COURSE INFORMATION Course Title: OPERATIONS RESEARCH

Code	Course Type	Regular Semester	Theory	Practice	Lab	Credits	ECTS
BUS 324	B	6	4	0	0	4	6

Academic staff member responsible for the design of the course syllabus (name, surname, academic title/scientific degree, email address and signature)	NA
Main Course Lecturer (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	Dr. Esmir Demaj edemaj@epoka.edu.al , Thursday, 09:00-11:30
Second Course Lecturer(s) (name, surname, academic title/scientific degree, email address and signature) and Office Hours:	NA
Teaching Assistant(s) and Office Hours:	NA
Language:	English
Compulsory/Elective:	Compulsory
Study program: (the study for which this course is offered)	Bachelor in Business Informatics (3 years)
Classroom and Meeting Time:	Tuesday, E-212, 08:45-10:30 and Wednesday, E-214, 08:45-10:30
Code of Ethics:	Code of Ethics of EPOKA University Regulation of EPOKA University "On Student Discipline"
Attendance Requirement:	min 60%
Course Description:	To familiarize the students with the basic concepts and principles of operations research and to improve the analytical thinking and modeling abilities of the students on quantitative management problems. The course includes topics such as systems, models and modeling approaches, decision analysis, certainty, risk and uncertainty conditions, linear programming, sensitivity analysis and transportation and assignment problems
Course Objectives:	To familiarize students with the basic concepts and principles of operations research and to improve analytical thinking and modeling abilities of students on quantitative management problems. The course includes topics such as modeling approaches, decision analysis, linear programming, sensitivity analysis and transportation, assignment problems, and project management issues.

BASIC CONCEPTS OF THE COURSE

1	OR Modelling
2	Linear programming
3	Simplex Method
4	Network optimization
5	Project Management
6	Decision Analysis

COURSE OUTLINE

Week	Topics
1	Course Overview and Operations Research (Chapter 1 & 2) Operations research begins by carefully observing and formulating the problem, including gathering all relevant data. The next step is to construct a scientific model, typically mathematical that attempts to abstract the essence of the real problem. OR must also provide positive, understandable conclusions to the decision maker when they are needed. OR works in an advisory capacity, not only it solves a problem, but it also advises management. OR teams now frequently find that their biggest data problem is not that too little is available, but that there is too much data. The mathematical model is expressed in terms of mathematical symbols and expressions, thus, if there are n related quantifiable decisions to be made, they are represented as the decision variable. The objective function is the mathematical function that represents the appropriate measure of performance of these decision variables. Any restriction on the values that can be assigned to the decision variables, are called constraints, and are typically expressed by means of inequalities or equations. The constants in the constraints and the objective function are called parameters. A common theme in OR is the search for an optimal, or best solution, which are optimal only with respect to the model being used.
2	Introduction to Linear Programming (Chapter 3) Linear programming uses a mathematical model to describe the problem of concern, linear means that all the mathematical functions are required to be linear functions, while programming is a synonym for planning. Linear programming is a powerful technique for dealing with resource allocation problems, cost benefit trade off problems, and fixed requirement problems. To formulate a linear programming problem, first we need to find decision variables of the model, while the objective is to find the values that maximize the total profit, subject to the restrictions imposed on their values by the limited production capacities available. When solving any linear programming problem with two decision variables, graphical method can be used. With considerably difficulty, it is possible to extend the method to three decision variables, but not more than three. Spreadsheet software, such as excel and its solver, is a popular tool for analyzing and solving small linear programming problems.
3	Linear Programming Problems (Chapter 3, p 81-89) Examples for Linear Programming, problems, which include drawing graphs, finding the slope intercept, formulating linear programming model for problems, using computer tools to solve model, using graphical analysis to determine the optimal solution(s).
4	Simplex Method (Chapter 4) The simplex method is an algebraic procedure, while in this chapter the main features of the simplex method will be described and illustrated. Solving a problem with simplex method, the first step in setting up the simplex method is to convert the functional inequality constraints to equivalent equality constraints. This is accomplished by introducing slack variables. This is the augmented form of the problem, and an augmented solution is a solution for the original variables that has been augmented by the corresponding values of the slack variables. A basic solution is an augmented corner point solution, and a basic feasible solution is an augmented corner point feasible solution. In a basic solution, each variable is designated as either a nonbasic or basic variable. The number of basic variables equals the number of functional constraints. The nonbasic variables are set qual to zero. The values of the basic variables are obtained as the simultaneous solution of the system of equations. If the basic variables satisfy the nonnegativity constraints, the basic solution is a BF solution.
5	Simplex Method in Tabular Form (Chapter 4, 4.4) The tabular form is needed when solving a problem by hand, which records only the essential information, namely, the coefficients of the variables, the constants on the righthand sides of the equations and the basic variable appearing in each equation. This tabular form permits highlighting the numbers involved in arithmetic calculations and recording the computations compactly. The tabular form of the simplex method uses a simplex tableau to compactly display the system of equations yielding the current BF solution. For this solution, each variable in the leftmost column equals the corresponding number in the rightmost column. We present the full algebraic form of the simplex method to convey its logic, and then we streamline the method to a more convenient tabular form.
6	Transportation Problem (Chapter 9) The transportation problem received this name because many of its applications involve determining how to optimally transport goods. In particular, the general transportation problem is concerned with distributing any commodity from any group of supply centers, called sources, to any group of receiving centers, called destinations, in such a way to minimize the total distribution cost. Each source has a certain supply of units to distribute to the destinations, and each destination has a certain demand for units to be received from the sources. The assumption that there is no leeway in the amounts to be sent or received means that there needs to be a balance between the total supply from all sources and the total demand at all destinations. In some real problems, the supplies actually represent maximum amounts rather than fixed amounts, to be distributed. Similarly, in other cases the demands represent the maximum amounts rather than fixed amounts, to be received. However, it is possible to reformulate the problem so that they then fit this model by introducing a dummy destination or a dummy source to take up the slack between the actual amounts and maximum amounts being distributed.
7	Queuing Problem + Simulation (Chpater 17, p731 & Chapter 20, p912) Queueing theory is the study of waiting in various guises, uses queueing models to represent the various types of queueing systems (systems that involve queues of some kind) that arise in practice. Formulas for each model indicate how the corresponding queueing system should perform, including the average amount of waiting that will occur, under a variety of circumstances. Therefore, these queueing models are very helpful for determining how to operate a queueing system in the most effective way. Providing too much service capacity to operate the system involves excessive costs. Simulation involves using a computer to imitate (simulate) the operation of an entire process or system. Simulation also is widely used to analyze stochastic systems that will continue operating indefinitely. For such systems, the computer randomly generates and records the occurrences of the various events that drive the system just as if it were physically operating. Because of its speed,
8	Midterm Exam
9	Project Management I (Chapter 10, p377) This chapter arises in numerous settings and in a variety of guises in the everyday life, widely used for problems in such diverse areas as production, distribution, project planning, facilities location, resource management, supply chain management and financial planning— to name just a few examples. This chapter provides such a powerful visual and conceptual aid for portraying the relationships between the components of systems that it is used in virtually every field of scientific, social, and economic endeavor. For example, both the transportation problem and the assignment problem discussed in the preceding chapter will be discussed. Although several other versions of the shortest-path problem (including some for directed networks) are mentioned at the end of the section, we shall focus on the following simple version. Consider an undirected and connected network with two special nodes called the origin and the destination. Associated with each of the links (undirected a
10	Project Management II (Chapter 10) In this one chapter we only scratch the surface of the current state of the art of network methodology, by also discussing the shortest-path problem. We also determine the most economical way to conduct a project so that it can be completed by its deadline. Either marginal cost analysis or linear programming then is used to solve for the optimal project plan. Not all applications of the shortest-path problem involve minimizing the distance traveled from the origin to the destination. In fact, they might not even involve travel at all. The links (or arcs) might instead represent activities of some other kind, so choosing a path through the network corresponds to selecting the best sequence of activities. The numbers giving the “lengths” of the links might then be, for example, the costs of the activities, in which case the objective would be to determine which sequence of activities minimizes the total cost. The minimum spanning tree problem bears some similarities to the mai
11	Decision Analysis (Chapter 16, p682) The decision analysis framework starts with the decision maker who needs to choose one of the decision alternatives. Nature then would choose one of the possible states of nature. Each combination of a decision alternative and state of nature would result in a payoff, which is given as one of the entries in a payoff table. analysis. Like other applications, management needed to make some decisions in the face of great uncertainty. Decision analysis has become an important technique for decision making in the face of uncertainty. It is characterized by enumerating all the available decision alternatives, identifying the payoffs for all possible outcomes, and quantifying the subjective probabilities for all the possible random events. When these data are available, decision analysis be- comes a powerful tool for determining an optimal course of action.
12	Inventory Management Models (Chapter 18, p800) In this chapter how inventories pervade the business world. Maintaining inventories is necessary for any company dealing with physical products, including manufacturers, wholesalers, and retailers. Similarly, both wholesalers and retailers need to maintain inventories of goods to be available for purchase by customers. Reducing storage costs by avoiding unnecessarily large inventories can enhance any firm’s competitiveness. The application of operations research techniques in this area (sometimes called scientific inventory management) is providing a powerful tool for gaining a competitive edge. We discuss how do companies use operations research to improve their inventory policy for when and how much to replenish their inventory, by using scientific inventory management. We discuss inventory models, components of inventory models, economic order quantity model or, for short, the EOQ model.
13	Project Presentations and Review
14	Final Exam

Prerequisite(s):	NA
Textbook(s):	Hillier, F.S. and Lieberman, G. (2021). Introduction to Operations Research, 11th Edition, McGraw-Hill, USA. ISBN13: 9781259872990
Additional Literature:	Course Notes
Laboratory Work:	NA
Computer Usage:	NA
Others:	No

COURSE LEARNING OUTCOMES

1	Understanding Model Formulation
2	Understanding Linear Programming
3	Understanding and Practicing Solution of LP by Graphical and Simplex Methods
4	Understanding and Practicing Transport Models
5	Understanding Forecasting
6	Understanding and Practicing Project Management

COURSE CONTRIBUTION TO... PROGRAM COMPETENCIES (Blank : no contribution, 1: least contribution ... 5: highest contribution)

No	Program Competencies	Cont.
Bachelor in Business Informatics (3 years) Program
1	Identify activities, tasks, and skills in management, marketing, accounting, finance, and economics.	4
2	Apply key theories to practical problems within the global business context.	5
3	Demonstrate ethical, social, and legal responsibilities in organizations.	3
4	Develop an open minded-attitude through continuous learning and team-work.	4
5	Integrate different skills and approaches to be used in decision making and data management.	5
6	Combine computer skills with managerial skills, in the analysis of large amounts of data.	4
7	Provide solutions to complex information technology problems.	3
8	Recognize, analyze, and suggest various types of information-communication systems/services that are encountered in everyday life and in the business world.	4

COURSE EVALUATION METHOD

Method	Quantity	Percentage
Midterm Exam(s)	1	30
Final Exam	1	40
Other	1	30
	Total Percent:	100%

ECTS (ALLOCATED BASED ON STUDENT WORKLOAD)

Activities	Quantity	Duration(Hours)	Total Workload(Hours)
Course Duration (Including the exam week: 16x Total course hours)	16	3	48
Hours for off-the-classroom study (Pre-study, practice)	16	3	48
Mid-terms	1	12	12
Assignments			0
Final examination	1	17	17
Other	5	5	25
Total Work Load:			150
Total Work Load/25(h):			6
ECTS Credit of the Course:			6

CONCLUDING REMARKS BY THE COURSE LECTURER

NA