Facility Location - Concepts, Models, Algorithms and Case Studies

Contents

Introduction

References

1 Distance Functions in Location Problems

1.1 Distance and Norms Specifications

1.2 Distances Function

1.3 Different Kinds of Distances

1.3.1 Aisle Distance

1.3.2 Distance Matrix

1.3.3 Minimum Lengths Path

1.3.4 Block Distance

1.3.5 Gauges Measures

1.3.6 Variance of Distances

1.3.7 Hilbert Curve

1.3.8 Mahalanobis Distance

1.3.9 Hamming Distance

1.3.10 Levenshtein Distance

1.3.11 Hausdorff Distance

1.4 Summary

References

2 An Overview of Complexity Theory

2.1 Advantage of Complexity Theory

2.1.1 Computational Complexity

2.2 Abstract Models of Computation: Abstract Machines

2.2.1 Preliminary Definitions

2.2.2 Turing Machine Models

2.3 Big-O Notation (Wood 1987)

2.3.1 Example

2.4 Time Complexity

2.4.1 Constant Time

2.4.2 Linear Time (Sipser 1996)

2.4.3 Polynomial Time (Papadimitriou 1994)

2.4.4 Exponential Time (Sipser 1996)

2.5 Decision Problems

2.6 Reduction

2.6.1 Linear Reduction

2.6.2 Polynomial Reduction

2.6.3 Polynomial Reduction: Many-One Polynomially Reducible

2.7 Examples

2.7.1 Traveling Salesman Optimization Problem

2.7.2 Satisfiability Problem

2.7.3 Hamiltonian Cycle Problem

2.7.4 Clique Problem

2.8 Complexity Classes

2.8.1 Class P

2.8.2 Class NP

2.8.3 Class NP-Complete

2.8.4 Class NP-Hard

2.9 Further Reading

References

3 Single Facility Location Problem

3.1 Problem Formulation

3.1.1 A General Formulation of the Problem

3.1.2 Rectilinear Distance with Point Facilities

3.1.3 Square Euclidean Distance with Point Facilities

3.1.4 Euclidean Distance with Point Facilities

3.1.5 LP-Norm Distance with Point Facilities

3.1.6 Regional Facilities Problem (Drezner 1986)

3.2 Solution Techniques

3.2.1 Techniques for Discrete Space Location Problems

(Heragu 1997)

3.2.2 Techniques for Continues Space Location Problems

3.3 Case Study (Heragu 1997)

References

4 Multifacility Location Problem

4.1 Applications and Classifications

4.2 Models

4.2.1 MiniSum

4.2.2 MiniMax

4.2.3 Other Models

4.3 Solution Techniques

4.3.1 MiniSum

4.3.2 MiniMax

4.3.3 Solution Techniques for other Models

4.3.4 Some Heuristic and Metaheuristic Methods

4.4 Case Study

References

5 Location Allocation Problem

5.1 Classification of Location-Allocation Problem

5.1.1 Classifications of Facilities

5.1.2 Classified on the Physical Space or Locations

5.1.3 Classifications of the Demand

5.2 Models

5.2.1 General LA Model (Cooper 1963)

5.2.2 LA Model Each Customer Covered by Only One Facility

5.2.3 LA Model with FacilityÌs Opening Cost

5.2.4 Capacitated LA Model with Stochastic Demands

(Zhou and Liu 2003)

5.3 Solution Techniques

5.3.1 Exact Solutions (Cooper 1963)

5.3.2 Heuristic Methods

Procedure 1

Procedure 2

5.3.3 Metaheuristic Methods (Salhi and Gamal 2003)

5.4 Case Study

5.4.1 A Facility Location Allocation Model for Reusing Carpet

Materials (Louwers et al. 1999)

5.4.2 A New Organ Transplantation Location-Allocation Policy

(Bruni et al. 2006)

References

6 Quadratic Assignment Problem

6.1 Formulations of QAP

6.1.1 Integer Programming Formulations (ILP)

6.1.2 Mixed Integer Programming Formulations (MILP)

6.1.3 Formulation by Permutations

6.1.4 Trace Formulation

6.1.5 Graph Formulation

6.2 QAP Related Problems

6.2.1 The Quadratic Bottleneck Assignment Problem (QBAP)

6.2.2 The Biquadratic Assignment Problem (BiQAP)

6.2.3 The Quadratic Semi-Assignment Problem (QSAP)

6.2.4 The Multiobjective QAP (MQAP)

6.2.5 The Quadratic Three-Dimensional Assignment Problem

(Q3AP)

6.2.6 The Generalized Quadratic Assignment Problem (GQAP)

6.2.7 Stochastic QAP (SQAP)

6.3 Solution Techniques

6.3.1 Computational Complexity

6.3.2 Lower Bounds

6.3.3 Exact Algorithms

6.3.4 Heuristic Algorithms

6.3.5 Metaheuristic Algorithms

6.3.6 Comparing QAP Algorithms

6.4 Case Study

6.4.1 Hospital Layout as a Quadratic Assignment Problem

(Elshafei 1977)

6.4.2 Backboard Wiring Problem (Steinberg 1961)

6.4.3 Minimizing WIP Inventories (Benjaafar 2002)

6.4.4 Zoning in Forest (Bos 1993)

6.4.5 Computer Motherboard Design Problem (Miranda 2005)

References

7 Covering Problem

7.1 Problem Formulation

7.2 Total Covering Problem

7.2.1 Maximizing the Number of Points Covered More than Once

7.2.2 Multiple Total Covering Problems (Mirchandani et al. 1990)

7.2.3 Total Covering Problem with the Preference of Selecting

Location of Existing Facilities (Daskin 1995)

7.2.4 Total Edge Covering Problem (Daskin 1995)

7.2.5 Notes on Total Covering Problems

7.3 Partial Covering Problem

7.3.1 Minimizing Costs Arisen from Not Covering Demand Points

(Mirchandani and Francis 1990)

7.3.2 Minimizing Costs of Locating Facilities and Costs Arisen

from Not Covering Demand Points

7.3.3 Maximum Covering Location Problems (Berman

et al. 2003)

7.3.4 Expected Maximum Covering Problem (Daskin 1995)

7.3.5 Maximum Covering Problem Considering Non-Ascending

Coverage Function (Berman et al. 2003)

7.4 The Bi-Objective Covering Tour Problem (Jozefowieza

et al. 2007)

7.5 A Fuzzy Multi Objective Covering Based Vehicle Location

Model for Emergency Services (Araz et al. 2007)

7.6 Solving Methods

7.6.1 Exact Methods

7.6.2 Heuristic Methods

7.6.3 Metaheuristic Methods

7.7 Case Study

7.7.1 Combination of MCDM and Covering Techniques

(Farahani and Asgari 2007)

References

8 Median Location Problem

8.1 Classification

8.1.1 1-Median

8.1.2 P-Median

8.1.3 An Example

8.2 Mathematical Models

8.2.1 Classic Model

8.2.2 Capacitated Plant Location Problem Model (CPLPM)

8.2.3 Capacitated P-median Problem (Lorenaa 2004)

8.3 Solution Techniques

8.3.1 Lemma

8.3.2 Solving 1-Median Problem Algorithm on Tree

(Goldman 1971)

8.3.3 Exact Methods

8.3.4 Heuristic Algorithms

8.3.5 Metaheuristic Algorithms

8.4 Comparison of Methods

8.5 Studying Statically the Methods for Solutions of Median

Problem (Reese 2005)

8.5.1 Classification of Solving Methods by Period

8.5.2 Classification of Different Solving Methods

8.6 Case Study

8.6.1 Post Center Locations (Alba and Dominquez 2006)

8.6.2 Entrance Exam Facilities (Correa et al. 2004)

8.6.3 Polling Station Location (Ghiani et al. 2002)

References

9 Center Problem

9.1 Applications and Classifications

9.1.1 K-Network P-Center Problem

9.1.2

Facility

-Centdian Problem

9.1.3

Centrum Multi-Facility Problem

9.1.4 P-Center Problem with Pos/Neg Weights

9.1.5 Anti P-Center Problem

9.1.6 Continuous P-Center Problem

9.1.7 Asymmetric P-Center Problem

9.2 Models

9.2.1 Vertex P-Center Problem

9.2.2 Vertex P-Center Problem with Demand-Weighted Distance

9.2.3 Capacitated Vertex P-Center Problem

9.3 Exact Solution Approaches

9.3.1 Center Problems on a Tree Network

9.3.2 Center Problems on a General Graph

9.4 Approximate Solution Approaches

9.5 Case Study

9.5.1 A Health Resource Case (Pacheco and Casado 2005)

References

10 Hierarchical Location Problem

10.1 Applications and Classifications

10.2 Flow-Based Hierarchical Location Problem

10.2.1 Flow-Based Formulation for Single-Flow Systems (S ahin

and S ural 2007)

10.2.2 Flow-Based Formulation for Multi-Flow Systems (S ahin

and S ural 2007)

10.3 Median-Based Hierarchical Location Problem

(Daskin 1995)

10.3.1 Median-Based Formulation for Globally Inclusive Service

Hierarchies

10.3.2 Median-Based Formulation for Locally Inclusive Service

Hierarchies

10.3.3 Median-Based Formulation for Successively Exclusive

Service Hierarchies

10.4 Coverage-Based Hierarchical Location Problem

(Daskin 1995)

10.4.1 Hierarchical Maximal Covering Location Problem

10.4.2 Hierarchical Maximal Covering Location Problem

with Covering all Kinds of Demands

10.5 Median-Based Hierarchical Relocation Problem (Teixeira

and Antunes 2008)

10.5.1 Median-Based Hierarchical Relocation Problem

with Closest Assignment

10.5.2 Median-Based Hierarchical Relocation Problem with Path

Assignment

10.6 Solving Algorithms for Hierarchical Location Problem

10.7 Case Study

10.7.1 A Hierarchical Model for the Location of Maternity

Facilities in the Municipality of Rio de Janeiro

(Galv Ú ao et al. 2002 and 2006)

10.7.2 Locational Analysis for Regionalization of Turkish Red

Crescent Blood Services (S ahin et al. 2007)

10.7.3 School Network Planning in Coimbra, Portugal (Teixeira

and Antunes 2008)

References

11 Hub Location Problem

11.1 Applications and Classifications

11.2 Models

11.2.1 Single Hub Location Problem (OÌKelly 1987)

11.2.2 P-Hub Location Problem (OÌKelly 1987)

11.2.3 Multiple Allocation P-Hub Location Model (P-Hub

Median Location Model) (Campbell 1991)

11.2.4 P-Hub Median Location Problem with Fixed Costs

(OÌ Kelly 1992)

11.2.5 Single Spoke Assignment P-Hub Median Location

Problem (Single Allocation P-Hub Location Problem)

(Daskin 1995)

11.2.6 The Extension Model of Fixed Cost for Connecting

a Spoke to a Hub (Campbell 1994)

11.2.7 Minimum Value Flow on any Spoke/Hub Connection

Problem (Campbell 1994)

11.2.8 Capacity Limitation of Hub Location Problem

(Campbell 1994)

11.2.9 P-Hub Center Location Problem (Campbell 1994)

11.2.10 Hub Covering Location Problem (Campbell 1994)

11.3 Solution Techniques

11.3.1 Various Kinds of Algorithms

11.3.2 Some Relevant Algorithms

11.4 Case Study

11.4.1 The Policy of Open Skies in the Middle East

(Adler and Hashai 2005)

11.4.2 A Hub Port in the East Coast of South America (Aversa

et al. 2005)

11.4.3 A Hub Model in Brunswick, Canada (Eiselt 2007)

11.4.4 A Hub/Spoke Network in Brazil (Cunha and Silva 2007)

References

12 Competitive Location Problem

12.1 Applications and Classifications

12.1.1 Game Theories (Winston and Wayne 1995)

12.1.2 Static Competition

12.1.3 Competition with Foresight

12.1.4 Dynamic Models and Competitive Equilibrium

12.1.5 Point vs. Regional Demand

12.1.6 Patronizing Behavior

12.1.7 Attraction Function

12.1.8 Decision Space

12.2 Models

12.2.1 Gravity Problem

12.2.2 The Maximum Capture Problem Model (MAXCAP)

(Serra and ReVelle 1995)

12.2.3 The Maximum Capture Problem with Price Model

(PMAXCAP) (Serra and ReVelle 1998)

12.2.4 Flow Capturing Location Allocation Problem Model

(FCLAP)

12.3 Case Study

12.3.1 A Case in Toronto (Aboolian et al. 2006)

12.3.2 A Case in Yuanlin Taiwan (Wu and Lin 2003)

References

13 Warehouse Location Problem

13.1 Classifications

13.2 Models

13.2.1 Warehouse Location Problem without Fixed

Installation Costs (William et al. 1958)

13.2.2 Warehouse Location Problem with Fixed Cost

of Establishment (Akinc and Khumawala 1977)

13.2.3 Capacitated Warehouse Location Problem with

Constraints in Customers Being Serviced (Nagy 2004)

13.2.4 Single Stage Capacitated Warehouse Location Model

(Sharma and Berry 2007)

13.2.5 Redesigning a Warehouse Network (Melachrinoudis

and Min 2007)

13.3 Solution Methods

13.3.1 Exact Solution Methods

13.3.2 Heuristic and Metaheuristic Methods

13.4 Case Study

13.4.1 Redesigning a Warehouse Network

(Melachrinoudis and Min 2007)

13.4.2 Warehouse Location Problems for Air Freight Forwarders

(Wan et al. 1998)

References

14 Obnoxious Facility Location

14.1 Applications and Classifications

14.1.1 Applications

14.1.2 Revolution of Undesirable Facility Problem

14.1.3 Classification of Undesirable Facility Problems

14.2 Models

14.2.1 Dispersion Problem (Daskin 1995)

14.2.2 Undesirable Facility Location Problem (Daskin 1995)

14.2.3 Hazardous Materials Routing Problem

14.2.4 Obnoxious Facilities Location-Routing Problem

14.2.5 Multiobjective Obnoxious Facilities Location Problem

(Rakas et al. 2004)

14.3 Solutions and Techniques

14.4 Case Study

14.4.1 Obnoxious Facility Location and Routing in Anatolian

Region of Turkey (Alumur and Kara 2007)

14.4.2 Designing Emergency Response Network for Hazardous

Materials Transportation (Berman et al. 2007)

14.4.3 Locating Waste Pipelines to Minimize their Impact

on Marine Environment (Ceceres et al. 2007)

References

15 Dynamic Facility Location Problem

15.1 Classifications

15.2 Mathematical Formulations

15.2.1 Static Model (Wesolowsky 1973)

15.2.2 Dynamic P-Median Model (Owen and Daskin 1998)

15.2.3 Multiperiod Model (Wesolowsky and Truscott 1975)

15.2.4 Probabilistic Model (Rosental et al. 1978)

15.3 Solution Techniques

15.3.1 Fundamental Lemmas

15.3.2 Single Relocation at Discrete Time

15.3.3 Multiple Relocations at Discrete Times

Without Relocation Costs (Z.-Farahani et al. 2009)

15.3.4 Multiple Relocations at Discrete Times

with Relocation Costs

15.3.5 Complete Enumeration

15.3.6 Non-Duplicating Enumeration

15.3.7 Incomplete DP

15.3.8 An Especial BIP

15.3.9 Relocation at Continues Times

15.3.10 Iterative Algorithm for Obtaining Optimal Solution

15.3.11 Static Stochastic Techniques

15.4 Case Study

15.4.1 A Dynamic Model for School Network Planning (Antunes

and Peeters 2000)

15.4.2 A Multiperiod Set Covering for Dynamic Redeployment

of Ambulances (Rajagopalan et al. 2008)

15.4.3 A Multi-period Model for Combat Logistics (Gue 2003)

References

16 Multi-Criteria Location Problem

16.1 Applications and Classifications

16.2 Models

16.2.1 Private and Public Facilities

16.2.2 Balancing Objective Functions

16.2.3 Pull, Push and PullÒPush Objectives

16.2.4 Mathematical Models

16.3 Solution Techniques

16.3.1 The MCDM Techniques

16.3.2 Metaheuristics for the MODM

16.3.3 Multi-Objective Combinatorial Optimization

16.4 Case Study

16.4.1 LRP (Lin and kwok 2006)

16.4.2 Facility Layout (Chiang et al. 2006)

16.4.3 Fire Station Locations

16.4.4 The 2-Facility Centdian Network Problem (Perez-Brito

et al. 1998)

16.4.5 Military Logistics (Z-Farahani and Asgari 2007)

16.4.6 A Paper Recycling System (Pati et al. 2008)

References

17 Location-Routing Problem

17.1 An Introduction to VRP

17.1.1 Definition of VRP

17.1.2 The Traveling Salesman Problem

17.1.3 A Classification of Capacitated VRP

17.2 LRP

17.2.1 Applications of LRP

17.2.2 Classifications of LRP

17.3 Models

17.3.1 Classifications

17.3.2 Mathematical Models

17.4 Solution Techniques

17.4.1 Heuristic Methods

17.4.2 Metaheuristic Methods

17.5 Case Study

17.5.1 Bill Delivery Services (Lin et al. 2002)

17.5.2 Contaminated Waste Disposal (Caballero et al. 2007)

17.5.3 Logistics System (Lin and Kwok 2006)

References

18 Storage System Layout

18.1 Assumptions and Classifications

18.2 Storage Location Assignment Problem Based on Product

Information

18.2.1 Dedicated Storage Location Policy

18.2.2 Cube-Per-Order Index (COI)

18.2.3 Class-Based Storage Location Policy

18.2.4 Class-Based Dedicated Storage Location Policy (COI)

18.2.5 Full Turn-over Based Storage

18.3 Storage Location Assignment Problem

Based on Item Information (SLAP/II)

18.3.1 Assignment Problem and Vector Assignment Problem

18.3.2 Shared Storage Policies

18.3.3 Duration-of-Stay Storage Policy

18.3.4 Shared Storage Policies for Unbalanced Input and Output

18.3.5 Static Shared Storage Policies

18.3.6 Adaptive Shared Storage Policies

18.4 Storage Location Assignment Problem

Based on No Information (SAP/NI)

18.4.1 Randomized Storage Location Policy

18.5 Comparing Storage Policies

18.6 Family Grouping

18.7 Continuous Warehouse Layout

18.7.1 Storage Region Configuration

18.8 Dynamic Storage Location Assignment Problems

(Gu 2005)

18.9 Case Study

References

19 Location-Inventory Problem

19.1 Applications and Classifications

19.2 Models

19.2.1 Model of Shen et al. (2003)

19.2.2 Model of Nozick and Turnquist (1998)

19.2.3 Model of Erlebacher and Meller (2000)

19.2.4 Model of Daskin et al. (2002)

19.2.5 Model of Shen and Qi (2007)

19.2.6 Model of Miranda and Garrido (2008)

19.3 Solution Approaches

19.3.1 Solution Approach of Erlebacher and Meller (2000)

19.3.2 Solution Approach of Daskin et al. (2002)

19.3.3 Solution Approach of Shen and Qi (2007)

19.3.4 Solution Approach of Miranda and Garrido (2006)

19.3.5 Solution Approach of Miranda and Garrido (2008)

19.4 Case Study

19.4.1 Distribution System for Finished Automobiles in US

(Nozick and Turnquist 1998)

References

20 Facility Location in Supply Chain

20.1 Design Phases in Supply Chain

20.2 Network Design in Supply Chain

20.2.1 The Role of Network Design in the Supply Chain

20.2.2 Factors Influencing Network Design Decisions

20.3 ClassicalModels

20.3.1 Fixed Charge Facility Location Problem (Daskin

et al. 2005)

20.3.2 Uncapacitated Facility Location Model with Single

Sourcing

20.3.3 Capacitated Facility Location Model

20.3.4 Locating Plants and Distribution Centers with Multiple

Commodity

20.4 Integrated Decision Making Models

20.4.1 Integrated Location-Routing Models (LR)

20.4.2 Integrated Inventory-Routing Models (IR)

20.4.3 Integrated Location-Inventory Models (LI)

20.5 Basic Model Formulation

20.5.1 Model Inputs

20.5.2 Model Outputs (Decision Variables)

20.5.3 Objective Function and its Constraints

20.6 Model with Routing Cost Estimation

20.7 Model with Capacitated DCs

20.8 Model with Multiple Levels of Capacity (Amiri 2006)

20.8.1 Model Inputs

20.8.2 Model Outputs (Decision Variables)

20.8.3 Objective Function and its Constraints

20.9 Model with Service Considerations

20.10 Profit Maximizing Model with Demand Choice Flexibility

20.11 Model with Multiple Commodities

20.12 Model with Unreliable Supply

20.12.1 Model Inputs

20.12.2 Model Outputs (Decision Variables)

20.12.3 Objective Function and its Constraints

20.13 Model with Facility Failures (Snyder 2003)

20.13.1 Objective Function and its Constraints

20.14 Planning Under Uncertainty (Snyder et al. 2007)

20.14.1 Model Inputs

20.14.2 Model Outputs (Decision Variables)

20.14.3 Objective Function and its Constraints

20.15 Solution Techniques

20.16 Case Study

20.16.1 An Industrial Case in Supply Chain Design

and Multilevel Planning in US (Sousa et al. 2008)

20.16.2 Multi-Objective Optimization of Supply Chain Networks

in Turkey (Altiparmak et al. 2006)

References

21 Classification of Location Models and Location Softwares

21.1 Classification of Location Models

21.1.1 Taxonomy vs. Classification Scheme

21.1.2 Taxonomy

21.1.3 Classification Schemes

21.2 Facility Location Softwares

21.2.1 LoLA

21.2.2 SITATION

21.2.3 S-Distance

21.2.4 Other Facility Location Softwares

References

22 Demand Point Aggregation Analysis for Location Models

22.1 Applications

22.1.1

Median

Problem

22.1.2

Center

Problem

22.1.3 Covering Problem

22.2 Aggregation Errors

22.2.1 Spatial Aggregation Demand

22.2.2 Methods for Reducing Aggregation Errors

22.3 Computational Approach

References

Appendix: Metaheuristic Methods

Genetic Algorithm

The Simple Genetic Algorithm

Tabu Search

Two Important Concepts

A Simple Tabu Search Algorithm

Ant Colony Optimization

Simulated Annealing

Neural Networks

References

Index