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Questions and Answers

What does the variable 'z' represent in the given model?

  • Perimeter of the rectangle
  • Length of the rectangle
  • Area of the rectangle (correct)
  • Width of the rectangle

    • Which of the following describes a feasible solution in the OR model?

  • A solution that maximizes the objective function only
  • A solution that has the maximum possible values
  • A solution that satisfies all constraints (correct)
  • A solution that minimizes the objective function only

    • When is a solution considered optimal in an OR model?

  • When it is feasible and has the highest return
  • When it satisfies constraints but not the objective function
  • When it maximizes or minimizes the objective function and is feasible (correct)
  • When it meets all resource allocation requirements

    • What type of problem is described when resources are allocated to maximize returns?

    <p>Maximization problem</p> Signup and view all the answers

    In linear programming, what is the transportation model used for?

    <p>Minimizing transportation costs while distributing commodities</p> Signup and view all the answers

    Which of the following is not a characteristic of the linear programming model?

    <p>Always yields an integer solution</p> Signup and view all the answers

    What best describes a minimization problem in the context of resource allocation?

    <p>Minimizing costs while meeting specified constraints</p> Signup and view all the answers

    When multiple factories manufacture the same commodity in different capacities, which model is appropriate for optimal distribution?

    <p>Transportation model</p> Signup and view all the answers

    What is the objective function representing the total cost of purchasing the tonics?

    <p>minimize z = 50x1 + 30x2</p> Signup and view all the answers

    Which constraint correctly represents the minimum daily requirement for Vitamin A?

    <p>2x1 + 4x2 ≥ 40</p> Signup and view all the answers

    In the context of this problem, what do x1 and x2 represent?

    <p>The quantities of tonics purchased</p> Signup and view all the answers

    What is the correct constraint representing the minimum daily requirement for Vitamin D?

    <p>3x1 + 2x2 ≥ 50</p> Signup and view all the answers

    Under what condition must x1 and x2 exist in this problem?

    <p>x1, x2 ≥ 0</p> Signup and view all the answers

    What caused the growth of the size and complexity of organizations since the industrial revolution?

    <p>The growth in division of labour and segmentation of management</p> Signup and view all the answers

    What major issue arises from the growing autonomy of components within an organization?

    <p>Components working at cross purposes</p> Signup and view all the answers

    Where can the origins of operations research (OR) be traced back to?

    <p>Military services during World War II</p> Signup and view all the answers

    What urgent need did the military face during World War II that contributed to the development of OR?

    <p>To allocate scarce resources effectively</p> Signup and view all the answers

    What is one of the main challenges that arises from increased complexity and specialization in organizations?

    <p>Difficulty in resource allocation for overall effectiveness</p> Signup and view all the answers

    What is operations research primarily concerned with solving?

    <p>Strategic and tactical organizational problems</p> Signup and view all the answers

    Which of the following was NOT a goal of the teams of scientists called upon during World War II?

    <p>Conduct human behavior research</p> Signup and view all the answers

    How did the increasing specialization of organizations impact the alignment of their components?

    <p>It often caused components to prioritize individual goals over collective objectives</p> Signup and view all the answers

    What information does an arc Arc(i, j) carry?

    <p>Transportation cost and amount to be shipped</p> Signup and view all the answers

    What is the main objective of the transportation model described?

    <p>Minimize the total transportation cost</p> Signup and view all the answers

    Which of the following represents a typical supply constraint in the transportation problem?

    <p>x21 + x22 ≤ 50</p> Signup and view all the answers

    In the objective function, what does the variable Z represent?

    <p>Total cost of shipping electricity</p> Signup and view all the answers

    If the shipping cost from Plant 2 to City 1 is $9, which of the following is true?

    <p>Plant 2 incurs a cost of $9 for each million kwh shipped to City 1</p> Signup and view all the answers

    What does the variable xij represent in the context of the transportation model?

    <p>Amount of electricity sent from plant i to city j</p> Signup and view all the answers

    What element is implicitly expressed in the transportation tableau?

    <p>Both shipping costs and supply/demand constraints</p> Signup and view all the answers

    If the total demand for electricity to City 1 is 45 million kwh, which statement is accurate given the constraints?

    <p>The total shipped to City 1 must equal 45 million kwh</p> Signup and view all the answers

    What is the starting basic solution Z calculated from the given data?

    <p>1080</p> Signup and view all the answers

    Which method is described as an improved version of the Least-Cost Method?

    <p>Vogel Approximation Method</p> Signup and view all the answers

    How is the penalty calculated in the Vogel Approximation Method?

    <p>The difference between the two smallest shipping costs in the row or column</p> Signup and view all the answers

    What action is taken when a row and a column are satisfied simultaneously in VAM?

    <p>Only one is crossed out, and the other is assigned zero supply or demand</p> Signup and view all the answers

    What is the total supply from Plant 1 according to the information provided?

    <p>35 million kwh</p> Signup and view all the answers

    What should be done if exactly one row or column with zero supply or demand remains uncrossed-out in VAM?

    <p>Stop the process</p> Signup and view all the answers

    What is the maximum supply from Plant 3 based on the data given?

    <p>30 million kwh</p> Signup and view all the answers

    What do you do after identifying the row or column with the largest penalty in VAM?

    <p>Identify the basic variable with the smallest shipping cost</p> Signup and view all the answers

    What is the primary focus of the Graphical Method in LP problems?

    <p>To visualize feasible regions for solutions</p> Signup and view all the answers

    Which method is used to find a Basic Feasible Solution for a Transportation Problem?

    <p>Vogel Approximation Method (VAM)</p> Signup and view all the answers

    What distinguishes the Assignment Model from the Transportation Problem?

    <p>Assignment Model has equal supply and demand</p> Signup and view all the answers

    In Network Optimization Models, what is the purpose of the Minimum Spanning Tree Problem?

    <p>To minimize the total cost connecting all nodes</p> Signup and view all the answers

    What is the key component of an Inventory Model's ABC Classification?

    <p>Categorization of items based on value</p> Signup and view all the answers

    How does the Simplex Algorithm determine optimal solutions?

    <p>By using corner points of the feasible region</p> Signup and view all the answers

    Which of the following best describes the purpose of PERT in project management?

    <p>To define task dependencies and timing</p> Signup and view all the answers

    What role do Symbols and Notations play in Queuing Models?

    <p>To standardize communication about queue parameters</p> Signup and view all the answers

    In the context of inventory systems, which method is used to balance order costs and carrying costs?

    <p>Basic EOQ Model</p> Signup and view all the answers

    Which of the following best describes the focus of the Maximum Flow Problem?

    <p>To maximize the flow through a network from a source to a sink</p> Signup and view all the answers

    What is a characteristic feature of the Least-Cost Method in transportation problems?

    <p>It prioritizes lower shipping costs while meeting demand.</p> Signup and view all the answers

    Which term accurately describes the sequence of events and tasks in PERT/CPM models?

    <p>Critical path calculations</p> Signup and view all the answers

    Which of the following best defines Basic Feasible Solution in the context of the Transportation Problem?

    <p>A potential allocation of routes that satisfies demand</p> Signup and view all the answers

    Study Notes

    Operations Research Lecture Notes

    • Notes compiled by Jane Aduda, November 6, 2013

    Contents

    • List of Figures (Page v)
    • List of Tables (Page viii)
    • Course Outline

    Introduction

    • History of Operations Research (Page 3)
    • Nature of Operations Research (Page 4)
    • Operations Research Models (Page 6)
    • Solving the OR Model (Page 8)

    Linear Programming

    • Basic Assumptions (Page 12)
    • Mathematical Formulation of a LP model (Page 13)
      • General Linear Programming Model (Page 14)
    • Resource Allocation Models (Page 15)
      • Maximization Problems (Page 15)
      • Minimization Problems (Page 18)

    Solving LP Problems

    • Graphical Method (Page 22)
    • Simplex Computations (Page 27)
      • Algebraic Determination of Corner Points (Page 29)
      • Simplex Algorithm (Page 30)
    • Transportation Problem (Page 39)
      • Finding Basic Feasible Solution for Transportation Problem (Page 43)
      • Methods for balanced TP (Page 43)
      • Northwest Corner Method (NWC) (Page 44)
      • Least-Cost Method (Page 45)
      • Vogel Approximation Method (VAM) (Page 46)
      • Iterative Computations of the Transportation Algorithm (Page 47)
      • Maximization using Transportation Algorithm (Page 47)
    • Assignment Model (Page 55)
      • Unbalanced assignment model (Page 63)
      • Maximization using Assignment algorithm (Page 66)

    Inventory Models

    • Types of Inventory (Page 68)
    • ABC Classification of Inventories (Page 70)
      • A-Class Items (Page 71)
      • B-Class Items (Page 72)
      • C-Class Items (Page 72)
    • Lot/Order Size Model with no Shortages or Basic EOQ Model (Page 77)
    • Derivation of Basic EOQ Model (Page 77)

    Network Optimization Models

    • Terminologies used in Networks(Page 81)
    • The Shortest Path Problem (Page 85)
    • The Minimum Spanning Tree Problem (Page 86)
    • The Maximum Flow Problem (Page 87)
    • The Minimum Cost Flow Problem (Page 89)

    PERT/CPM Models for Project Management

    • Basic difference between PERT and CPM (Page 91)
    • PERT (Program Evaluation Review Technique) (Page 91)
    • CPM (Critical Path Method) (Page 91)
      • CPM Network Components & Precedence Relationship (Page 92)
    • Critical Path Calculations (Page 95)
    • Determination of the Critical Path (Page 96)
    • Project Management PERT(Page 98)

    Waiting Line Theory or Queuing Model

    • Queuing System or Process (Page 101)
    • Input Process (Page 102)
    • Service Mechanism or Service Facility (Page 103)
    • Queuing Problems (Page 105)
    • Symbols used in Queuing Models (Page 106)
      • Notations (Page 107)

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