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Turkish Naval Academy. Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System. Mehmet ÇAVDAR 1 , A.Özgür TOY 2 , Emre BERK 3. 1 Turkish Naval Academy, Institute of Naval Sciences and Engineering , İstanbul, Türkiye

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slide1

Turkish Naval Academy

Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System

Mehmet ÇAVDAR1, A.Özgür TOY2, Emre BERK3

1 Turkish Naval Academy, Institute of Naval Sciences and Engineering , İstanbul, Türkiye

2 Turkish Naval Academy, Industrial Engineering Department, İstanbul,Türkiye

3 Bilkent University, Faculty of Business Administration, Ankara, Türkiye

slide2

Outline

  • Introduction
  • Literature Review
  • Problem Definition
  • Simulation Model and Meta-heuristics
  • Numerical Results
  • Conclusion
slide3

Introduction

Multi Echelon Inventory Systems

Item

Distributer

Manufacturer

Retailer

Demand

slide4

Introduction

(S-1, S) Continous Inventory Policy

  • High Value Items
  • Low Demand Rate

Whenever a satisfied demand occurs,

an order is placed at the same time

slide5

H

B

C

I

D

J

E

K

F

L

On hand

On hand

On hand

On hand

On order

On order

On order

On order

Introduction

(S-1, S) Continous Inventory Policy

Inventory Position of the Warehouse

Inventory Position of the Retailer

G

M

Demand

Time = t

G

A

slide6

Introduction

Stockout Condition

Leadtime Dependent Backorder

Backorder Decision

Backorder

Lostsale

slide7

Simulation Optimization with

Search Methods & Meta-heuristics

Introduction

(S-1, S) Policy with Leadtime Dependent Backorder

  • Multi Echelon
  • Multi Retailer
  • Arbitrary Demand Arrival

No Exact Solution

  • Constant Shelflife
  • Nonlinear Holding Cost & Backorder Cost
slide8

Literature Review

(S-1, S) Single Echelon Inventory Systems

(S-1, S) Multi Echelon Inventory Systems

slide9

Literature Review

Simulation Optimization of Inventory Systems

slide10

DEMAND

Ample Supplier

Warehouse

Retailers

Problem Definition

- Two echelon

- Single item

slide11

Problem Definition

Assumptions

  • (S-1,S)continous review
  • Full backorder at warehouse
  • Partial backorder at retailer(s)
  • Constant and deterministic leadtime
  • No lateral transhipment between retailer(s)
  • Arbitrary demand distributions
  • Constant shelflife at retailer level
  • Each demand is only for one unit
slide12

Problem Definition

Objective Function

(Minimize)

  • Total Cost
    • Warehouse
      • Holding Cost
    • Retailers
      • Holding Cost
      • Backorder Cost
      • Lostsale Cost
slide13

Problem Definition

Decision Variables

Optimal inventory levels to minimize the total cost

  • : Order up to level at warehouse
  • : Order up to level at retailer r (r:1..R)
slide14

Problem Definition

Objective Function

: Unit holding cost at warehouse

: Unit holding cost at retailer r

: Unit backorder cost/time at retailer r

: Unit Lostsale cost at retailer r

: Expected Onhand inventory at warehouse

: Expected Onhand inventory at retailer r

: Expected Backorder at retailer r

: Expected Lostsale at retailer r

slide15

Problem Definition

Nonlinear

Linear

Holding Cost

Backorder Cost

slide16

Simulation Model

We used “Discrete Event Simulation”

  • Retailer Demand Arrival
  • Retailer Item Arrival
  • Retailer Item Perish
  • Warehouse Item Arrival
slide17

Simulation Model

Demands & Waiting Tolerance

  • Constant
  • Exponential Distribution
  • Erlang Distribution
  • Normal Distribution
  • Uniform Distribution
  • Weibull Distribution
slide18

Simulation Optimization

Meta-heuristics

  • Simulated Annealing Algorithm
  • Tabu Search Algorithm
  • Scatter Search Algorithm
slide19

Simulation Optimization

Simulated Annealing Algorithm

  • Kirk Patrick et al (1983)
  • To supply consistency of the metal by annealing
  • Fast Search (Look only one of neighbor solutions)
slide20

Simulation Optimization

Simulated Annealing Algorithm

Solution Space

slide21

Simulation Optimization

Simulated Annealing Algorithm

  • Solution
  • A solution is neighbor of the current solution when ;
  • Temperature
slide22

Simulation Optimization

Simulated Annealing Algorithm

Figure for 1 Warehouse - 1 Retailer

slide23

Simulation Optimization

Simulated Annealing Algorithm

Figure for

1 Warehouse - 3 Retailers

slide25

Simulation Optimization

Tabu Search Algorithm

  • Glover (1986)
  • Fast Search (Look only neighbor solutions)
  • Tabu list (Avoid from the local optimum)
slide26

Simulation Optimization

Tabu Search Algorithm

Solution Space

slide27

Simulation Optimization

Tabu Search Algorithm

  • Solution
  • A solution is neighbor of the current solution when ;
  • TabuList:A solution is in the tabu list if this solution is selected as current solution at last iteration
slide29

Simulation Optimization

Scatter Search Algorithm

Glover et al (1997)

  • Take some best and diverse solutions from inital set.
  • Linear Combination of 2 solutions
  • Generate good solutions
slide30

Simulation Optimization

Scatter Search Algorithm

Solution Space

RefSet

ScatterSet

Diverse

Better

Generate New Solutions

slide31

Simulation Optimization

Scatter Search Algorithm

Generate New Solutions

*

*

*

*

slide33

C++ Programming Language

  • We find theoptimal inventory position levels “S”for one warehouse and retailer(s) for given parameters.
slide34

Numerical Results

Experiments for Sensitivity Analysis

  • Poisson arrival process
  • No Shelflife
  • Linear Holding & Backorder Cost
slide35

Numerical Results

Effectiveness of the Meta-heuristics

1 Warehouse

1 retailer

slide36

Numerical Results

Effectiveness of the Meta-heuristics

1 Warehouse

3 retailers

slide37

Conclusion

  • The meta-heuristics are efficient to find the optimal/near optimal solution of the multi echelon inventory system.
    • Simulate Annealing is the fastest algorithm.
    • Tabu search is generally find the best solution among the meta-heuristics. The computational time of this algorithm is long because it computes the all neighbors‘ total costs.
slide38

Future Study

  • The future study may include lateral transshipment among retailers to analyze the effectiveness.
  • The model can be generalized for other inventory policies.
  • Another meta-heuristics can be developed to find the optimal/near optimal inventory for each SKU.
slide39

Turkish Naval Academy

Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System

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