Free Access

The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application

Carlos F. Daganzo
Carlos F. Daganzo
University of California, Berkeley, California
Search for more papers by this author

University of California, Berkeley, California

Published Online:1 Nov 1984https://doi.org/10.1287/trsc.18.4.331

This article is part of the Transportation Science Classics collection, celebrating the 50th anniversary of the journal.

Cited by
- Recent developments in location-routing problems
  European Journal of Operational Research, Vol. 332, No. 3
- Incentive-compatible auction mechanisms for crowdshipping: Modeling, solution approach, and systemic impacts
  Transportation Research Part E: Logistics and Transportation Review, Vol. 212
- Network-based formulations and solution algorithm for paratransit districting
  Transportation Research Part C: Emerging Technologies, Vol. 189
- From willingness to wait to sustainable impact: Smoothing e-commerce delivery volume peaks
  Transportation Research Part D: Transport and Environment, Vol. 156
- Operational and environmental disparities in parcel last-mile delivery across spatial contexts: Why an urban-centric perspective falls short
  Journal of Transport Geography, Vol. 134
- Collaboration in parcel locker networks - A cooperative game for the joint placement of lockers
  International Journal of Production Economics, Vol. 59
- Economic and environmental impacts of integrated drone delivery systems
  Transportation Research Part E: Logistics and Transportation Review, Vol. 209
- Districting in last‐mile delivery with stochastic customers
  20 November 2024 | International Transactions in Operational Research, Vol. 33, No. 3
- Deep Learning for Data-Driven Districting-and-Routing
  Arthur Ferraz,
  Cheikh Ahmed,
  Quentin Cappart,
  Thibaut Vidal
  18 March 2026 | Transportation Science, Vol. 60, No. 3
- The value of crowdshipping from microhubs in urban environments
  23 April 2026 | Decision Sciences, Vol. 122
- Accurately estimating optimal SDVRP solution values using regression models
  Computers & Operations Research, Vol. 188
- Optimizing online grocery service: From customer understanding to multichannel profitability
  European Journal of Operational Research, Vol. 76
- A holistic continuous approximation framework for strategic last-mile distribution planning
  Transportation Research Interdisciplinary Perspectives, Vol. 35
- Tactical planning of a demand-responsive connector
  EURO Journal on Transportation and Logistics, Vol. 15
- Assessing the viability of parking slot utilization as transhipment points for parcel carriers: a case study in Barcelona
  17 July 2024 | Central European Journal of Operations Research, Vol. 33, No. 4
- A strategic assessment of first-mile post-consumer textile collection strategies
  Cleaner Logistics and Supply Chain, Vol. 17
- Moving-micro hubs: Redefining last-mile logistics with autonomous hub vehicles (AHVs) and delivery robots (ADRs)
  Transportation Research Part E: Logistics and Transportation Review, Vol. 203
- Designing profit-maximizing omnichannel distribution networks for high responsiveness
  International Journal of Production Economics, Vol. 286
- Peer-to-Peer Crowdshipping as an Omnichannel Retail Strategy
  Ho-Yin Mak
  6 March 2025 | Transportation Science, Vol. 59, No. 3
- Package delivery by electric vertical takeoff and landing aircraft? An attractiveness assessment
  Journal of Air Transport Management, Vol. 124
- Analytical model for large-scale design of sidewalk delivery robot systems with bounded makespans
  Transportation Research Part C: Emerging Technologies, Vol. 171
- A multi-criteria districting approach with a lexicographic compactness metric: An application to the Chilean postal service
  Computers & Operations Research, Vol. 173
- Sustainability challenges of last-mile logistics and transition to online grocery retailing in sparsely populated areas
  2 September 2024 | Industrial Management & Data Systems, Vol. 124, No. 12
- A strategic variable fee for business-to-consumer carriers: A case study in Barcelona
  Transportation Research Part A: Policy and Practice, Vol. 190
- From operational to strategic modelling: A continuous multi-scale approach for last-mile analysis
  Transportation Research Part E: Logistics and Transportation Review, Vol. 191
- A large-scale analytical residential parcel delivery model evaluating greenhouse gas emissions, COVID-19 impact, and cargo bikes
  International Journal of Transportation Science and Technology, Vol. 15
- Estimating optimal split delivery vehicle routing problem solution values
  Computers & Operations Research, Vol. 168
- Stochastic modeling of integrated order fulfillment processes with delivery time promise: Order picking, batching, and last-mile delivery
  European Journal of Operational Research, Vol. 316, No. 3
- A continuous approximation approach to integrated truck and drone delivery systems
  Omega, Vol. 126
- Analysis of Real-Time Order Fulfillment Policies: When to Dispatch a Batch?
  Natarajan Gautam,
  Joseph Geunes
  30 October 2023 | Service Science, Vol. 16, No. 2
- Winning the race to customers with micro-fulfillment centers: an approach for network planning in quick commerce
  18 January 2024 | Central European Journal of Operations Research, Vol. 32, No. 2
- Integrating mobile parcel lockers into last-mile delivery networks: an operational design for home delivery, stationary, and mobile parcel lockers
  14 March 2024 | International Journal of Physical Distribution & Logistics Management, Vol. 54, No. 4
- A decision-making framework for automating distribution centers in the Retail supply
  Heliyon, Vol. 10, No. 10
- Dynamic vehicle routing problem with drone resupply for same-day delivery
  Transportation Research Part C: Emerging Technologies, Vol. 162
- An improved model for estimating optimal VRP solution values
  6 December 2023 | Optimization Letters, Vol. 18, No. 3
- A bi-level approach for last-mile delivery with multiple satellites
  Transportation Research Part C: Emerging Technologies, Vol. 160
- Neural Network Estimators for Optimal Tour Lengths of Traveling Salesperson Problem Instances with Arbitrary Node Distributions
  Taha Varol,
  Okan Örsan Özener,
  Erinç Albey
  12 December 2023 | Transportation Science, Vol. 58, No. 1
- Retail
  15 December 2023
- Transforming distribution networks in metropolitan Sydney in response to COVID-19
  Transportation Research Procedia, Vol. 79
- Estimating the marginal cost to deliver to individual customers
  9 January 2023 | Optimization and Engineering, Vol. 24, No. 4
- Same-day delivery time-guarantee problem in online retail
  Communications in Transportation Research, Vol. 3
- Route efficiency implications of time windows and vehicle capacities in first- and last-mile logistics
  European Journal of Operational Research, Vol. 311, No. 1
- Territorial design for customers with demand frequency
  European Journal of Operational Research, Vol. 309, No. 1
- Assessing economic, social and ecological impact of parcel-delivery interventions in integrated simulation
  Transportation Research Part D: Transport and Environment, Vol. 121
- Iterated tour partitioning for Euclidean capacitated vehicle routing
  21 December 2022 | Random Structures & Algorithms, Vol. 62, No. 4
- Smart and sustainable city logistics: Design, consolidation, and regulation
  European Journal of Operational Research, Vol. 307, No. 3
- Strategic Multi-Echelon and Cross-Modal CO 2 Emissions Calculation in Parcel Distribution Networks: First Step Toward a Common Language
  28 January 2023 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2677, No. 6
- Solving large-scale dynamic vehicle routing problems with stochastic requests
  European Journal of Operational Research, Vol. 306, No. 2
- The two-echelon stochastic multi-period capacitated location-routing problem
  European Journal of Operational Research, Vol. 306, No. 2
- Who has access to e-commerce and when? Time-varying service regions in same-day delivery
  Transportation Research Part B: Methodological, Vol. 170
- Assessing last-mile distribution resilience under demand disruptions
  Transportation Research Part E: Logistics and Transportation Review, Vol. 172
- Experience-based territory planning and driver assignment with predicted demand and driver present condition
  Transportation Research Part E: Logistics and Transportation Review, Vol. 171
- Exploratory Analysis of Transportation System for Modular Vehicle Concept Operated as Passenger and Goods Transport Using Continuum Approximation Techniques
  12 March 2023
- Using regression models to understand the impact of route-length variability in practical vehicle routing
  17 May 2022 | Optimization Letters, Vol. 17, No. 1
- Approximating the Length of Vehicle Routing Problem Solutions Using Complementary Spatial Information
  8 March 2022 | Geographical Analysis, Vol. 55, No. 1
- MATH-HEURISTIC FOR THE CAPACITATED TWO-ECHELON VEHICLE ROUTING PROBLEM
  1 January 2023 | Pesquisa Operacional, Vol. 43
- The Value of Pooling in Last-Mile Delivery
- Investigating the financial impact of collection-and-delivery points in last-mile E-commerce distribution
  Research in Transportation Business & Management, Vol. 45
- A cost-based comparative analysis of different last-mile strategies for e-commerce delivery
  Transportation Research Part E: Logistics and Transportation Review, Vol. 164
- Expected Length of the Shortest Path of the Traveling Salesman Problem in 3D Space
  Journal of Advanced Transportation, Vol. 2022
- Locating Urban Consolidation Centers under Shipper Rationality
  Journal of Advanced Transportation, Vol. 2022
- Improving the Accuracy of Vehicle Routing Problem Approximation Using the Formula for the Average Distance Between a Point and a Rectangular Area
  11 December 2022
- Assessing the Economic, Social and Ecological Impact of Combined Green Parcel-Delivery Interventions in an Integrated Simulation Approach
  SSRN Electronic Journal, Vol. 10
- Assessing Three-Dimensional Impact of Combined Green Parcel-Delivery Interventions in Integrated Simulation Approach
  SSRN Electronic Journal, Vol. 10
- Balanced dynamic multiple travelling salesmen: Algorithms and continuous approximations
  Computers & Operations Research, Vol. 136
- Designing multi-tier, multi-service-level, and multi-modal last-mile distribution networks for omni-channel operations
  European Journal of Operational Research, Vol. 294, No. 3
- A Heuristic Algorithm for solving a large-scale real-world territory design problem
  Omega, Vol. 103
- The balancing traveling salesman problem: application to warehouse order picking
  21 May 2020 | TOP, Vol. 29, No. 2
- Improving the Return Loading Rate Problem in Northwest China Based on the Theory of Constraints
  16 June 2021 | Mathematics, Vol. 9, No. 12
- The location-or-routing problem
  Transportation Research Part B: Methodological, Vol. 147
- Optimal rebalancing and on-board charging of shared electric scooters
  Transportation Research Part B: Methodological, Vol. 147
- Economical-traveling-distance-based fleet composition with fuel costs: An application in petrol distribution
  Transportation Research Part E: Logistics and Transportation Review, Vol. 147
- Route Duration Prediction in a Stochastic and Dynamic Vehicle Routing Problem with Short Delivery Deadlines
  Procedia Computer Science, Vol. 180
- An exploratory evaluation of urban street networks for last mile distribution
  Cities, Vol. 107
- A Discrete-Continuous Hybrid Approach to Periodic Routing of Waste Collection Vehicles With Recycling Operations
  IEEE Transactions on Intelligent Transportation Systems, Vol. 21, No. 12
- Statistical Modeling of Quartiles, Standard Deviation, and Buffer Time Index of Optimal Tour in Traveling Salesman Problem and Implications for Travel Time Reliability
  10 October 2020 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2674, No. 12
- Last-Mile Shared Delivery: A Discrete Sequential Packing Approach
  Junyu Cao,
  Mariana Olvera-Cravioto,
  Zuo-Jun (Max) Shen
  17 September 2020 | Mathematics of Operations Research, Vol. 45, No. 4
- A concise guide to existing and emerging vehicle routing problem variants
  European Journal of Operational Research, Vol. 286, No. 2
- Carbon emissions reductions in last mile and grocery deliveries utilizing air and ground autonomous vehicles
  Transportation Research Part D: Transport and Environment, Vol. 85
- Omnichannel logistics network design with integrated customer preference for deliveries and returns
  Computers & Industrial Engineering, Vol. 144
- The value of physical distribution flexibility in serving dense and uncertain urban markets
  Transportation Research Part A: Policy and Practice, Vol. 136
- Quantifying the impact of urban road networks on the efficiency of local trips
  Transportation Research Part A: Policy and Practice, Vol. 135
- Impact Assessment Model for the Implementation of Cargo Bike Transshipment Points in Urban Districts
  16 May 2020 | Sustainability, Vol. 12, No. 10
- Continuum approximation models for joint delivery systems using trucks and drones
  17 November 2018 | Enterprise Information Systems, Vol. 14, No. 4
- A column generation-based decomposition and aggregation approach for combining orders in inland transportation of containers
  15 February 2020 | OR Spectrum, Vol. 42, No. 1
- A hybrid K-means and integer programming method for commercial territory design: a case study in meat distribution
  29 December 2017 | Annals of Operations Research, Vol. 286, No. 1-2
- Minimization of urban freight distribution lifecycle CO2e emissions: Results from an optimization model and a real-world case study
  Transport Policy, Vol. 86
- Integrating first-mile pickup and last-mile delivery on shared vehicle routes for efficient urban e-commerce distribution
  Transportation Research Part B: Methodological, Vol. 131
- Product Sourcing and Distribution Strategies under Supply Disruption and Recall Risks
  1 January 2020 | Production and Operations Management, Vol. 29, No. 1
- An Analytical Model for the Many-to-One Demand Responsive Transit Systems
  30 December 2019 | Sustainability, Vol. 12, No. 1
- Integrating collection-and-delivery points in the strategic design of urban last-mile e-commerce distribution networks
  Transportation Research Part E: Logistics and Transportation Review, Vol. 131
- The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs
  European Journal of Operational Research, Vol. 276, No. 3
- Modeling Quartiles and Variance of Optimal Traveling Salesman Tour Lengths
- An empirical validation and data‐driven extension of continuum approximation approaches for urban route distances
  18 February 2019 | Networks, Vol. 73, No. 4
- The Delivery Dispatching Problem with Time Windows for Urban Consolidation Centers
  W. J. A. van Heeswijk,
  M. R. K. Mes,
  J. M. J. Schutten
  28 August 2017 | Transportation Science, Vol. 53, No. 1
- Total distance approximations for routing solutions
  Computers & Operations Research, Vol. 102
- The Environmental Impact of the Advent of Online Grocery Retailing
  SSRN Electronic Journal, Vol. 63
- A continuous approximation approach to the planar hub location-routing problem: Modeling and solution algorithms
  Computers & Operations Research, Vol. 100
- Evaluating Potential Demand and Operational Effects of Coordinated Americans with Disabilities Act Paratransit and Taxi Service
  20 September 2018 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2672, No. 8
- Coordinated Logistics with a Truck and a Drone
  John Gunnar Carlsson,
  Siyuan Song
  23 October 2017 | Management Science, Vol. 64, No. 9
- Shared Mobility for Last-Mile Delivery: Design, Operational Prescriptions, and Environmental Impact
  Wei Qi,
  Lefei Li,
  Sheng Liu,
  Zuo-Jun Max Shen
  7 June 2018 | Manufacturing & Service Operations Management, Vol. 20, No. 4
- Designing logistics systems for home delivery in densely populated urban areas
  Transportation Research Part B: Methodological, Vol. 115
- High‐Resolution Last‐Mile Network Design
  1 June 2018
- Establishing a Robust Urban Logistics Network at FEMSA through Stochastic Multi‐Echelon Location Routing
  1 June 2018
- System modeling of demand responsive transportation services: Evaluating cost efficiency of service and coordinated taxi usage
  Transportation Research Part E: Logistics and Transportation Review, Vol. 112
- Estimating Emissions from Regional Freight Delivery under Different Urban Development Scenarios
  15 April 2018 | Sustainability, Vol. 10, No. 4
- Continuous approximation for demand balancing in solving large-scale one-commodity pickup and delivery problems
  Transportation Research Part B: Methodological, Vol. 109
- Advancements in continuous approximation models for logistics and transportation systems: 1996–2016
  Transportation Research Part B: Methodological, Vol. 107
- Peer-to-Peer Crowdshipping as an Omnichannel Retail Strategy
  SSRN Electronic Journal, Vol. 53
- Planning of parking enforcement patrol considering drivers’ parking payment behavior
  Transportation Research Part B: Methodological, Vol. 106
- Continuous approximation models in freight distribution management
  6 September 2017 | TOP, Vol. 25, No. 3
- Investigating the financial viability of urban consolidation centre projects
  Research in Transportation Business & Management, Vol. 24
- E-commerce last-mile in Belgium: Developing an external cost delivery index
  Research in Transportation Business & Management, Vol. 24
- Stakeholder’s profitability of carrier-led consolidation strategies in urban goods distribution
  Transportation Research Part E: Logistics and Transportation Review, Vol. 104
- Online Grocery Retail: Revenue Models and Environmental Impact
  Elena Belavina,
  Karan Girotra,
  Ashish Kabra
  31 May 2016 | Management Science, Vol. 63, No. 6
- Agility and Proximity Considerations in Supply Chain Design
  Michael K. Lim,
  Ho-Yin Mak,
  Zuo-Jun Max Shen
  8 April 2016 | Management Science, Vol. 63, No. 4
- Coalition-formation problem for sourcing contract design in supply networks
  European Journal of Operational Research, Vol. 257, No. 2
- Considering Congestion Costs and Driver Behaviour into Route Optimisation Algorithms in Smart Cities
  26 May 2017
- Worst-case demand distributions in vehicle routing
  European Journal of Operational Research, Vol. 256, No. 2
- Strategic fleet planning for city logistics
  Transportation Research Part B: Methodological, Vol. 95
- A GRASP‐Tabu Heuristic Approach to Territory Design for Pickup and Delivery Operations for Large‐Scale Instances
  29 October 2017 | Mathematical Problems in Engineering, Vol. 2017, No. 1
- Product Geographical Distribution under Recall Risk
  SSRN Electronic Journal, Vol. 6
- Evidence-Based Vehicle Planning for Humanitarian Field Operations
  SSRN Electronic Journal, Vol. 58
- Solution of Two-Echelon Facility Location Problems by Approximation Methods
  1 January 2017 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2610, No. 1
- Integrated Modeling for Location Analysis
  18 October 2016 | Foundations and Trends® in Technology, Information and Operations Management, Vol. 9, No. 1-2
- Estimating distribution costs in a supply chain network optimisation tool, a case study
  19 October 2015 | Operational Research, Vol. 16, No. 3
- Demand responsive transit systems with time-dependent demand: User equilibrium, system optimum, and management strategy
  Transportation Research Part B: Methodological, Vol. 92
- Reliable Location-Routing Design Under Probabilistic Facility Disruptions
  Weijun Xie,
  Yanfeng Ouyang,
  Sze Chun Wong
  4 September 2015 | Transportation Science, Vol. 50, No. 3
- Approximating the Performance of a “Last Mile” Transportation System
  Hai Wang,
  Amedeo Odoni
  22 September 2014 | Transportation Science, Vol. 50, No. 2
- Enabling Urban Logistics Services at La Poste through Multi-Echelon Location-Routing
  Matthias Winkenbach,
  Paul R. Kleindorfer,
  Stefan Spinler
  15 October 2015 | Transportation Science, Vol. 50, No. 2
- Thirty years of heterogeneous vehicle routing
  European Journal of Operational Research, Vol. 249, No. 1
- Disaster Response Logistics: Chief Findings of Fieldwork Research
  18 December 2015
- Transportation in the Supply Chain
  31 March 2016
- Simulating Logistic Innovation in a Growing Urban Environment
  Transportation Research Procedia, Vol. 12
- A continuous approximation model for locating warehouses and designing physical and timely distribution strategies for home delivery
  EURO Journal on Transportation and Logistics, Vol. 4, No. 4
- Facility location design under continuous traffic equilibrium
  Transportation Research Part B: Methodological, Vol. 81
- The Traveling Salesman Problem with Imperfect Information with Application in Disaster Relief Tour Planning
  17 November 2014 | IIE Transactions, Vol. 47, No. 8
- Solution Approaches for the Stochastic Capacitated Traveling Salesmen Location Problem with Recourse
  19 August 2014 | Journal of Optimization Theory and Applications, Vol. 166, No. 1
- Continuous approximation models for mixed load school bus routing
  Transportation Research Part B: Methodological, Vol. 77
- A distribution-free TSP tour length estimation model for random graphs
  European Journal of Operational Research, Vol. 243, No. 2
- Optimization of ATM cash replenishment with group-demand forecasts
  Expert Systems with Applications, Vol. 42, No. 7
- Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning
  European Journal of Operational Research, Vol. 242, No. 1
- The Analysis of Carbon Emission Costs under Milk Run Logistics Strategy
  Journal of the Korean Operations Research and Management Science Society, Vol. 40, No. 1
- The Post-Disaster Debris Clearance Problem Under Incomplete Information
  Melih Çelik,
  Özlem Ergun,
  Pınar Keskinocak
  17 February 2015 | Operations Research, Vol. 63, No. 1
- Estimating the long-term cost to serve new customers in joint distribution
  Computers & Industrial Engineering, Vol. 80
- Modeling Mixed Load School Bus Routing
  28 November 2014
- An Approximate Dynamic Programming Approach to Urban Freight Distribution with Batch Arrivals
  20 October 2015
- A CDT-Based Heuristic Zone Design Approach for Economic Census Investigators
  Mathematical Problems in Engineering, Vol. 2015
- Approximating the length of Chinese postman tours
  5 June 2014 | 4OR, Vol. 12, No. 4
- Analogies between Internet network and logistics service networks: challenges involved in the interconnection
  30 September 2012 | Journal of Intelligent Manufacturing, Vol. 25, No. 6
- Dynamic system‐optimal traffic assignment for a city using the continuum modeling approach
  18 April 2013 | Journal of Advanced Transportation, Vol. 48, No. 7
- Vehicle routing problems in which consistency considerations are important: A survey
  7 October 2014 | Networks, Vol. 64, No. 3
- Retail Store Density and the Cost of Greenhouse Gas Emissions
  Gérard P. Cachon
  27 January 2014 | Management Science, Vol. 60, No. 8
- The Stochastic Capacitated Traveling Salesmen Location Problem: A Computational Comparison for a United States Instance
  Procedia - Social and Behavioral Sciences, Vol. 108
- Online Fresh Grocery Retail: A La Carte or Buffet?
  SSRN Electronic Journal, Vol. 58
- Analysis of Competitiveness of Freight Tricycle Delivery Services in Urban Areas
  1 January 2014 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2410, No. 1
- Vehicle routing and the value of postponement
  21 December 2017 | Journal of the Operational Research Society, Vol. 64, No. 9
- A continuous approximation approach for assessment routing in disaster relief
  Transportation Research Part B: Methodological, Vol. 50
- Planning Dial-a-Ride Services
  1 January 2013 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2352, No. 1
- Demand dispersion and logistics costs in one-to-many distribution systems
  European Journal of Operational Research, Vol. 223, No. 2
- A continuous approximation model for the fleet composition problem
  Transportation Research Part B: Methodological, Vol. 46, No. 10
- Continuous Approximation Model for the Vehicle Routing Problem for Emissions Minimization at the Strategic Level
  Journal of Transportation Engineering, Vol. 138, No. 11
- Reliable Traffic Sensor Deployment Under Probabilistic Disruptions and Generalized Surveillance Effectiveness Measures
  Xiaopeng Li,
  Yanfeng Ouyang,
  26 September 2012 | Operations Research, Vol. 60, No. 5
- A New Model of the Length of Urban Distribution Trips
  1 September 2012 | Applied Mechanics and Materials, Vol. 198-199
- The potential of parsimonious models for understanding large scale transportation systems and answering big picture questions
  EURO Journal on Transportation and Logistics, Vol. 1, No. 1-2
- Integrated inventory model with stochastic lead time and controllable variability for milk runs
  Journal of Industrial and Management Optimization, Vol. 8, No. 3
- A Comparison of Contract Types for Procuring Trucking Services: A Case Study of A Large Swedish Retailer
  Transportation Journal, Vol. 51, No. 2
- Agility and Proximity Considerations in Supply Chain Design - An Analytical Approach
  SSRN Electronic Journal, Vol. 36
- Joint inventory-location problem under the risk of probabilistic facility disruptions
  Transportation Research Part B: Methodological, Vol. 45, No. 7
- A dynamic traffic assignment model for a continuum transportation system
  Transportation Research Part B: Methodological, Vol. 45, No. 2
- Integrated Supply Chain Design Models
  15 February 2011
- Optimizing Complex Logistics Systems with Approximative Consideration of Short-Term Costs
- Retail Store Density and the Cost of Greenhouse Gas Emissions
  SSRN Electronic Journal, Vol. 4
- Reliable Facility Location Design Under the Risk of Disruptions
  Tingting Cui,
  Yanfeng Ouyang,
  Zuo-Jun Max Shen,
  9 April 2010 | Operations Research, Vol. 58, No. 4-part-1
- The impacts of congestion on commercial vehicle tour characteristics and costs
  Transportation Research Part E: Logistics and Transportation Review, Vol. 46, No. 4
- The Stochastic Multiperiod Location Transportation Problem
  Walid Klibi,
  Francis Lasalle,
  Alain Martel,
  Soumia Ichoua,
  5 March 2010 | Transportation Science, Vol. 44, No. 2
- A continuum approximation approach to reliable facility location design under correlated probabilistic disruptions
  Transportation Research Part B: Methodological, Vol. 44, No. 4
- Economic and Risk Implications in the Distribution of Petrol Products to Service Stations under Retailer Managed and Vendor Managed Inventories
  International Journal of Sustainable Transportation, Vol. 4, No. 3
- A simulation/metaheuristic approach to newspaper production and distribution supply chain problems
  International Journal of Production Economics, Vol. 121, No. 2
- Planning approximations to the average length of vehicle routing problems with time window constraints
  Transportation Research Part B: Methodological, Vol. 43, No. 4
- Solving continuous location–districting problems with Voronoi diagrams
  Computers & Operations Research, Vol. 36, No. 1
- Challenges and Opportunities in Attended Home Delivery
- Planning Approximations to the Average Length of Vehicle Routing Problems with Varying Customer Demands and Routing Constraints
  1 January 2008 | Transportation Research Record: Journal of the Transportation Research Board, Vol. 2089, No. 1
- Design of vehicle routing zones for large-scale distribution systems
  Transportation Research Part B: Methodological, Vol. 41, No. 10
- Planning and approximation models for delivery route based services with price-sensitive demands
  European Journal of Operational Research, Vol. 183, No. 1
- The relative impact of consignee behaviour and road traffic congestion on distribution costs
  Transportation Research Part B: Methodological, Vol. 41, No. 9
- Analysis of the efficiency of urban commercial vehicle tours: Data collection, methodology, and policy implications
  Transportation Research Part B: Methodological, Vol. 41, No. 9
- Territory Planning and Vehicle Dispatching with Driver Learning
  Hongsheng Zhong,
  Randolph W. Hall,
  Maged Dessouky,
  1 February 2007 | Transportation Science, Vol. 41, No. 1
- Two-dimensional Continuum Modeling Approach to Transportation Problems
  Journal of Transportation Systems Engineering and Information Technology, Vol. 6, No. 6
- A model for the fleet sizing of demand responsive transportation services with time windows
  Transportation Research Part B: Methodological, Vol. 40, No. 8
- Performance and Design of Mobility Allowance Shuttle Transit Services: Bounds on the Maximum Longitudinal Velocity
  Luca Quadrifoglio,
  Randolph W. Hall,
  Maged M. Dessouky,
  1 August 2006 | Transportation Science, Vol. 40, No. 3
- A note on asymptotic formulae for one-dimensional network flow problems
  24 May 2006 | Annals of Operations Research, Vol. 144, No. 1
- Discretization and Validation of the Continuum Approximation Scheme for Terminal System Design
  Yanfeng Ouyang,
  Carlos F. Daganzo,
  1 February 2006 | Transportation Science, Vol. 40, No. 1
- A multiplicatively-weighted Voronoi diagram approach to logistics districting
  Computers & Operations Research, Vol. 33, No. 1
- Multi-Depot Vehicle Routing Problem: A One-Stage Approach
  IEEE Transactions on Automation Science and Engineering, Vol. 2, No. 4
- Bounds and Approximations for the Transportation Problem of Linear Programming and Other Scalable Network Problems
  Carlos F. Daganzo,
  Karen R. Smilowitz,
  1 August 2004 | Transportation Science, Vol. 38, No. 3
- Supply Chains
- Técnicas da pesquisa operacional aplicadas na otimização dos serviços postais
  Gestão & Produção, Vol. 8, No. 1
- 網路購物商品之最適配送策略
  Journal of the Chinese Institute of Industrial Engineers, Vol. 17, No. 6
- A continuous approach to the design of physical distribution systems
  Computers & Operations Research, Vol. 27, No. 9
- Designing multi-vehicle delivery tours in a grid-cell format
  European Journal of Operational Research, Vol. 119, No. 3
- Comparing strategies for addressing delivery shortages in stochastic demand settings
  Transportation Research Part E: Logistics and Transportation Review, Vol. 35, No. 1
- On Planning and Design of Logistics Systems for Uncertain Environments
- The performance of route modification and demand stabilization strategies in stochastic vehicle routing
  Transportation Research Part B: Methodological, Vol. 32, No. 8
- Applications of Set Covering, Set Packing and Set Partitioning Models: A Survey
- Coordinated supply chain management
  European Journal of Operational Research, Vol. 94, No. 1
- Continuous approximation models in freight distribution: An overview
  Transportation Research Part B: Methodological, Vol. 30, No. 3
- Pickup and delivery systems for overnight carriers
  Transportation Research Part A: Policy and Practice, Vol. 30, No. 3
- Estimating the length of the optimal TSP tour: An empirical study using regression and neural networks
  Computers & Operations Research, Vol. 22, No. 10
- Using small trucks to circumvent large truck restrictions: Impacts on truck emissions and performance measures
  Transportation Research Part A: Policy and Practice, Vol. 29, No. 6
- Transportation with common carrier and private fleets: system assignment and shipment frequency optimization
  27 April 2007 | IIE Transactions, Vol. 27, No. 2
- Application of mixed integer programming to a large-scale logistics problem
  International Journal of Production Economics, Vol. 36, No. 2
- Use of continuous approximations within discrete algorithms for routing vehicles: Experimental results and interpretation
  11 October 2006 | Networks, Vol. 24, No. 1
- Heuristic Procedures for Practical‐Sized Uncapacitated Location‐Capacitated Routing Problems*
  7 June 2007 | Decision Sciences, Vol. 24, No. 5
- DISTANCE APPROXIMATIONS FOR ROUTING MANUAL PICKERS IN A WAREHOUSE
  31 May 2007 | IIE Transactions, Vol. 25, No. 4
- Design for local area freight networks
  Transportation Research Part B: Methodological, Vol. 27, No. 2
- Determining profit-maximizing production/shipping policies in a one-to-one direct shipping, stochastic demand environment
  European Journal of Operational Research, Vol. 64, No. 1
- Location and allocation for distribution systems with transshipments and transportion economies of scale
  Annals of Operations Research, Vol. 40, No. 1
- An application of sizing service territories
  European Journal of Operational Research, Vol. 63, No. 2
- Operational estimators for the length of a traveling salesman tour
  Computers & Operations Research, Vol. 19, No. 6
- A Decision Support System for Physical Distribution Planning
  31 May 2012 | Journal of Decision Systems, Vol. 1, No. 2-3
- Characteristics of multi-shop/ multi-termal delivery routes, with backghauls and unique items
  Transportation Research Part B: Methodological, Vol. 25, No. 6
- Deriving route lengths from radial distances: Empirical evidence
  European Journal of Operational Research, Vol. 50, No. 1
- Spatial Search for the Lowest Price
  3 September 2010 | Geographical Analysis, Vol. 22, No. 4
- Implementing vehicle routing models
  Transportation Research Part B: Methodological, Vol. 24, No. 4
- TRADE-OFF BETWEEN LOGISTIC COST AND CUSTOMER SERVICE FOR GOODS DISTRIBUTION IN AN URBAN AREA
  Doboku Gakkai Ronbunshu, Vol. 1990, No. 413
- Design of multiple-vehicle delivery tours satisfying time constraints
  Transportation Research Part B: Methodological, Vol. 23, No. 2
- A comparison of in-vehicle and out-of- vehicle freight consolidation strategies
  Transportation Research Part B: Methodological, Vol. 22, No. 3
- Integrated Facility Location and Vehicle Routing Models: Recent Work and Future Prospects
  American Journal of Mathematical and Management Sciences, Vol. 7, No. 1-2
- Design of multiple-vehicle delivery tours—I a ring-radial network
  Transportation Research Part B: Methodological, Vol. 20, No. 5
- Configuration of physical distribution networks
  11 October 2006 | Networks, Vol. 16, No. 2
- Use of continuous space modeling to estimate freight distribution costs
  Transportation Research Part A: General, Vol. 19, No. 2

Volume 18, Issue 4

November 1984

Pages 315-414

Article Information

Metrics

Information

Published Online:November 01, 1984

Cite as

Carlos F. Daganzo, (1984) The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application. Transportation Science 18(4):331-350.

https://doi.org/10.1287/trsc.18.4.331

PDF download

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

The Distance Traveled to Visit N Points with a Maximum of C Stops per Vehicle: An Analytic Model and an Application

Volume 18, Issue 4

Article Information

Metrics

Information

Cite as

Sign Up for INFORMS Publications Updates and News