# Virtual University of Pakistan

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## MTH601 : Operations Research

### Course Overview

#### Course Synopsis

This course presents the principles and techniques for solving Decision-making problems in the industry using Mathematical Models. It is the science of planning and executing operations to make the most economical use of resources available, also known as Management Science. The operation can be as simple as making a cup a tea as complicated as planning the movement of a fleet of tankers around the world. The techniques include Decision Analysis, Linear Programming, Transportation model, Assignment Model, Network Model, and Forecasting. The course emphasizes the process of model development and solution analysis.

#### Course Learning Outcomes

By the end of the course, students should be able:

• To formulate a decision-making problem and apply the method of depicting a series of decisions and outcomes by decision trees.
• To formulate the problems into mathematical model and apply the quantitative methods (graphical method and simplex method) for maximization and minimization problems
• To formulate the transportation and assignment problems and apply the transportation simplex and Hungarian methods.
• To define the concept of network analysis, develop the network diagram and perform network analysis.
• To identify different types of forecast, to measure forecast accuracy and apply time-series forecasting models

#### Course Calendar

 Topic Lecture Resource Page An overview 1 Handout 1-5 OR Process 2 Handout 6-8 OR Techniques and Applications 3 Handout 9-17 Fundamental Concepts and Applications 4 Handout 18-20 Construction of Networks 5 Handout 21-24 Activities,Times and Floats 6 Handout 25-32 To Find Critical Path 7 Handout 33-34 To Find Critical Path 8 Handout 35-37 CPM Model and PERT Model 9 Handout 38-42 Assignment No 1 Resource Leveling 10 Handout 43-44 Inventory Cost and Economic Order Quantities 11 Handout 45-47 Purchasing Model and no Shortages 12 Handout 48-49 Purchasing Model with Shortages 13 Handout 50-54 Maunfacturing Model with no Shortages 14 Handout 55-56 Manufacturing Model with Shortages 15 Handout 57-59 Graded Disscussion Board No 1 Revision and Analysis 16 Handout 60-70 Introduction to Linear Programming 17 Handout 71-76 Formulation of LP Problems 18 Handout 77 Formulation Exercises 19 Handout 78-82 Solution of LP Problems 20 Handout 83-105 Quiz No 1 Solution of LP Problems:Simplex Method 21 Handout 106-111 Artificial Variables Techniques:Big M Method 22 Handout 112-122 Mid Term exams Big M Method:Examples 23 Handout 123-129 Artificial Variables Techniques:Two Phase method 24 Handout 130-135 Variant of Simplex Method 25 Handout 136 Variant of Simplex Method:Degeneracy 26 Handout 137-139 Variant of Simplex Method:Various Form of Solutions 27 Handout 140-144 Variants of Simplex Method 28 Handout 145-151 Duality Theory 29 Handout 152-157 Post Optimality Analysis 30 Handout 158-161 Graded Disscussion Board No 2 Transportation Models,Finding Initial Basic Feasible Solution 31 Handout 162-165 Vogels approximation method 32 Handout 166-172 Optimal Solution of Transportation Problems 33 Handout 173-179 Examples on Transportation Problems 34 Handout 180-192 Degeneracy 35 Handout 193-198 Introduction to Assignment Problems and their Solutions 36 Handout 199-203 Solution to Assignment Problem,Hungarian Algorithm 37 Handout 204-222 Assignment No 2 Introduction 38 Handout 223-231 Single Channel Infinite Population 39 Handout 232-242 Replacment of Items with Gradual Deterioration 40 Handout 243-247 Items Detoriating and Failing 41 Handout 248-256 Quiz No 2 Basic Concepts and Development 42 Handout 257-260 Solution of Dynamic Programming Problems 43 Handout 261-270 Sequencing,Game Theory,Markov Chain,Integer Programming,Non Linear Programming 44 Handout 271-277 Summing and Close Up 45 Handouts Final Term Exams