Quantitative Methods for Transport Management

1
Quantitative Methods for Transport Management

• Lecturers
• Agachai Sumalee
• Nakorn Indra-Payoong
• Sumet Ongkittikul

2
Course structure

• Eights topics
• Class participation (20), Term project (55),
  Final exam (25)
• Class participation ? Just attending the class
• Term project Group (30), Individual (15),
  Presentation (10)
• Exam 3 hour, 4 A4 info pages allowed, simple
  calculator allowed
• More information could be found at
  http//bmc.buu.ac.th/Module/916531/916531.htm

3
My topics

• Decision Model (3 hrs)
• Transport and Logistic Problem (3 hrs,3 hrs,1
  hrs)
• Multi-Commodity Network Flow Problem (3 hrs,
  3hrs)
• Recommended reading list
• Optimization in Operations Research, Ronald L.
  Rardin (can be found in BMC library)

4
Myself

• Education
• BEng (first class) from KMITL, Thailand
• MEng (first class) First rank from ITS, Leeds
• PhD candidate ITS, Leeds
• Career
• System Analyst IBI Group (London, UK)
• Research Fellow (Asst. Prof) ITS, University of
  Leeds (UK)
• Columnist (LM)
• Project and expertise
• Optimization and operations research
• Risk and uncertainty analysis (grant holder of UK
  DfT project)
• Modelling of transport and logistics system
• Transport pricing and economics
• Personality
• For you to find out!!!

5
Decision Model and Operations Research

• Lecturer
• Agachai Sumalee

6
Decision Process and Roles of OR
Optimization
7
Problems, models, and method
8
Mapping between ModelReal World
9
Mapping between ModelReal World
Real-World (Example problem)
Model
decision
Unit of production of each product
Variables
state
Level of labour/machine engineering parameters
Maximise Profits
Objective
Material required
Technology
Time
Available time
Constraints
Budget
Initial budget
Safety
Labour and Machine
Consider everything. Keep the good. Avoid evil
whenever you notice it.
10
Example of problem formulation
Cost per item of each product
Price per item of each product
Decision variables (amount of each product)
Material constraints
Budget constraints
Labor constraints
Safety constraint
State variable relationship
11
Types of variables

• Continuous (14.2323456, 100, 4.519225)
• Non-negativity (gt 0)
• Discrete (as contrast to real number)
• 1-0 (binary)
• Distinguish between parameters and variables (Q1)

12
Type of function (for obj and con)

• For objective (linear or non-linear also single
  or multiple not cover)
• Equality or inequality
• Non-negativity
• Others?

13
Linear or Non-Linear (2 dimensions)

• Anything relationship that can be drawn as a
  straight line is a linear function otherwise it
  is a non-linear function !!! (simple ?)

14
Linear or Non-linear (n dimensions)
15
Type of optimization problem
16
Linear program

• All functions involved in the problem are linear
• We can guarantee Global optimum! But not
  uniqueness (it is OK anyway)
• Solution must be at one of the corners of the
  constraint space
• Algorithms used are Simplex or Interior-point
  algorithm

17
Non-linear program

• One of the functions involved is not linear
• If all functions are convex or concave (will be
  explained later), then problem become quiet easy
  (global solution can be guaranteed)
• Of course, the solution may be an interior one
• Solution algorithms could be Newton method, Quasi
  Newton, SQP, etc.

18
Convex Concave function
19
Discrete program

• As the name suggested, some of the variables are
  discrete variables
• Quiet difficult problem but with some
  qualification the problem can be solved as if it
  is a normal continuous problem
• Sometime people use meta-heuristic optimization
  method (GA or SA)
• Not cover in this course

20
Some way to solve the problem

• Develop your own optimization algorithm (need to
  be an expert but allow you a lot of flexibility)
• Adopt some existing optimization solvers (i.e.
  Solver in Excel, Some optimisation library, GAMS,
  AMPL, MATLAB, etc.)
• Hire consultant to do the job!
• But still you need to know what going on

21
Some questions to be asked

• Assumption
• Is the model realistic?
• Optimality of solution
• Uncertainty of data and representation
• Sensitivity of solution and model
• After all, does the results make sense to you???

22
Other face of Model (forecasting)

• Do we plan for today or yesterday?
• Mostly, the application of OR involves
  forecasting (demand forecasting, price
  forecasting, market forecast, etc.)
• Mathematical model representing the real world
  developed must be able to do this job as well!!!
• Involves high technical statistics and economic
  theory.(class of Aj. Nakorn and Aj. Sumet will
  discuss about this further)

23
Case study (1)
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Case study (2)
25
Our own case