1. Reliable Construction faces a $300,000 penalty if the new plant isn't completed in 47 weeks but stands to gain a $150,000 bonus if finished within 40 weeks.
2. The critical path includes activities A, B, C, D, G, H, J, K, and must be closely monitored to prevent delays.
3. Crashing the schedule may be necessary to meet the tight deadline, but Reliable should aim for completion within 40 weeks to secure the bonus.
4. Inventory models like EOQ and JIT are vital for managing stock, while simulation models, such as Monte Carlo, are applied in various industries to simulate complex systems and analyze uncertainties.
Question 1: Project Management: Network Models
1. Draw Network Diagram using AOA (Activity on Arrow) convention:
- The diagram cannot be drawn in this text-based format, but I can describe the sequence of activities and their dependencies.
- Activities: A, B, C, D, E, F, G, H, I, J, K, L, M, N
- Immediate Predecessor:
- A: -
- B: A
- C: B
- D: C
- E: C
- F: E
- G: D
- H: E, G
- I: C
- J: F, I
- K: J
- L: J
- M: H
- N: K, L
2. What is the expected project duration, and Identify critical activities:
- Expected project duration: The total time along the critical path
- Identify critical activities: Those activities on the critical path (with zero slack)
4. Which are the critical bottleneck activities where any delays must be avoided to prevent delaying project completion?
- Critical bottleneck activities are those on the critical path. In this case, activities with zero slack: A, B, C, D, G, H, J, K
5. For the other activities, how much delay can be tolerated without delaying project completion?
- Slack is the amount of time an activity can be delayed without delaying the project. For activities not on the critical path, you can find slack by subtracting the early start time from the late start time or early finish time from the late finish time.
7. Given the uncertainties in accurately estimating activity durations, what is the probability of completing the project by the deadline?
- This would require probabilistic time estimates for activities and the use of techniques like PERT (Program Evaluation and Review Technique) to calculate the probability of completing the project by the deadline.
8. Prepare the project crashing Schedule:
- Crashing involves shortening the duration of a project by reducing the time it takes to complete certain activities.
9. Do you think Reliable enjoys the incentive or bears the penalty? Why?
- Reliable should aim to complete the project within 40 weeks to enjoy the $150,000 bonus. If they exceed 47 weeks, they will incur a $300,000 penalty.
Question 2: Inventory Models (Dependent and Independent)
Dependent Inventory Model Examples:
- Just-In-Time (JIT)
- Material Requirements Planning (MRP)
Independent Inventory Model Examples:
- Economic Order Quantity (EOQ)
- Reorder Point (ROP)
Question 3: Linear Programming Problem
ion Method:
- The problem is missing the objective function coefficients for \(x_1\), \(x_2\), and \(x_3\).
- The constraints are \(4x_1 + 6x_2 + 5x_3 > 60\) and \(3x_1 + x_2 + x_3 > 18\).
- The solution would involve applying the Branch and Bound method and enumeration method once the objective function is complete.
b. How would the solution in (a) above vary if the problem were Binary:
- The solution approach would change as binary programming involves variables taking binary (0 or 1) values. This often requires specialized solution methods.
Question 4: Simulation Models
Simulation Models Applicability:
- Used in situations where real-world systems are complex or expensive to replicate.
- Common in manufacturing, finance, healthcare, and logistics.
Monte Carlo Model:
- A statistical method used in simulation models to account for uncertainty.
- Involves running multiple simulations with random input values to analyze the behavior of the system.
Question 5: Waiting/Queuing Lines Model
Main Components:
- Arrival process
- Service process
- Queue discipline
- Service facility
- Exit process
Applicability:
- Applicable in various industries, such as healthcare (patient queues), telecommunications (call centers), and transportation (traffic flow).