2024_Handout - Operations Research

University Course Overview

• University Name: University of Mine and Technology Tarkwa

• Faculty: Faculty of Mineral Resources Technology

• Department: Mining Engineering Department

• Course: BSc Programme

• Course Code: EL/MC/ES/PE/CE/RN 459

• Course Lecturer: Dr. Bright O. Afum, P. Eng., MAusIMM (CP)

• Compiled by: Assoc. Prof. Victor A. Temeng

• Date: January 2024

Course Presentation and Student Assimilation

• Course taught through lectures with limited hand-outs.

• Importance of attending lectures, reading references, and completing assignments on schedule.

• Tutorials: Problem-solving integrated with lectures to demonstrate applications of theories/models.

• Assignments: Quizzes for each topic to consolidate understanding.

Assessment of Students

• Final Mark Composition:

  • Continuous Assessment: 40%

    • Quizzes and Assignments: 30%

    • Attendance: 10%

  • Final Examination: 60%

Recommended References

1. James E. Shambin and Steves, G.T., Jr. (1974). Operations Research – A Fundamental Approach.

2. Ackoff, R.L. and Sasieni, M.W. (1968). Fundamentals of Operations Research.

3. Hillier and Lieberman (1992). Introduction to Operations Research.

4. Theifrauf, R.J., et al. (1985). Management Science: Model Formulation Approach with Computer Applications.

5. Battersby, A. (1979). Network Analysis: for Planning and Scheduling.

6. Smith, D. (1973). Linear Programming Models in Business.

7. Pegden, C. D., et al. (1995). Introduction to Simulation Using Siman.

8. Taylor, B. W. (1982). Introduction to Management Science.

9. Winston, W. L. (1994). Operations Research – Applications and Algorithms.

10. Krajewski, L. J. and Thompson, H. E. (1981). Management Science: Quantitative Methods in Context.

Course Aims and Objectives

• Aims:

  • Prepare students as engineers using Operations Research (OR) scientific approach for problem-solving.

  • Equip students with OR skills for objective managerial decision-making.

• Objectives:

  • Introduce basic OR concepts and techniques.

  • Encourage the use of OR techniques for industrial problem-solving.

Expected Outcomes of Course

• Understanding of OR concepts and methodologies.

• Ability to analyze and solve problems using OR methods.

Table of Contents

1. INTRODUCTION

   • History of Operations Research

   • Nature of Operations Research

   • Modelling Approach in Operations Research

2. LINEAR PROGRAMMING

   • Model Formulation

   • General Form of the Linear Programming Model

   • Properties of the General Linear Programming Model

   • Solving Linear Programming Problems

   • Graphical Interpretation of Linear Programming

   • Special Cases of the General Linear Programming Problem

   • The Simplex Method

   • The Simplex Method in Application to a Maximisation Problem

   • The Minimisation Problem

   • A Mixed Constraint Problem

   • Negative Variables

   • Other Complications and their Resolutions

   • The Two Phase Simplex Method

3. POSTOPTIMALITY ANALYSIS

   • Duality

   • Economic Interpretation of the Primal

   • Dual Form of a Linear Programming Model

   • Economic Interpretation of the Dual Form

   • Exceptions to the Primal Dual Relationship

   • Sensitivity Analysis

   • Changes in the Right-Hand-Side (bi) Values

   • Changes in Objective Function Coefficients

   • Computer Solution of Linear Programming Problems

4. TRANSPORTATION PROBLEM

   • The Balanced Transportation Problem

   • Initial Solution Methods: Northwest Corner and Vogel’s Approximation Method

   • The Stepping Stone Method

   • Modified Distribution Method

   • The Unbalanced Transportation Problem

   • Degeneracy

   • Multiple Optimal Solutions

   • A Maximisation Transportation Problem

5. THE ASSIGNMENT PROBLEM

   • The Hungarian Method

   • Unequal Supply and Demand

6. SIMULATION

   • Types of Simulation Models

   • The Simulation Process

   • Stochastic Simulation

   • Simulation of a Queuing System

   • A Random Process Generator

   • Generating a Random Variate with a Probability Density Function

   • Analysis of Simulation Output

   • Terminating and Non-terminating Systems

   • Constructing Confidence Intervals on the Mean

   • Simulation Languages

7. NETWORK SCHEDULING

   • Components of CPM/PERT Network and Precedence Relationships

   • Activity Scheduling

   • Uncertainties in Activity Times (PERT)

   • Project Crashing

8. INTEGER PROGRAMMING

   • Integer Programming Solution Methods

   • Rounding Approach

   • Branch-and-Bound Method

   • Integer Programming Applications

Appendix

• Additional detailed examples and exercises are provided for each concept in the course.