Turkish Naval Academy
Download
1 / 39

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


  • 78 Views
  • Uploaded on

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

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Meta-heuristics Application for Simulation Optimization of the Multi Echelon Inventory System' - raine


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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


Outline

  • Introduction

  • Literature Review

  • Problem Definition

  • Simulation Model and Meta-heuristics

  • Numerical Results

  • Conclusion


Introduction

Multi Echelon Inventory Systems

Item

Distributer

Manufacturer

Retailer

Demand


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


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


Introduction

Stockout Condition

Leadtime Dependent Backorder

Backorder Decision

Backorder

Lostsale


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


Literature Review

(S-1, S) Single Echelon Inventory Systems

(S-1, S) Multi Echelon Inventory Systems


Literature Review

Simulation Optimization of Inventory Systems


DEMAND

Ample Supplier

Warehouse

Retailers

Problem Definition

- Two echelon

- Single item


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


Problem Definition

Objective Function

(Minimize)

  • Total Cost

    • Warehouse

      • Holding Cost

    • Retailers

      • Holding Cost

      • Backorder Cost

      • Lostsale Cost


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)


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


Problem Definition

Nonlinear

Linear

Holding Cost

Backorder Cost


Simulation Model

We used “Discrete Event Simulation”

  • Retailer Demand Arrival

  • Retailer Item Arrival

  • Retailer Item Perish

  • Warehouse Item Arrival


Simulation Model

Demands & Waiting Tolerance

  • Constant

  • Exponential Distribution

  • Erlang Distribution

  • Normal Distribution

  • Uniform Distribution

  • Weibull Distribution


Simulation Optimization

Meta-heuristics

  • Simulated Annealing Algorithm

  • Tabu Search Algorithm

  • Scatter Search Algorithm


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)


Simulation Optimization

Simulated Annealing Algorithm

Solution Space


Simulation Optimization

Simulated Annealing Algorithm

  • Solution

  • A solution is neighbor of the current solution when ;

  • Temperature


Simulation Optimization

Simulated Annealing Algorithm

Figure for 1 Warehouse - 1 Retailer


Simulation Optimization

Simulated Annealing Algorithm

Figure for

1 Warehouse - 3 Retailers



Simulation Optimization

Tabu Search Algorithm

  • Glover (1986)

  • Fast Search (Look only neighbor solutions)

  • Tabu list (Avoid from the local optimum)


Simulation Optimization

Tabu Search Algorithm

Solution Space


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



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


Simulation Optimization

Scatter Search Algorithm

Solution Space

RefSet

ScatterSet

Diverse

Better

Generate New Solutions


Simulation Optimization

Scatter Search Algorithm

Generate New Solutions

*

*

*

*



  • C++ Programming Language

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


Numerical Results

Experiments for Sensitivity Analysis

  • Poisson arrival process

  • No Shelflife

  • Linear Holding & Backorder Cost


Numerical Results

Effectiveness of the Meta-heuristics

1 Warehouse

1 retailer


Numerical Results

Effectiveness of the Meta-heuristics

1 Warehouse

3 retailers


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.


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.


Turkish Naval Academy

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


ad