700.303 (18W) Mathematical Modeling Methods for Transportation and Logistics

Wintersemester 2018/19

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Erster Termin der LV
02.10.2018 12:00 - 14:00 , L4.1.02 ICT-Lab
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Überblick

Lehrende/r
LV-Titel englisch
Mathematical Modeling Methods for Transportation and Logistics
LV-Art
Kurs (prüfungsimmanente LV )
Semesterstunde/n
2.0
ECTS-Anrechungspunkte
3.0
Anmeldungen
4 (5 max.)
Organisationseinheit
Unterrichtssprache
Englisch
LV-Beginn
02.10.2018
eLearning
zum Moodle-Kurs

LV-Beschreibung

Intendierte Lernergebnisse

The aim of this lecture is to provide students with the mathematical knowledge and skills needed for the analysis, understanding, control and forecasting of systems/scenarios/phenomena in the fields of Transportation and Logistics. A particular attention will be devoted to both graphical  and mathematical modeling  of processes in transportation and logistics. Models will be obtained/derived to explain and control the dynamics of systems, processes, scenarios, and phenomena in transportation. Theoretical concepts/methods will be developed to model/represent concrete and real-life systems, scenarios, and phenomena in transportation. 

Overall, the main objectives of this lecture are expressed by the following keywords: Methods and models in transportation; Traffic and transport; Supply chains and logistics; Graphical and mathematical modeling ; Transportation Engineering; Logistics.

The general expectation regarding the knowledge to be provided/acquired is as follows:

  • Understanding of basic systems, scenarios and phenomena in Transportation Engineering.
  • Mastering of the basics of graph theory.
  • Mastering of the basics of traffic theory.
  • Mastering of the basic-tools  (or basic- instruments) for the statistical analysis (e.g. identification and measurement) of stochastic processes/variables.
  • Mastering of the mathematical modeling of shortest path problems (SPP) with applications in Transportation.
  • Mastering of the mathematical modeling of traveling salesman problems (TSP) with applications in Transportation.
  • Mastering of the mathematical modeling of traffic flow at microscopic level using Ordinary Differential Equations (ODEs); Applications in practice for the modeling of real traffic scenarios on arterial roads.
  • Mastering of the mathematical modeling of traffic flow at macroscopic level using Partial Differential Equations (PDEs); Applications in practice for the modeling of real traffic scenarios on arterial roads.
  • Understanding of the functioning principle of supply chain networks (SCN) and their modeling principles (in both graphical and mathematical forms).
  • Acquiring some basic knowledge in logistics and scheduling.

Lehrmethodik

  • The slides are available for the whole lecture. These slides are uploaded in the MOODLE system. The full content of each slide is systematically explained by the Lecturer. Additional examples which are not included in slides will be proposed by the Lecturer to allow good understanding of the information provided.  
  • The slides contain exercises with solutions for the good understanding of the content of each chapter. These solutions are systematically explained (during the lecture) by the Lecturer.
  • The Slides contain exercises without solutions to be solved by students during the lecture (this is part of oral exam). The students are fully assisted by the Lecturer in order to obtain correct/exact solutions to the proposed exercises. This will help to check whether the students have understood the chapters or not.
  •  Several exercises will be proposed by the Lecturer to be solved by students as projects. This will help to test the self-learning potential of students.

Inhalt/e

Chapter 1. General introduction: Definition of some keywords (e.g. Method, Transportation, Informatics, Logistics, System, Dynamic Systems, System Theory, Modeling, Model, System identification, Simulation, etc.); Principles of modeling Dynamic Systems; Examples of systems' models in engineering.

Chapter 2. Basics of graph theory: Examples of communication schemes (V2V, V2I, Road traffic scenarios, self-organized road traffic control, etc.); Overview on graph theory; Shortest path (SP); Shortest Path spanning tree (SPST); Minimum spanning tree (MST); Traveling Salesman Problem (TSP); Applications of SP, SPST, MST, TSP in transportation; Graphs and Matrix representations.

Chapter 3. Statistical analysis of stochastic phenomena: Deterministic vs. Stochastic formalisms; Fundamental parameters of a stochastic process and measurements; Normal vs. Standard normal distributions (Z-score); Level of confidence; Factors affecting the confidence interval range; The Z-score table; Application examples in transportation.

Chapter 4. Basics of traffic theory: Overview of traffic processes; Probability distributions; Overview of queuing (main phases of a queuing process , elements of a queuing system, and some applications of queuing); General queuing notation (Kendall 1951); Queuing models; State analysis of queue models/systems; Mathematical modeling of a single-server queuing system).  

Chapter 5. Mathematical modeling of graph theoretical problems: Shortest Path Problem (SPP) and Traveling Salesman Problem (TSP).  

Chapter 6. Mathematical modeling of traffic flow on arterial roads: Key parameters of traffic flow: Flow, speed, and density; Greenshields model; Calibration of Greenshields Model; Shock waves; Rarefaction waves; Macroscopic traffic flow models expressed by PDEs. Microscopic traffic flow models expressed by ODEs; Presentation of concrete traffic flow scenarios with corresponding mathematical models.

Chapter 7. Basics of traffic signals control at isolated junction: Performance criteria of a junction and mathematical models; Identification of a traffic junction; Classification of traffic into streams; Phase- groups; Traffic signal phasing and timing plan; Protected- and Unprotected- turns; Critical lane concept; Cycle length; Green time; All-red interval; Delays; Dilemma zones; Pedestrian crossing time; Level of service (LOS); Some illustrative examples from practice.

Chapter 8. Basics of supply chain networks (SCN) and modeling principles: Supply chain management (SCM): Integration and management of business processes; Structure of a SCN; Framework for SCM; Different types of intercompany business process links; Different types of intercompany business process links brackdown; Fundamental management components in a supply chain network; General design principle of a SCN; Graphical modeling of a SCN; Mathematical modelling of a SCN.

Literatur

Textbooks 

[1] Martin Treiber, and Arne Kesting, „Traffic Flow Dynamics: Data, Models and Simulation,“ Springer-Verlag, Berlin Heidelberg, ISBN 978-3-642-32460-4, 2013

[2]. F. M. Ham and I. Kostanic, „Principles of Neurocomputing for Science , & Engineering,“ New York, NY, USA: McGraw-Hill, 2001.

[3] Adam B. Levy, „The Basics of Practical Optimization,“ SIAM, The society of industrial and applied mathematics, ISBN 978-0-898716-79-5, 2009

[4] Nocedal J. and Wright S.J., „Numerical Optimization,“ Springer Series in Operations Research, Springer, 636 pp, 1999.

[5] Saidur Rahman, „Basics of Graph Theory,“ Springer, ISBN: 978-3-319-49474-6, 2017


Journal Papers 

[1]  J. C. Platt and A. H. Barr, “Constrained differential optimization for neural networks,” American Institute of Physics, Tech. Rep. TR- 88-17, pp. 612-621, Apr. 1988.

[2] I. G. Tsoulos, D. Gavrilis, and E. Glavas, “Solving differential equations with constructed neural networks,” Neurocomputing, vol. 72, nos. 10–12, pp. 2385–2391, Jun. 2009.

Prüfungsinformationen

Prüfungsmethode/n

1. Written exam: Will be held at the end of the Lecture (50%)

2. Oral exam: Will be held during the lecture (it is about the involvement of the students in all chapters of the lecture) (30%)

3. Homework: This measures the potential of students with regard to self-learning or learning/working autonomously (20%)

Prüfungsinhalt/e

1. Graphical modeling of scenarios in transportation (e.g. scenario 1: Traffic control at local junction; scenario 2: A network of coupled/interacting traffic junctions, etc.).

2. Measurement of stochastic variables and derivation of the confidence interval (e.g. scenario 1: Measurement of the travel- time experienced by cars/vehicles moving between two traffic junctions; scenario 2: Measurement of the travel- time experienced by cars/vehicles moving between  multiple traffic junctions).  

3. Mathematical modeling of the shortest path problem (SPP) in graph networks: Case 1: Directed graphs; Case 2: Undirected graphs

4. Mathematical modeling of the Traveling Salesman Problem (TSP) in both Directed and undirected graph networks

5. Modeling of a traffic control scenario at isolated junction in form of graph; matrix representation.

6. Design of a strategy/framework for the optimal control of traffic at given isolated junction and calculation of the optimal parameters (e.g. Optimal cycle time, optimal sharing of green times duration assigned to different phase groups, etc.). 

7. Mathematical modeling of  4- echelon supply chain networks 

Beurteilungsschema

Note/Grade Benotungsschema

Position im Curriculum

  • Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
    • Fach: Information and Communications Engineering: Supplements (NC, ASR) (Wahlfach)
      • Wahl aus dem LV-Katalog (Anhang 4) ( 0.0h VK, VO, KU / 14.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)
  • Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
    • Fach: Technical Complements (NC, ASR) (Wahlfach)
      • Wahl aus dem LV-Katalog (Anhang 5) ( 0.0h VK, VO, KU / 12.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)
  • Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
    • Fach: Information and Communications Engineering: Supplements (NC, ASR) (Wahlfach)
      • Wahl aus dem LV-Katalog (Anhang 4) ( 0.0h VK, VO, KU / 14.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)
  • Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
    • Fach: Technical Complements (NC, ASR) (Wahlfach)
      • Wahl aus dem LV-Katalog (Anhang 5) ( 0.0h VK, VO, KU / 12.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)
  • Masterstudium Information and Communications Engineering (ICE) (SKZ: 488, Version: 15W.1)
    • Fach: Autonomous Systems and Robotics: Advanced (ASR) (Wahlfach)
      • Wahl aus dem LV-Katalog (siehe Anhang 3) ( 0.0h VK, VO / 30.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)
  • Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
    • Fach: Technischer Schwerpunkt (Intelligent Transportation Systems) (Pflichtfach)
      • 1.4-1.5 Kurs oder Labor ( 4.0h KU / 6.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)
  • Masterstudium Information Technology (SKZ: 489, Version: 06W.3)
    • Fach: Technische Ergänzung II (Pflichtfach)
      • 3.4-3.5 Kurs oder Labor ( 4.0h KU / 6.0 ECTS)
        • 700.303 Mathematical Modeling Methods for Transportation and Logistics (2.0h KS / 3.0 ECTS)

Gleichwertige Lehrveranstaltungen im Sinne der Prüfungsantrittszählung

Wintersemester 2019/20
  • 700.303 KS Mathematical Modeling Methods for Transportation and Logistics (2.0h / 3.0ECTS)
Wintersemester 2017/18
  • 700.303 KS Methods of Transportation Informatics and Logistics (2.0h / 3.0ECTS)
Wintersemester 2016/17
  • 700.303 KS Methods of Transportation Informatics and Logistics (2.0h / 3.0ECTS)
Wintersemester 2015/16
  • 700.303 KS Methods of Transportation Informatics and Logistics (2.0h / 3.0ECTS)
Wintersemester 2014/15
  • 700.303 KU Methods of Transportation Informatics and Logistics (2.0h / 3.0ECTS)
Wintersemester 2013/14
  • 700.303 KU Methods of Transportation Informatics and Logistics (2.0h / 3.0ECTS)
Wintersemester 2012/13
  • 700.303 KU Methods of Transportation Informatics and Logistics (2.0h / 3.0ECTS)