Course Instructor Office Hours Phone E-mail

UNIVERSITY OF NEW YORK TIRANA Komuna e Parisit,Tirana, Albania
Tel.: 00355-(0)4-273056-8 – Fax: 00355-(0)4-273059 Web Site Address:

Operations Research, Scheduling and Optimization Spring 2012

: Operations Research, Scheduling and Optimization (4 credit hours) : Prof. Lulezim Hanelli
: 042 233881 / 0692185378 / 0674062515

: Course Location and Time

4B, Monday 16 – 18, Friday 15 -17.

Catalog Description

Operations research, scheduling and optimization problems arise from modeling a wide variety of systems in science, technology, industry and commerce: the design of product, allotment of resources, search for innovative solution, development of efficient process and planning, to name a few. This module aims to introduce those aspects of the subject which are of importance in solving real-life problems. Theoretical aspects are also studied, including fundamental results regarding optimality conditions and the convergence of the methods.

Scheduling and optimization practice is mostly through digital computation. This module uses MATLAB programming to illustrate and implement the various techniques of optimization. The use of graphic to empower visualization for explaining concepts is also an useful element.

The important problem of linear programming and the Simplex method is studied in some detail. A general treatment of the theory of constrained and unconstrained optimization is given, including Lagrange multipliers, optimality conditions, convexity and duality.

A detailed treatment of numerical methods for the one-dimensional problem is given. Most attention is paid to Newton and quasi-Newton methods which provide the best approach for such problems.

Advanced numerical techniques for unconstrained optimization such as Powell’s Method, Conjugate Gradient Method, Davidon-Fletcher-Powell Method and many examples related are analyzed. Indirect and direct methods for constrained case are also treated.

Another important problem is that of discrete optimization. The powerful optimization technique of dynamic programming is illustrated by an example from network problems.
Optimization toolbox from Matlab and some engineering applications close the subject.

Course Purpose

This course will provide a sound mathematical understanding of some modern approaches to solving scheduling and optimization problems, including some recent aspects of implementation (illustrated with practical examples and using MATLAB programming)

At the end of the course each student should be able to:

  1. a)  formulate organizational, scheduling and optimization problems, both linear

    and nonlinear

  2. b)  solve manually different optimization problems of a low dimension
  3. c)  program independently in MATLAB different numerical techniques, debug

    errors, and incorporate improvements as part of his learning experience

  4. d)  generate and translate his own ideas into numerical techniques and deploy

    them through MATLAB

  5. e)  accomplish an individual computational project as a challenge for the

    instilling of the ideas developed in the course

Course Prerequisites

Students enrolling this course must have successfully completed CALCULUS II

Required Readings

1) P.Venkataraman,AppliedOptimizationwithMATLABProgramming, Wiley; 2 edition (March 23, 2009)

2) K.Sigmon,T.A.Davis,MATLABPrimer,Chapman&Hall/CRC

Content of the Course

Introduction to Operations Research, Scheduling and Optimization Introduction to MATLAB
Linear Programming and the Simplex Method
The Transportation and Assignment Problems

Duality in Linear Programming
Nonlinear Programming and Optimality Conditions Numerical Techniques – The One-dimensional problem Numerical Techniques for Unconstrained Optimization Numerical Techniques for Constrained Optimization Discrete Optimization
Optimization Toolbox from Matlab
Mathematical Programming Applications in Engineering

Course Requirements

Students are required to attend lectures and labs. Lecture handouts and lab notes will be available before commencement of the class. Students are expected to participate in class discussions. In the event of illness or emergency, contact your instructor IN ADVANCE to determine whether special arrangements are possible.

Participation: Participation extends beyond mere attendance. You may miss up to two classes without penalty. Each absence beyond the first two will cost you points off of your participation grade. The only exceptions to this rule are severe illness (doctor’s note required) and UNYT approved trips/activities. Appropriate documentation for absences beyond the first two is necessary and is to be provided on the class day directly before or after the one you miss. Students are expected to collect materials from the online course page, their classmates or see the instructor during consultation hours.

Exams: Two examinations will be taken one midterm and one final. Test format may combine a mixture of Definitions, exercises, short and simple MATLAB codes, two or three Essay questions covering all readings, lecture, and hand-out and class discussion content. No Student may miss a scheduled exam without receiving permission before the administration of the exam. Make-up exams might be significantly different from the regular tests, and will be administered at a time of instructor own convenience.

Reading assignments: You will be required to read all the handouts, slides, and other relevant materials. Each week, I will notify you in class what specific materials to read and/or assignments to prepare for the week. The reading assignments are selected to give you adequate understanding of the course material.

Project: I will announce projects usually based on the chapters/materials covered in class. Due dates will be specified accordingly. Projects must be submitted as specified to be considered on-time. Late assignments are accepted with the following penalties: -2 if submitted the next day it is due, and -1 for each day late after that. I will accept e-mail submissions.

Make-up policy Midterm/Final exam: Only students who miss an exam for university-approved and verifiable reasons will be allowed to take a make-up exam. Even then, except in the most extreme circumstances, no student may miss a scheduled exam without receiving permission before the administration of the exam. Make-up exams might be significantly different in format from the regular tests, and will be administered at a time of my own convenience.

Cheating policy: Cheating policy: Exams, assignments, projects and quizzes are subject to the STUDENT HONOUR CODE. The University’s rules on academic dishonesty (e.g. cheating, plagiarism, submitting false information) will be strictly enforced. Please familiarize yourself with the STUDENT HONOUR CODE, or ask me for clarification.

Grading Policy

Active participation






Midterm Exam


Final Exam


Grading Scale (Standard UNYT grading scale)

Letter Grade

Percent (%)

Generally Accepted Meaning



Outstanding work





Good work, distinctly above average







Acceptable work







Work that is significantly below average







Work that does not meet minimum standards for passing the course

Technology Expectations

  1. Continued and regular use of e-mail is expected
  2. Students must keep copies of all assignments and projects sent by e-mail.

February 21th 2012 by Prof. Lulezim Hanelli