General Variable Neighborhood Search applied to the picking process in a warehouse

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

General Variable Neighborhood Search applied tothe picking process in a warehouse

Borja Menendez 1, Eduardo G. Pardo 2, Abraham Duarte 3,Antonio Alonso-Ayuso 4, Elisenda Molina 5

Universidad Rey Juan Carlos 1 2 3 4, Universidad Carlos III 5

borja.menendez@urjc.es 1, eduardo.pardo@urjc.es 2, abraham.duarte@urjc.es 3,antonio.alonso@urjc.es 4, emolina@est-econ.uc3m.es 5

October 8, 2014

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Outline

1 Introduction

2 Order Batching Problem

3 General Variable Neighborhood Search

4 Computational experiments

5 Conclusions

Borja Menendez GVNS applied to warehouses

3/22

IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Outline

1 Introduction

2 Order Batching Problem

3 General Variable Neighborhood Search

4 Computational experiments

5 Conclusions

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Introduction

A very important issue in the last few years

Two different problems:

Batching

Routing

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Outline

1 Introduction

2 Order Batching Problem

3 General Variable Neighborhood Search

4 Computational experiments

5 Conclusions

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Order Batching Problem

Two basic order-picking strategies:

Strict-order pickingOrder batching

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Order Batching Problem

Two basic order-picking strategies:

Strict-order pickingOrder batching

Order batching: several orders into batches

Weight constraint

Batches assigned to pickers

Objective: to minimize total time to collect batches

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Warehouse considerations

Parallel aisles (equal lenght). Two crossing aisles.

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Routing strategies (S-Shape)

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Routing strategies (Largest gap)

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Routing strategies (Combined)

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

State of the art

Proved to be NP-hard (number of orders per batch > 2)

Three heuristic categories (De Koster et al., 1999):

Basic methods as FCFSSeed methods generates batches sequentiallySaving methods as Clarke and Wright

Albareda-Sambola et al. (2009) → VND (Exchange)

Exchange is, as far as we know, the best method

Borja Menendez GVNS applied to warehouses

13/22

IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Outline

1 Introduction

2 Order Batching Problem

3 General Variable Neighborhood Search

4 Computational experiments

5 Conclusions

Borja Menendez GVNS applied to warehouses

14/22

IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

General Variable Neighborhood Search

VNS: based on systematic changes of neighborhood

Three straightforward facts:

A local minimum in a neighborhood structure is not necessarilya local minimum in another oneA global minimum is local minimum with respect to allpossible neighborhood structuresFor many problems, local minima with the same or a differentneighborhood structure are relatively close

Different schemes → General VNS (GVNS)

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Pseudocode GVNS

Algorithm 1 GVNS(f , maxiter , kmax)

1: for i ← 1 to maxiter do2: k ← 13: repeat4: f ′ ← Shake(f , k)5: f ′′ ← VND(f ′)6: NeighborhoodChange(f , f ′′, k)7: until k = kmax

8: end for9: return f

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Outline

1 Introduction

2 Order Batching Problem

3 General Variable Neighborhood Search

4 Computational experiments

5 Conclusions

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Computational experiments

Test cases:

600 (selected 20 to adjust parameters), fromAlbareda-Sambola et al.Instances divided into five groups (number of orders)Order size: 1-7 items, 1 kg per item, capacity: 12 kg

Parameters: kmax and maxiter set to 5

Execution: Java 6, Intel Core i7 (3.4 GHz), 4 GB RAM

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Comparison with Exchange algorithm

Dev. (%) CPUt (ms) #Best

GlobalGVNS 0.55 248.55 335

Exchange 1.12 421.12 134

Table : Comparison of GVNS and Exchange algorithms

Wilcoxon test: statistically significant differences

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Outline

1 Introduction

2 Order Batching Problem

3 General Variable Neighborhood Search

4 Computational experiments

5 Conclusions

Borja Menendez GVNS applied to warehouses

20/22

IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

Conclusions

Order Batching Problem in a parallel aisle warehouse

Proposed a General VNS

GVNS compared with best previous algorithm

GVNS outperforms it, differences statistically significant

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

References

Albareda-Sambola, M, A Alonso-Ayuso, E Molina and CSimon de Blas (2009), “Variable neighborhood search fororder batching in a warehouse”, Asia-Pacific Journal ofOperational Research, 1, 655–683.

De Koster, R, E van der Poort and M Wolters (1999),“Efficient orderbatching methods in warehouses”, Int J ProdRes, 37 (7), 1479–1504

Borja Menendez GVNS applied to warehouses

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IntroductionOrder Batching Problem

General Variable Neighborhood SearchComputational experiments

Conclusions

General Variable Neighborhood Search

applied to the picking process in a warehouse

Borja Menendez 1, Eduardo G. Pardo 2, Abraham Duarte 3,Antonio Alonso-Ayuso 4, Elisenda Molina 5

Universidad Rey Juan Carlos 1 2 3 4, Universidad Carlos III 5

borja.menendez@urjc.es 1, eduardo.pardo@urjc.es 2, abraham.duarte@urjc.es 3,antonio.alonso@urjc.es 4, emolina@est-econ.uc3m.es 5

Borja Menendez GVNS applied to warehouses