Selection of Inventory Control Points in Multistage Pull Systems

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Selection of Inventory Control Points in
Multistage Pull Systems

• Ronald G. Askin
• Shravan Krishnan
• Systems Industrial Engineering
• University of Arizona
• Tucson, AZ 85721

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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

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Tucson Sonoran Desert
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Kanban Controlled Pull System
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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

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Kanban Control with Distant Workstations
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Background Literature

• 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

• General Texts
• Y. Monden, TPS, 1998 ( T. Ono)
• Askin Goldberg, Lean Production Systems, 2002
• R. Schoenberger, Japanese Mfg. Tech., 1982

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Selecting the Control Points
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Model 1 Container Size Known

• 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
• a Service rate
• ? Standard dev. demand/time

• Variables

lead time i thru j
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Known Container Size n

• Minimize Costs (Fixed, Setup, Cycle, SS)
• Subject to
• All stages assigned
• Identify Control Points
• Continuous Sections
• Last Stage has Buffer

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Shortest Path Analogy
Relevant Cost if j and k are consecutive
control points
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Single Control Section Result
Note Sufficient condition almost always holds
since for a, b gt0,
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Model 2 Selecting n

• Case 1 Fixed Processing time
• Case 2Variable Processing time

Add WIP cost to objective function
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Model 2 Case 2

• Theorem 1 still holds for any n
• Shortest Path Problem given n

Nonlinear!
where
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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
• a 0.95
• s 5 units
• c 0.2 days for each stage
• p 0.1 days for each stage
• Number of stages 6.

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Model 3 Stage Dependent Container

• Nesting property
• Objective function

Integer r
Subject to
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Heuristic
1. Estimate container sizes (working backwards
from m to 1)
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Heuristic cont.
2. Compute heuristic flow costs for shortest path
algorithm
Case 1
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Case 2
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Summary and Future

• 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)