Exploiting Network Structures on Transportation and Logistics

Exploiting Network Structures on Transportation and Logistics

Problems August 9, 2013

Andrés Medaglia, Ph.D. Associate Professor

Industrial Engineering Department Centro de Optimización y Probabilidad Aplicada

(http://copa.uniandes.edu.co)

Pan-American Advanced Studies Institute (PASI) on Modeling, Simulation and Optimization of Globalized Physical Distribution Systems

Santiago (Chile)

http://copa.uniandes.edu.co/

Andrés Medaglia, Ph.D. Departamento de Ingeniería Industrial

http://copa.uniandes.edu.co 2

Andrés L. Medaglia Associate Professor of Industrial Engineering at Universidad de los Andes (Bogotá, Colombia) Director of Centro para la Optimización y Probabilidad Aplicada (COPA – http://www.copa.uniandes.edu.co) Ph.D. in Operations Research (OR) from North Carolina State University (2001). Since 1999 and until the completion of his postdoctoral fellowship, he worked as an optimization specialist

developing Web-based decision support systems for the Supply Chain Center at SAS Institute Inc. In 2002, he joined the Industrial Engineering Department at Universidad de los Andes (ABET accredited

program). His current research interests include the development and application of optimization techniques to

transportation and logistics, project selection, and engineering design. His research has been published in Annals of Operations Research, Automation in Construction, Building

and Environment, Computers & Operations Research, Computers & Structures, Decision Support Systems, Engineering Applications of Artificial Intelligence, European Journal of Operational Research, Fuzzy Sets and Systems, Insurance: Mathematics and Economics, Interfaces, International Journal of Production Economics, Journal of Heuristics, Operations Research Letters, Optimization Letters, Socio-Economic Planning Sciences, The Engineering Economist, and Transportation Science, among others.

He has served as Secretary and Vicepresident of the Latin-Ibero American Association of Operations Research (ALIO); and as Vicepresident of Central/South America for the Institute of Industrial Engineers (IIE).

He currently serves the editorial board of the Journal of Industrial and Management Optimization. He has been the recipient of several prizes, most recently, the first prize in the 2011 INFORMS Railway

Application Section (RAS) Problem Solving Competition (with L. Lozano and J. González). More information at http://wwwprof.uniandes.edu.co/~amedagli.


http://www.copa.uniandes.edu.co/

http://wwwprof.uniandes.edu.co/~amedagli



Agenda

Part 0: A primer on (underlying) networks Part 1: Bus rapid transit (BRT) route design

Part 2: Split

Part 3: Pulse Algorithm




Agenda

Part 0: A primer on (underlying) networks Part 1: Bus rapid transit (BRT) route design

Part 2: Split

Part 3: Pulse Algorithm



http://copa.uniandes.edu.co

Production planning Sailco Corporation must determine how many sailboats should be

produced during each of the next four quarters. The demand during each of the next four quarters is as follows: first quarter, 40 sailboats; second quarter, 60 sailboats; third quarter, 75 sailboats; fourth quarter, 25 sailboats. Sailco must meet demands on time. At the beginning of the first quarter, Sailco has an inventory of 10 sailboats. At the beginning of each quarter, Sailco must decide how many sailboats should be produced during that quarter. For simplicity, we assume that sailboats manufactured during a quarter can be used to meet demand for that quarter. During each quarter, Sailco can produce up to 40 sailboats with regular-time labor at a total cost of $400 per sailboat. By having employees work overtime during a quarter, Sailco can produce additional sailboats with overtime labor at a total cost of $450 per sailboat. At the end of each quarter, a holding cost of $20 per sailboat is incurred. Determine a production schedule to minimize the sum of production and inventory costs during the next four quarters. 5

Winston (1991)




Production planning

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Production planning

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Production planning

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Production planning as a Minimum Cost Network Flow (MCNF) Problem

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s.a.,

Minimum Cost Network Flow (MCNF) Problem

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Exploiting Network Structures on Transportation and Logistics

Part 1: Bus rapid transit (BRT) route design

August 9, 2013

11

Andrés Medaglia, Ph.D. Associate Professor

Industrial Engineering Department Centro de Optimización y Probabilidad Aplicada

(http://copa.uniandes.edu.co)

Pan-American Advanced Studies Institute (PASI) on Modeling, Simulation and Optimization of Globalized Physical Distribution Systems

Santiago (Chile)

Joint work with: Michel Gendreau (CIRRELT, Canada), Dominique Feillet (EMSE, France),

Jose L. Walteros (U. Florida), Jaime E. González (U. de los Andes),




Bus Rapid Transit Systems (BRT)

Bus Rapid Transit (BRT) systems are urban transportation solutions that combine buses, stations, dedicated lanes, and intelligent transportation systems.

Performance of a BRT system is equivalent to a railway system, but its cost is lower (Hodgson et al., 2013).

Key characteristics: Buses can pass other buses. Express routes stop at fewer stations. Route transfers are allowed (and

some times needed).

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Worldwide growth of BRT systems

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120 cities 280 corridors 4,300 km 6,700 stations 30,000 buses 28,000,000

passengers/day

Source: Hidalgo, D., & Gutiérrez, L., BRT and BHLS around the world: Explosive growth, large positive impacts and many issues outstanding, Research in Transportation Economics (2012)




Bogotá’s BRT System: TransMilenio

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Bogotá has a population of nearly 7 million people. TM currently has 87km, 115 stations, and 90 routes. TM transports 186.124 persons in a peak hour (September, 2012). Fleet of 1,392 buses. Average speed: 26 km/h. Travel times have been reduced by 32%.

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Transmilenio S.A.(2013)




BRT - Problem Hierarchy

Road/Station design: Identifies roads and station locations.

Route design: Determines the stopping sequence for

each route. Dispatching:

Determines dispatching frequencies and timetable.

Fleet assignment: Assigns vehicles to the timetable.

Rostering: Assigns drivers to vehicles.

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Ceder and Wilson (1986)




Road/Station design: Identifies roads and station locations.

Route design: Determines the stopping sequence for

each route. Dispatching:

Determines dispatching frequencies and timetable.

Fleet assignment: Assigns vehicles to trips.

Rostering: Assigns drivers to vehicles.

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BRT - Problem Hierarchy

Ceder and Wilson (1986)




BRT Route Design Problem (BRTRDP)

Finding a manageable set of routes that minimizes total passenger travel time while satisfying system technical constraints (OD matrix, min/max bus frequencies), without overcrowding the network (stations, buses, and lanes).

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BRTRDP: concepts

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Bus corridor: series of physically connected bus lanes holding a set of adjacent stations. Route: a series of stops (at stations) along a bus corridor.

Express Routes

Regular Routes




BRTRDP: Naïve approach Decomposition:

Route design Frequency determination

Key route design variable:

:1, if stations i and j along corridor c are directly connected by route k; 0, otherwise.

Many other variables: Route-corridor relations Cummulative distance per route Passengers served directly by a route Passengers served with transfers. Routes with common stations (for possible transfers) …




BRTRDP: Naïve approach

Instance Instance TM / Phase I TM (circa 2004)

Stations 60 78 Corridors 7 10

Routes 12 13 Variables 530,771 1,049,574

Constraints 1,535,694 3,050,502

Arana, Medaglia & Palacios (2004)




Hybrid Algorithm for Route Design on BRT Systems

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Network Model: Four-station Example




Network Model: Three-station Example

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Network Formulation

Sets




Network Formulation

Parameters

Variables




Minimize travel time

Balance / flow constraints

Bus capacity constraints

Manageable set of routes

Network Formulation




The set of possible routes is huge. The nodes are proportional to the number of routes. There is a binary variable for every possible route. The binary variables “destroy" the network structure

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Network Formulation: challenges




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Network Formulation: solution approach




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1 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1




Computational Results: instances

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Problem size and LR information for the 14 Instances

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Performance of HGA and comparison with the LR

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17,561.27




Network Formulation: solving the relaxation




Simultaneous column and cut generation (SCCG).

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Network Formulation: solving the relaxation




Network Formulation: solving the LR with SCCG









González et al. (2013)

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González et al. (2013)

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BRTRDP: open problems

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Integrality of the route choice variables (𝑦𝑘) Benders decomposition Matheuristics

Nonlinearity arising from the interrelation of the bus

frequencies and waiting times.

Dealing with the re-design problem using key variables such as congestion.


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Exploiting Network Structures on Transportation and Logistics