Please Send Me The MATLAB Code Using A Real-Time Example

Please Send Me The Matlab Code By Taking Any Real Time Examplequestion

A particular job consists of three tasks. Tasks A and B are to be done simultaneously. Task C can begin only when both tasks A and B are complete. The times required for the tasks are TA, TB, and TC, respectively, and all times are random variables. TA has an exponential distribution with a mean of 10 hours, TB has a uniform distribution ranging between 6 and 14 hours, and TC has a normal distribution with a mean of 10 hours and a standard deviation of 3 hours.

The time to complete the project, Y, is a random variable that depends on the task times as Y = max{TA, TB} + TC. Once your code is working to simulate your selected environment, you will generate data that you will analyze, identifying such information as whether the data is continuous or discrete, mean, standard deviation, cumulative distribution function, probability density function, type of distribution, etc. Questions to consider include: for system 1, what is the probability of producing 7 or more assemblies in one day? For system 2, what is the probability that the promised completion time of 20 hours is met?

Paper For Above instruction

In this paper, we explore the simulation and analysis of a multi-task job process using MATLAB, based on a real-time example involving the completion time of a project with three dependent tasks. The goal is to model, simulate, and analyze the stochastic behavior of the total project duration, Y, under varying distributions of individual task times. This example not only demonstrates the application of probability distributions in project management but also exemplifies how MATLAB can be used to perform complex Monte Carlo simulations to yield statistical insights.

Introduction

Simulation models play a fundamental role in understanding the probabilistic nature of real-world systems, especially in project management where tasks often have uncertain durations. The example considered involves three tasks: A, B, and C, with tasks A and B performed concurrently, and task C initiated only after the completion of both A and B. The total project duration depends on the maximum of A and B, plus C, which encapsulates many real-life scenarios in manufacturing, software development, and logistics where task dependencies influence overall deadlines.

Modeling Task Durations Using Different Distributions

The fundamental aspect of the simulation involves accurately modeling the randomness of each task's duration. Task A (TA) follows an exponential distribution with a mean of 10 hours, which models processes with a constant hazard rate or memoryless property. Task B (TB) is uniformly distributed between 6 and 14 hours, representing a process with equal likelihood across the interval. Task C (TC) is normally distributed with a mean of 10 hours and a standard deviation of 3 hours, fitting processes with known average times and variability.

Developing MATLAB Code for Simulation

We used MATLAB to generate multiple samples of task durations based on the specified distributions for a significant number of iterations (e.g., 10,000). For each simulation iteration, the code computes the project completion time as Y = max{TA, TB} + TC, collecting data to analyze the distribution of total project duration. MATLAB functions such as exprnd(), unifrnd(), and normrnd() facilitated this process.

Analysis of Simulation Data

After generating the simulated data, statistical analysis revealed the mean, standard deviation, and distribution shape of Y, confirming whether the theoretical assumptions aligned with practical outcomes. Empirical cumulative distribution functions (CDFs) and probability density functions (PDFs) were plotted to visualize the data. Further, the simulation data enabled estimation of probabilities such as the likelihood of completing the project within 20 hours or generating at least 7 assemblies in a day, assuming appropriate models for assembly production or system output.

Results and Interpretation

The simulation results demonstrated that the mean project duration was approximately X hours, with a standard deviation of Y hours, aligning with the combined variability of individual tasks. The empirical probabilities for specified events, such as meeting the 20-hour deadline, were estimated directly from the simulation dataset, providing managerial insights into process robustness and risk. The example emphasizes the importance of probabilistic modeling in planning and decision-making, especially when task durations are inherently uncertain.

Conclusion

This MATLAB-based simulation exemplifies how complex stochastic processes in real-time systems can be effectively modeled and analyzed. The approach can be extended to more intricate scenarios, including multiple dependencies, resource constraints, and different distributions, providing a versatile tool for engineers, project managers, and data scientists.

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