 1,..., n, k = 0,..., L + 1 O k i x jk Z + j = 1,..., m, k = 0,..., L + 1 :=(S i D L i k i ) + k L

11 Basic Model Joint Formulation max s.t. IE[Alloc(S, ξ)] n c i S i B i=1 S i Z + i = 1,..., n ( Joint(B) )

12 Basic Model Deterministic Joint Formulation max 1 N s.t. k N w m j r jk x /h jk h=1 j=1 k=0 m µ=0 j=1 L+1 k=0 x /h jk ( JointD (B) ) = P/h j j = 1,..., m, h = 1..., N a ij x /h jµ Ok/h i i = 1,..., n, k = 0,..., L + 1, h = 1..., N n c i S i B i=1 S i Z + i = 1,..., n x /h jk Z + j = 1,..., m, k = 0,..., L + 1, h = 1..., N

13 Outline 1 Introduction Assemble-to-Order(ATO) Literature Review Basic Model 2 Component Commonality Zhang System Remove Component Commonality Λ System

14 Zhang System Zhang System Component i c i Product L i j Mean StdDev r j Bill of Material Problem setting of Zhang s system(1997)

15 Zhang System Zhang Optimal Solution Budget C 1 C 2 C 3 C 4 C 5 LB UB Optimal base stock levels and Type-II Service Levels

16 Zhang System Questions? 1 What zeros mean? 2 Impact of budget B 3 What happens between 5,000 and 8,000? 4 Standard Budget: B := m i=1 n j=1 a ij D i (L i + 1) c i

17 Remove Component Commonality Remove Component Commonality 1 Separate inventories of the same component for different products. 2 Keep other parameters unchanged 3 Update the bill of material accordingly

18 Remove Component Commonality new Bill of material C 11 C 21 C 31 C 12 C 22 C 32 C 23 C 33 C 43 C 44 C 54 P P P P Zhang -BOM

19 Remove Component Commonality Zhang Optimal Solution Budget CC-UB WCC-UB CC-LB WCC-LB Objective Value:CC VS WCC

20 Remove Component Commonality CC vs WCC 350 CC V.S. WCC OBJ, Realization:50, Sample: CC UB WCC UB CC LB WCC LB Budget

21 Λ System Λ Configuration C 1 P 1 1 P 2 1 Λ-BOM C 1 P 1 P 2 C 1 C 2 P P Λ -BOM C 1 P 1 C 2 P 2

22 Λ System One Realization Let f (B),g(B) be the optimal objective of CC, respectively, WCC. Theorem f and g are both monotonically non-decreasing functions. f (B) g(b) since an optimal solution of CC is feasible for WCC {f (B) < g(b)} {min(d 1, D 2 ) < B < D 1 +D 2 +max(p 1, P 2 )}.

23 Λ System CC vs WCC B min = min 2 i=1 {mink j=1 {Dj i }} B + min = mink j=1 {Dj 1 + Dj 2 } B + max = max k j=1 {Dj 1 + Dj 2 } B Σ max = k j=1 {max{dj 1 + Pj 1, Dj 2 + Pj 2 }} Budg # real. [0, B min ] (B min, B + min ] (B+ min, B+ max] (B max, + Bmax] Σ (Bmax, Σ + 1 = < < < 2 = < = k = < or > = f(b) vs g(b) for Λ System

24 Outline 1 Introduction Assemble-to-Order(ATO) Literature Review Basic Model 2 Component Commonality Zhang System Remove Component Commonality Λ System 3 Conclusions & Future Work Benefits Future Work Conclusions

25 Benefits Advantages of WCC 1 Fits both startup and large companies 2 Reduce capital cost 3 Increased return on every $ invested 4 Easy to use

26 Future Work CC or WCC 1 Further analysis of CC vs WCC 2 BOM optimization 3 Optimality for BOM optimization

27 Conclusions Conclusions 1 Impact of the budget in component commonality for ATO systems 2 A framework and computational results substantiating the potential benefits arising from decoupling components. 3 A theoretical analysis for Λ System showing the impact of component commonality Thank You!

28 Reference Reference I N. Agrawal, M.A. Cohen: Optimal material control in an assembly system with component commonality. Naval Research Logistics, 48: , Y. Akcay, S.H. Xu: Joint Inventory Replenishment and Component Allocation Optimization in an Assemble-to-Order System, Management Science Vol.50:99-116, 2004 Y. Zhao,D. Simchi-Levi: Peformance analsyis and evaluaation of assemble to order systems with stochastic sequential lead times. Operations Research, 54(4): , Dogru, M., M. Reiman, Q. Wang. A stochastic programming based inventory policy for assemble-to-order systems with application to the W model. Working paper, Alcatel-Lucent Bell Labs. NJ. John R. Birge and Franois V. Louveaux. Introduction to Stochastic Programming. Springer Verlag, New York, Holweg, M. and Pil, F. (2001),?Successful Build-to-Order Strategies start with the Customer?, MIT Sloan Management Review, Fall issue, Vol. 43, No. 1, p Mirchandani, P. and A. Mishra, Component Commonality: Models with Product-specific Service Constraints, Production and Operations Management, 11 (2002), B. Barney: Introduction to Parallel Computing. comp/