Operations Research: an Active Learning Approach

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Overview

Operations management deals with operational planning and control issues, and is needed in all sectors of the society. One of the challenges to operations manager is how to make use of the available resources in the best way for meeting a certain objective. Quantitative approaches are inevitably needed in tackling many of such problems.

Operations Research (OR) deals with problem formulation and application of analytical methods to assist in decision-making of operational problems in planning and control. The techniques of OR are useful quantitative tools to assist operations managers, and has a wide applicability in engineering, manufacturing, construction, financial and various service sectors.

Operations Research is an applied mathematics subject and is also a course in many engineering and management programmes. This course is designed for both students learning OR and learners who are practitioners in their respective professionals. The mathematical procedures for the OR techniques are introduced in details in the examples provided in the course. This helps learners to master the methodology and the techniques and apply them to achieve their goals through active learning.

This course introduces two prominent OR techniques and their extended topics. The Simplex Method for Linear Programming (LP) has been considered one of the top 10 algorithms of the 20th century. LP is an optimization technique for solving problems such as finding the optimal product mix, production plan, and shipment allocation, in order to maximize the profir or minimize the cost. The Critical Path Method (CPM) is a popular technique employed by project managers in scheduling project activities. Some extended topics of CPM are also introduced to deal with certain special situations in project management.

In reality, many systems operate under stochastic environment and the operational problems cannot be solved by the known analytical methods. To this end, the simulation approach is introduced in the last chapter of this course. Simulation is a powerful technique for tackling OR problems under such situations.

Syllabus

Chapter 0: Introduction to Operations Research

Chapter 1: Linear Programming and Simplex Method

Introduction to of linear programming (LP) problem, formulating a problem as an LP problem, simplex method in solving maximization and minimization LP problems

Chapter 2: Further Techniques in Simplex Method

Artificial variables in simplex method, M-method, two-phase method, sensitivity analysis, special cases in simplex

Chapter 3: Transportation Problem and Assignment Problem

Introduction and modelling of transportation problem, transportation algorithm, introduction to assignment model, solving assignment problems by the Hungarian method

Chapter 4: Critical Path Method for Project Scheduling

Introduction to project management and network models, network representations for projects, determination of project duration by the critical path method (CPM), using a time schedule in assisting project planning and control

Chapter 5: Further Topics in Critical Path Method

Project crashing, Program evaluation and review techniques (PERT)

Chapter 6: Simulation

Introduction to simulation, generation of random variates, examples of applications of simulation

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