Selection of Inventory Control Points in Multistage Pull Systems

1. Selection of Inventory Control Points in Multistage Pull Systems Ronald G. Askin Shravan Krishnan Systems & Industrial Engineering University of Arizona Tucson, AZ 85721

2. Overview • Problem Introduction • Brief Literature Review • Model 1 – Known Container Size • Model 2 – Selecting the Container Size • Model 3 – Stage Dependent Containers • Summary and Conclusions

3. Tucson: Sonoran Desert

4. Kanban Controlled Pull System

5. Kanban Uses & Advantages • Low – Moderate Variety • Moderate – High Volume, Low Variability • Reliable Processes (Predictable Lead Time) • Low Information System Requirement • Self-adjusting (to minor variation/uncertainty) • Minimal Inventory Accumulation

6. Kanban Control with Distant Workstations

7. Background Literature General Texts: • Y. Monden, TPS, 1998 (+ T. Ono) • Askin & Goldberg, Lean Production Systems, 2002 • R. Schoenberger, Japanese Mfg. Tech., 1982 • Research: • Askin et al. IIE Trans., 1993 • Mitra & Mitrani, Mgmt Sci., 1990, • Wang & Wang, IJPR, 1990, • Spearman et al., IJPR, 1990 (CONWIP) • Philipoom eta al, IJPR, 1987

8. Selecting the Control Points

9. Notation: a = setup cost plus MH cost/n at i C = collection time at stage i D = Demand (mean/time) f = Fixed buffer cost/time M = # stages h = holding cost per unit/time at i L = Production lead time at i t = transport time from i α = Service rate  = Standard dev. demand/time Variables: Model 1:Container Size Known = lead time i thru j

10. Known Container Size n Minimize Costs (Fixed, Setup, Cycle, SS) Subject to: All stages assigned; Identify Control Points; Continuous Sections; Last Stage has Buffer

11. Shortest Path Analogy = Relevant Cost if j and k are consecutive control points

12. Single Control Section Result Note: Sufficient condition almost always holds since for a, b >0,

13. Model 2:Selecting n • Case 1: Fixed Processing time • Case 2:Variable Processing time Add WIP cost to objective function

14. Model 2 Case 2 • Theorem 1 still holds for any n • Shortest Path Problem given n Nonlinear! where

15. Model 2:Computational Results • Case 1: • f = $0, $1000 (two configurations) • a = [0.1,0.12,0.13,0.08,0.15,0.22] • h = [1,2,3,4,5,6], [1,1,1,1,1,1] (2 configurations) • D = 100 units per day • α = 0.95 • σ= 5 units • c = 0.2 days for each stage • p = 0.1 days for each stage • Number of stages = 6.

16. Model 3:Stage Dependent Container • Nesting property: • Objective function: Integer r Subject to

17. Heuristic 1. Estimate container sizes (working backwards from m to 1)

18. Heuristic cont. 2. Compute heuristic flow costs for shortest path algorithm Case 1

19. Case 2

21. Single control point often optimal for simple system Expression for container size Multiple control points for highly varying costs (high value added) Multiple products with limited processor time Assembly and General product structures Discrete (Poisson) demand Batch vs. Unit processors (eg. Ovens) Summary and Future