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

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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

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

(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

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

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

Simulation Optimization of Inventory Systems

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

Objective Function

(Minimize)

- Total Cost
- Warehouse
- Holding Cost
- Retailers
- Holding Cost
- Backorder Cost
- Lostsale Cost

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)

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

We used “Discrete Event Simulation”

- Retailer Demand Arrival
- Retailer Item Arrival
- Retailer Item Perish
- Warehouse Item Arrival

Demands & Waiting Tolerance

- Constant
- Exponential Distribution
- Erlang Distribution
- Normal Distribution
- Uniform Distribution
- Weibull Distribution

Meta-heuristics

- Simulated Annealing Algorithm
- Tabu Search Algorithm
- Scatter Search Algorithm

Simulated Annealing Algorithm

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

Simulated Annealing Algorithm

- Solution

- A solution is neighbor of the current solution when ;

- Temperature

Tabu Search Algorithm

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

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

Scatter Search Algorithm

Glover et al (1997)

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

Scatter Search Algorithm

Solution Space

RefSet

ScatterSet

Diverse

Better

Generate New Solutions

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

Experiments for Sensitivity Analysis

- Poisson arrival process
- No Shelflife
- Linear Holding & Backorder Cost

- 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.

- 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.

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

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