# 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 OR Process 2 OR Techniques and Applications 3 Fundamental Concepts and Applications 4 Construction of Networks 5 Activities,Times and Floats 6 To Find Critical Path 7 To Find Critical Path 8 CPM Model and PERT Model 9 Resource Leveling 10 Inventory Cost and Economic Order Quantities 11 Purchasing Model and no Shortages 12 Purchasing Model with Shortages 13 Maunfacturing Model with no Shortages 14 Manufacturing Model with Shortages 15 Revision and Analysis 16 Introduction to Linear Programming 17 Formulation of LP Problems 18 Formulation of LP Problems 19 Solution of LP Problems 20 Solution of LP Problems: Simplex Method 21 Artificial Variables Techniques: Big M Method 22 Big M Method:Examples 23 Artificial Variables Techniques: Two Phase method 24 Variant of Simplex Method 25 Variant of Simplex Method: Degeneracy 26 Variant of Simplex Method: Various Form of Solutions 27 Variants of Simplex Method 28 Duality Theory 29 Post Optimality Analysis 30 Transportation Models, Finding Initial Basic Feasible Solution 31 Vogels approximation method 32 Optimal Solution of Transportation Problems 33 Examples on Transportation Problems 34 Degeneracy 35 Introduction to Assignment Problems and their Solutions 36 Solution to Assignment Problem, Hungarian Algorithm 37 Introduction 38 Single Channel Infinite Population 39 Replacment of Items with Gradual Deterioration 40 Items Detoriating and Failing 41 Basic Concepts and Development 42 Solution of Dynamic Programming Problems 43 Sequencing, Game Theory, Markov Chain, Integer Programming, Non Linear Programming 44 Summing and Close Up 45 Final Examination Any kind of change in the schedule during semester will be announced on VULMS.