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Questions and Answers
What is one of the topics covered in the Complex Task Allocation Approach?
What is one of the topics covered in the Complex Task Allocation Approach?
Which approach was covered in the previous week before Complex Task Allocation?
Which approach was covered in the previous week before Complex Task Allocation?
Which category was NOT mentioned for the simple task allocation approaches learned in the prior week?
Which category was NOT mentioned for the simple task allocation approaches learned in the prior week?
How much does the final exam contribute to the overall course assessment?
How much does the final exam contribute to the overall course assessment?
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What tool was used for demonstration in the Complex Task Allocation Approach?
What tool was used for demonstration in the Complex Task Allocation Approach?
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What percentage does the Knowledge Test contribute to the overall assessment?
What percentage does the Knowledge Test contribute to the overall assessment?
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Which of the following is an example of a topic covered in Week 10?
Which of the following is an example of a topic covered in Week 10?
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What is the focus of the Week 11 content?
What is the focus of the Week 11 content?
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What is a primary benefit of using Linear Programming for resource allocation?
What is a primary benefit of using Linear Programming for resource allocation?
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Which of the following is a limitation of Linear Programming?
Which of the following is a limitation of Linear Programming?
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How does Linear Programming support decision making?
How does Linear Programming support decision making?
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What is the maximum profit per box for wood screws in the given Linear Programming example?
What is the maximum profit per box for wood screws in the given Linear Programming example?
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What is a characteristic of Linear Programming models?
What is a characteristic of Linear Programming models?
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What does the integer constraint in Linear Programming refer to?
What does the integer constraint in Linear Programming refer to?
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What do Linear Programming problems require the coefficients in the objective function to be?
What do Linear Programming problems require the coefficients in the objective function to be?
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What role does automation play in Linear Programming?
What role does automation play in Linear Programming?
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What is the objective function to maximize in the linear programming problem?
What is the objective function to maximize in the linear programming problem?
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Which constraint corresponds to the slotting machine in the linear programming problem?
Which constraint corresponds to the slotting machine in the linear programming problem?
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What is the main decision variable represented by 'x' in the problem?
What is the main decision variable represented by 'x' in the problem?
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What is the crashing cost per day for Task B?
What is the crashing cost per day for Task B?
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Which task has the highest normal duration among the listed tasks?
Which task has the highest normal duration among the listed tasks?
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What is the total normal duration of the network path ACF?
What is the total normal duration of the network path ACF?
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What constraint must also be considered alongside production constraints in the linear programming problem?
What constraint must also be considered alongside production constraints in the linear programming problem?
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Which task does not have crashing cost information available?
Which task does not have crashing cost information available?
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What is the purpose of Linear Programming?
What is the purpose of Linear Programming?
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Which of the following is NOT a key component of Linear Programming?
Which of the following is NOT a key component of Linear Programming?
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In the context of a scheduling project, the objective function aims to:
In the context of a scheduling project, the objective function aims to:
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What is the objective of the linear programming model presented?
What is the objective of the linear programming model presented?
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What does the feasible region in Linear Programming represent?
What does the feasible region in Linear Programming represent?
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What is the total project duration determined by the linear programming solution?
What is the total project duration determined by the linear programming solution?
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In the given scheduling example, which task has predecessors?
In the given scheduling example, which task has predecessors?
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Which variable corresponds to the largest value in the solution?
Which variable corresponds to the largest value in the solution?
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Which of the following best describes decision variables in Linear Programming?
Which of the following best describes decision variables in Linear Programming?
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Which constraint has the relationship x4 − x2 ≥ 5?
Which constraint has the relationship x4 − x2 ≥ 5?
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Which statement is true regarding the constraints in Linear Programming?
Which statement is true regarding the constraints in Linear Programming?
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What type of solution does linear programming ensure?
What type of solution does linear programming ensure?
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Which of the following is a valid implementation method for Linear Programming?
Which of the following is a valid implementation method for Linear Programming?
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Which of the following is a requirement stated for the variables x1, x2, x3, x4, and x5?
Which of the following is a requirement stated for the variables x1, x2, x3, x4, and x5?
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Which constraint ensures that the difference between x3 and x4 is greater than or equal to 10?
Which constraint ensures that the difference between x3 and x4 is greater than or equal to 10?
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What does the variable x represent in the solution?
What does the variable x represent in the solution?
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Which of the following represents a constraint related to land use?
Which of the following represents a constraint related to land use?
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What does the term 'LHS' most likely represent in the context of the solutions provided?
What does the term 'LHS' most likely represent in the context of the solutions provided?
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In the solution table, what does 'Z' represent?
In the solution table, what does 'Z' represent?
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What is the formula for calculating the profit P?
What is the formula for calculating the profit P?
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What does the linear programming model only guarantee under optimal conditions?
What does the linear programming model only guarantee under optimal conditions?
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At the point (0, 20), how much profit is generated?
At the point (0, 20), how much profit is generated?
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Which point in the feasible region yields the maximum profit?
Which point in the feasible region yields the maximum profit?
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What constraint is represented by the equation 30x + 20y ≤ 480?
What constraint is represented by the equation 30x + 20y ≤ 480?
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In linear programming, what does the term feasible region refer to?
In linear programming, what does the term feasible region refer to?
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If the manpower constraint is represented as x + 2y ≤ 36, what does this imply for the variables x and y?
If the manpower constraint is represented as x + 2y ≤ 36, what does this imply for the variables x and y?
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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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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.
