Optimal Districting and Territory Design (International Series in Operations Research & Management Science, 284)

Preface
Contents
Contributors
Part I Introduction and Literature Reviews
	1 Research Trends in Optimization of Districting Systems
		1.1 Motivation
		1.2 Research Contributions
			1.2.1 Part I: Introduction and Literature Reviews
			1.2.2 Part II: Theory, Models, and Algorithms
			1.2.3 Part III: Applications and Case Studies
		1.3 Closing Remarks
		References
	2 Police Districting Problem: Literature Review and Annotated Bibliography
		2.1 Introduction
		2.2 The Police Districting Problem
		2.3 Literature Review
			2.3.1 Attributes
				2.3.1.1 Workload
				2.3.1.2 Response Time
				2.3.1.3 Geometry
				2.3.1.4 Other Attributes
			2.3.2 Methodologies and Approaches
				2.3.2.1 Optimization Models
				2.3.2.2 Geographic Information Systems (GIS)
				2.3.2.3 Other Methods
		2.4 Annotated Bibliography
			2.4.1 Mitchell ch2:Mitchell1972
			2.4.2 Bodily ch2:Bodily1978
			2.4.3 Benveniste ch2:Benveniste1985
			2.4.4 Sarac et al. ch2:Sarac1999
			2.4.5 D\'Amico et al. ch2:DAmico2002
			2.4.6 Curtin et al. ch2:Curtin2005
			2.4.7 Scalisi et al. ch2:Scalisi2009
			2.4.8 Curtin et al. ch2:Curtin2010
			2.4.9 Wang ch2:Wang2012
			2.4.10 Zhang and Brown ch2:Zhang2013
			2.4.11 Zhang et al. ch2:zhang2013comparison
			2.4.12 Zhang and Brown ch2:zhang2014sa
			2.4.13 Zhang and Brown ch2:zhang2014simulation
			2.4.14 Bucarey et al. ch2:bucarey2015shape
			2.4.15 Camacho-Collados et al. ch2:camacho2015multi
			2.4.16 Camacho-Collados and Liberatore ch2:camacho2015decision
			2.4.17 Cheung et al. ch2:cheung2015optimization
			2.4.18 Chow et al. ch2:chow2015optimization
			2.4.19 Liberatore and Camacho-Collados ch2:liberatore2016comparison
			2.4.20 Piyadasun et al. ch2:piyadasun2017rationalizing
		2.5 Conclusions
		References
	3 A Review of Districting Problems in Health Care
		3.1 Introduction
		3.2 Districting of Home Health Care Services
			3.2.1 Special Characteristics and Criteria
			3.2.2 Model Formulations
			3.2.3 Literature Review and Future Research Directions
		3.3 Districting of Primary and Secondary Health Care Services
			3.3.1 Special Characteristics and Criteria
			3.3.2 Model Formulations
			3.3.3 Literature Review and Future Research Directions
		3.4 Districting of Emergency Health Services
			3.4.1 Literature Review
			3.4.2 Model Formulation
			3.4.3 Future Research Directions
		3.5 Conclusion
		References
	4 Computational Geometric Approaches to Equitable Districting: A Survey
		4.1 Introduction
			4.1.1 Notational Conventions
			4.1.2 Applications of Geometric Districting
		4.2 The Voronoi Paradigm
			4.2.1 Weighted Voronoi Partitions
			4.2.2 Complementary Slackness and Weighted Voronoi Diagrams
			4.2.3 Further Uses of the Voronoi Paradigm
		4.3 The Ham Sandwich Paradigm
			4.3.1 Red and Blue Points
			4.3.2 General Measures
		4.4 Other Recursive Schemes for Equitable Partitioning
		4.5 Cake Cutting
		4.6 Equal Boundary Partitioning
		4.7 Conclusions
		References
Part II Theory, Models, and Algorithms
	5 Bounding Procedures and Exact Solutions for a Class of Territory Design Problems
		5.1 A Class of Territory Design Problems
		5.2 Problem Description and Mathematical Models
			5.2.1 Integer Linear Programming Model
			5.2.2  Lagrangian Relaxation
			5.2.3 Integer Quadratic Programming Model
		5.3 Solution Methods and Bounding Procedures
		5.4 Computational Results
		5.5 Final Remarks
		References
	6 Mathematical Programming Formulations for Practical Political Districting
		6.1 Territory Design for Political Districting
		6.2 Mathematical Programming for Political Districting
		6.3 Mathematical Programming Formulations for Political Districting: Milestone Models and Recent Advances
			6.3.1 Classical PD Formulations
			6.3.2 Recent and New Ideas for PD Modeling
				6.3.2.1 Flow-Based Contiguous PD Models
				6.3.2.2 Order-Based PD Contiguous Models
		6.4 Conclusions and New Perspectives in Political Districting Modeling
		References
	7 Multi-Period Service Territory Design
		7.1 Introduction
		7.2 Problem Description and Literature Review
		7.3 Mathematical Formulations
			7.3.1 A Mathematical Formulation for the MPSTDP
			7.3.2 Computational Experiments
			7.3.3 Symmetry
			7.3.4 Computational Experiments
			7.3.5 Mathematical Formulations for Weekday Regularities
				7.3.5.1 Strict Weekday Regularities
				7.3.5.2 Partial Weekday Regularities
		7.4 Solving the Scheduling Subproblem
			7.4.1 A Heuristic Algorithm for the MPSTDP-S
			7.4.2 A Branch-and-Price Algorithm for the MPSTDP-S
			7.4.3 Computational Experiments
		7.5 Conclusions
		References
	8 Designing Ambulance Service Districts Under Uncertainty
		8.1 Introduction
		8.2 Literature Review
			8.2.1 Ambulance Location/Allocation
			8.2.2 Ambulance Dispatching and Redeployment
			8.2.3 Service District Design
		8.3 Model Formulation
		8.4 Computational Results
			8.4.1 Discussion of the Model Output
			8.4.2 Model Evaluation
		8.5 Conclusion
		References
Part III Applications and Case Studies
	9 Spatial Optimization Problem for Locating Polling Facilities and Stations and Policy Implications
		9.1 Introduction
		9.2 Background
		9.3 Modeling Issues and Data
		9.4 Model Formulation
		9.5 Computational Experiments and Implications
		9.6 Concluding Remarks
		References
	10 Territory Design for Sales Force Sizing
		10.1 Introduction
		10.2 Related Work
		10.3 Sales Force Sizing Problem
			10.3.1 Routing-Clustering Heuristic
		10.4 Case Studies
			10.4.1 Mexico City Depot
			10.4.2 Monterrey Depot
		10.5 Conclusions
		References
Index