PMGT3623 Scheduling - Week 10
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Questions and Answers

What is one of the topics covered in the Complex Task Allocation Approach?

  • Linear Programming (correct)
  • Time Management Techniques
  • Financial Planning
  • Risk Assessment Strategies

Which approach was covered in the previous week before Complex Task Allocation?

  • Advanced Scheduling Methods
  • Simple Task Allocation Approach (correct)
  • Resource Optimization Techniques
  • Probabilistic Approach

Which category was NOT mentioned for the simple task allocation approaches learned in the prior week?

  • Methodology-centric
  • Resource-centric
  • Task-centric
  • Team-centric (correct)

How much does the final exam contribute to the overall course assessment?

<p>40% (B)</p> Signup and view all the answers

What tool was used for demonstration in the Complex Task Allocation Approach?

<p>Excel Solver (A)</p> Signup and view all the answers

What percentage does the Knowledge Test contribute to the overall assessment?

<p>20% (C)</p> Signup and view all the answers

Which of the following is an example of a topic covered in Week 10?

<p>Artificial Intelligence in Scheduling (A)</p> Signup and view all the answers

What is the focus of the Week 11 content?

<p>Earned Value Analysis (C)</p> Signup and view all the answers

What is a primary benefit of using Linear Programming for resource allocation?

<p>It optimizes resource allocation effectively. (A)</p> Signup and view all the answers

Which of the following is a limitation of Linear Programming?

<p>It assumes relationships between variables are linear. (D)</p> Signup and view all the answers

How does Linear Programming support decision making?

<p>By enabling informed and objective decisions through quantitative data. (B)</p> Signup and view all the answers

What is the maximum profit per box for wood screws in the given Linear Programming example?

<p>$10 (D)</p> Signup and view all the answers

What is a characteristic of Linear Programming models?

<p>They simplify the analysis of complex problems. (B)</p> Signup and view all the answers

What does the integer constraint in Linear Programming refer to?

<p>Decision variables must only take integer values. (A)</p> Signup and view all the answers

What do Linear Programming problems require the coefficients in the objective function to be?

<p>Known with certainty. (A)</p> Signup and view all the answers

What role does automation play in Linear Programming?

<p>It allows for the handling of complex calculations efficiently. (B)</p> Signup and view all the answers

What is the objective function to maximize in the linear programming problem?

<p>P = 10x + 17y (A)</p> Signup and view all the answers

Which constraint corresponds to the slotting machine in the linear programming problem?

<p>3x + 2y ≤ 3600 (C)</p> Signup and view all the answers

What is the main decision variable represented by 'x' in the problem?

<p>The number of boxes for wood screws (B)</p> Signup and view all the answers

What is the crashing cost per day for Task B?

<p>$33 (B)</p> Signup and view all the answers

Which task has the highest normal duration among the listed tasks?

<p>Task G (C)</p> Signup and view all the answers

What is the total normal duration of the network path ACF?

<p>21 days (B)</p> Signup and view all the answers

What constraint must also be considered alongside production constraints in the linear programming problem?

<p>Non-negativity constraints: x ≥ 0 and y ≥ 0 (D)</p> Signup and view all the answers

Which task does not have crashing cost information available?

<p>Task D (D)</p> Signup and view all the answers

What is the purpose of Linear Programming?

<p>To optimise a linear objective function under constraints (D)</p> Signup and view all the answers

Which of the following is NOT a key component of Linear Programming?

<p>Random Variables (D)</p> Signup and view all the answers

In the context of a scheduling project, the objective function aims to:

<p>Minimise the total project duration or cost (C)</p> Signup and view all the answers

What is the objective of the linear programming model presented?

<p>Optimize the project duration based on constraints (B)</p> Signup and view all the answers

What does the feasible region in Linear Programming represent?

<p>All possible solutions that satisfy the constraints (B)</p> Signup and view all the answers

What is the total project duration determined by the linear programming solution?

<p>22 days (D)</p> Signup and view all the answers

In the given scheduling example, which task has predecessors?

<p>Integration Testing (D)</p> Signup and view all the answers

Which variable corresponds to the largest value in the solution?

<p>x5 (A)</p> Signup and view all the answers

Which of the following best describes decision variables in Linear Programming?

<p>Values that represent decisions to be made (C)</p> Signup and view all the answers

Which constraint has the relationship x4 − x2 ≥ 5?

<p>Constraint 4 (C)</p> Signup and view all the answers

Which statement is true regarding the constraints in Linear Programming?

<p>They limit the possible solutions to the problem (C)</p> Signup and view all the answers

What type of solution does linear programming ensure?

<p>Optimal solution (C)</p> Signup and view all the answers

Which of the following is a valid implementation method for Linear Programming?

<p>Programming language and software tools (D)</p> Signup and view all the answers

Which of the following is a requirement stated for the variables x1, x2, x3, x4, and x5?

<p>They must be non-negative (D)</p> Signup and view all the answers

Which constraint ensures that the difference between x3 and x4 is greater than or equal to 10?

<p>Constraint 5 (A)</p> Signup and view all the answers

What does the variable x represent in the solution?

<p>Number of hectares for barley (D)</p> Signup and view all the answers

Which of the following represents a constraint related to land use?

<p>x + y ≤ 20 (A)</p> Signup and view all the answers

What does the term 'LHS' most likely represent in the context of the solutions provided?

<p>Left-Hand Side of constraints (C)</p> Signup and view all the answers

In the solution table, what does 'Z' represent?

<p>The objective function value (D)</p> Signup and view all the answers

What is the formula for calculating the profit P?

<p>P = 100x + 120y (B)</p> Signup and view all the answers

What does the linear programming model only guarantee under optimal conditions?

<p>Single optimal solution (A)</p> Signup and view all the answers

At the point (0, 20), how much profit is generated?

<p>$2,400 (D)</p> Signup and view all the answers

Which point in the feasible region yields the maximum profit?

<p>(4, 16) (C)</p> Signup and view all the answers

What constraint is represented by the equation 30x + 20y ≤ 480?

<p>Cost of production limitation (B)</p> Signup and view all the answers

In linear programming, what does the term feasible region refer to?

<p>The area where all constraints are satisfied (A)</p> Signup and view all the answers

If the manpower constraint is represented as x + 2y ≤ 36, what does this imply for the variables x and y?

<p>The total of x and double y cannot exceed 36 (C)</p> Signup and view all the answers

Flashcards

Complex Task Allocation

A method for assigning tasks to resources considering constraints and optimizing resource utilization.

Linear Programming

A mathematical technique to optimize a linear objective function subject to linear constraints.

Excel Solver

A tool within Microsoft Excel used for solving optimization problems, including linear programming.

AI in Scheduling

The application of Artificial Intelligence techniques to optimize scheduling processes.

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Resource-centric approach

Prioritizes resource availability and capacity in scheduling.

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Task-centric approach

Prioritizes the task requirements and dependencies in scheduling.

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Methodology-centric approach

Prioritizes the method or procedure for task completion in scheduling.

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Simple Task Allocation Approaches

Basic strategies for assigning tasks to resources, categorized into resource-centric, task-centric, and methodology-centric.

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Linear Programming (LP)

A mathematical method to optimize a linear objective function, considering linear constraints.

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Objective Function

The linear equation that defines the goal of the optimization problem, e.g., minimum cost or maximum profit.

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Decision Variables

Represent the decisions to be made in the problem, like start times or resource amounts.

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Constraints

Linear inequalities that limit the possible solutions; e.g., resources or deadlines.

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Feasible Region

The region formed by the constraints showing the solution space satisfying the restrictions.

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Linear Optimization

Another name for Linear Programming, used to find the best possible outcome from a problem by using objective functions and constraints to create a linear representation to solve.

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Project Scheduling

Applying LP to optimize task scheduling, resource allocation, and project timelines.

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Task Predecessors

Tasks that must be completed before another task can begin.

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Variables (x1, x2, etc.)

Decision variables in a linear programming model that represent the quantities to be determined.

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Optimal Solution

The solution that maximizes or minimizes the objective function while satisfying all constraints.

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Project Duration

The total time needed to complete a project.

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Scheduling

The process of planning and arranging events to occur in a specific order and time frame.

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Network Diagram

A graphical representation of the tasks and relationships in a project or system.

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Solution (x1, x2, ... x5, Z)

The values of the decision variables (x1, x2, .. x5) and the objective function (Z) that maximize the objective function, while satisfying all constraints.

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Linear Programming's Strength

Linear Programming can handle a wide variety of problems with different constraints, making it adaptable to many situations.

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Resource Allocation

Linear Programming excels at finding the best way to distribute resources, like time or materials, to maximize efficiency or profit.

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Linearity Assumption

Linear Programming assumes that relationships between variables are straight lines, which might not reflect real-world complexities.

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Uncertainty in Linear Programming

Linear Programming requires precise values for all factors, but real-world situations often involve unknowns or changing conditions.

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Integer Constraint

Linear Programming often assumes continuous values, but sometimes decisions require whole numbers (like whole items or people).

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Formulating Linear Programming Problems

Creating a Linear Programming model can be challenging, requiring a strong understanding of math and optimization techniques.

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Wood Screw vs. Metal Screw

A company making wood screws and metal screws needs to maximize profit while considering machine time limitations.

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Maximizing Profit

The goal is to find the best combination of wood screws and metal screws to make the highest profit possible given limited resources.

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LP Problem Formulation

Representing a scheduling problem as a mathematical model using variables, objective function, and constraints.

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Crashing Costs

The extra cost associated with reducing the duration of a task.

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Normal Duration

The standard time to complete a task without any extra effort or cost.

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Crash Duration

The shortest possible time to complete a task after applying extra effort and spending additional costs.

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Network Path

A sequence of tasks that must be completed one after the other, determining the overall project duration.

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Graphical Solution

Solving a linear programming problem by plotting the constraints and finding the optimal point on the graph.

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Study Notes

PMGT3623 Scheduling - Week 10

  • Topic: Complex Task Allocation Approach
  • Lecturer: Dr Shahadat Uddin
  • Topics Covered: Complex Task Allocation, Linear Programming (with Excel Solver demonstrations), Artificial Intelligence (AI) in Scheduling
  • Previous Week's Learning: Simple task allocation approaches were categorized into Resource-centric, Task-centric, and Methodology-centric approaches. Exercises were completed on these approaches. Advanced allocation approaches will be covered this week.

Linear Programming

  • Definition: A mathematical technique for optimization, where a linear objective function is maximized or minimized subject to a set of linear constraints.
  • Scheduling Applications: Applied to optimize resource allocation, task scheduling, and project timelines to achieve specific goals (e.g., minimizing costs or maximizing resource utilization).
  • Simplified Approach: The material will be presented as simply as possible, despite its mathematical nature.
  • Alternative Name: Also known as Linear Optimization.
  • Implementation Methods: Can be implemented using Excel and programming languages.

Linear Programming (cont.) - Key Components

  • Objective Function: A linear equation representing the goal of optimization. In scheduling, it could aim to optimize project cost or duration.
  • Decision Variables: Variables representing decisions to be made (start times of tasks, resource allocation, or the amount of time allocated to each task).
  • Constraints: Linear equations representing limitations or requirements of the problem (resource availability, task dependencies, and deadlines).
  • Feasible Region: The set of all possible solutions that satisfy the constraints. The optimal solution lies within this region.

Linear Programming (cont.) - Example Application in Scheduling

  • Project: Development of a Software Application
  • Tasks: Requirements Gathering (2 days), UI/UX Design (5 days), Front-End Dev (10 days), Back-End Dev (10 days), Integration Testing (5 days)
  • Task Dependencies: UI/UX Design depends on Requirements Gathering, Front/Back-End Dev depends on UI/UX Design, Integration Testing depends on Front/Back-End Dev. Specifically:
  • UI/UX Design (x2) starts after Requirements Gathering (x1): x2 ≥ x1 + 2
  • Front-End Development (x3) starts after UI/UX Design (x2): x3 ≥ x2 + 5
  • Back-End Development (x4) starts after UI/UX Design (x2): x4 ≥ x2 + 5
  • Integration Testing (x5) starts after both Front-End (x3) and Back-End Development (x4): x5 ≥ x3 + 10, x5 ≥ x4 + 10
  • Objective: Minimize total project duration (Z = x5 + 5)

Linear Programming - Formulated Program

  • Minimise Z = x5 + 5
  • Subject to:
    • X2 - X1 >= 2
    • X3 - X2 >= 5
    • X4 - X2 >= 5
    • X5 - X3 >= 10
    • X5 - X4 >= 10
    • X1, X2, X3, X4, X5 ≥ 0

Linear Programming - Advantages and Limitations

  • Advantages: Optimal solution, flexibility, resource allocation effectiveness, applicable to various scenarios, handling large-scale problems, clarity of structure, decision support.
  • Limitations: Often assumes that relationships are linear; certainty assumption concerning coefficients isn't always realistic in real world applications; variables can often be continuous when integers are needed.

Linear Programming and Crashing (Week 6)

  • Problem Statement: Minimize total project cost while meeting a project deadline of 18 days.
  • Decision Variables: Crashed days for each task
  • Target Variable: Project cost.

Artificial Intelligence (AI) in Scheduling (Week 10)

  • Generative AI (Large Language Model): A potential next-generation approach to scheduling is highlighted.

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Related Documents

PMGT3623 Scheduling Lecture Notes PDF

Description

Explore the Complex Task Allocation Approach in this week's PMGT3623 scheduling course. Cover topics such as Linear Programming using Excel Solver and the role of AI in scheduling. This quiz builds upon last week's lesson by introducing advanced allocation techniques to enhance project management skills.

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