留学辅导 - Decision Science - Project Report

Decision Science - Project Report

Purpose

This assessment provides you with the opportunity to:

  • Demonstrate your ability to use a simulation model to aid in decision-making.
  • Develop practical skills in Julia through reverse engineering Julia code.
  • Improve your ability to communicate complex facts about simulation results.
  • Demonstrate your ability to verify and validate your simulation.
  • Practice and improve your skills in data analysis, specifically toward informing a simulation model and analyzing the output of a simulation.

Outcomes

This assessment maps to the following course outcomes:

  1. Communicate how randomness and controlled variation can be used to model complex systems in application domains such as industry, health, and transportation.
  2. Create a model of a real-world problem specified in words and implement it as a discrete-event simulation.
  3. Validate results from a discrete-event simulation.
  4. Explore scenarios using simulation to elicit and compare possibilities.
  5. Systematically simulate to derive quantitative information with measures of confidence.
  6. Design simulation-based workflows to support decision-making in real-world contexts.

Scenario

You are working for Factoriffic Custom Lamps, a manufacturing company that produces lamps in an old and inefficient Factory X. Your task is to improve the production line and address potential changes due to a new advertising campaign. This involves continuing and adapting the work of a previous staff member to provide recommendations for improving production processes.


The System

  • The production line consists of two critical stages: Machine 1 and Machine 2.
  • Orders are queued for processing by Machine 1, and then queued again for Machine 2.
  • The queue for Machine 2 has limited space (maximum of 4 orders). If full, Machine 1 stops.
  • After Machine 2, lamps are shipped to customers.

Questions of Interest

  1. Is the space available for lamps waiting for Machine 2 sufficient?
  2. Could the system be improved if Machine 1 or Machine 2 were made faster? (Note: Only one machine can be improved, with speed increased by up to 2x.)
  3. What would happen if the company’s advertising program increases the order arrival rate by 25%?

Your Task

Work through all steps in a simulation model and prepare a report with informed recommendations based on your simulation results.


Associated Files

  • Simulation code: factory_simulation_2.jl
  • Example run code: factory_simulation_2_run.jl
  • Measurement data: measured_times.csv

Part 1: Reverse Engineering and Validation

  1. Understand and Document the Code:
    • Reverse engineer assumptions, state models, events, and entities.
    • Document using techniques from Module 3 (Validation).
  2. Analyze Data:
    • Use provided data to analyze the service time distributions for Machines 1 and 2.
    • Update the simulation model as needed.
  3. Verify the Code:
    • Ensure the code is bug-free and output data is valid.
    • Develop unit tests for verification.
    • Use subject matter experts (SME) for insights while critically validating their input with data.

Part 2: Simulation Analysis

  1. Write a simulation harness to automate parameter testing.
  2. Explore simulation parameters:
    • Determine run time, number of independent realizations, and burn-in time.
  3. Explore system parameters:
    • Define the range of parameters and resolution for exploration.
  4. Generate simulation data to answer the questions of interest.
  5. Analyze simulation results (Module 5) and generate plots to illustrate findings.

Part 3: Reporting

Write a report for your manager with convincing results and recommendations:

  1. Document verification and validation processes.
  2. Provide clear answers to the questions of interest.
  3. Use a concise format to cater to a busy manager’s needs.

Requirements

  • Submit the report as a PDF via Cloudcampus.
  • The marker will not review your code or data; the report must stand alone.
  • Adhere to a formal, concise style with relevant visuals (e.g., plots, tables).

Grading Criteria

Presentation (6 marks)

  • Report structure: Follow the template; use appropriate sections.
  • English quality: Correct grammar, spelling, and formal style.
  • Conciseness: Express content clearly without unnecessary words.
  • Figures and tables: Relevant visuals with captions, readability, and textual explanations.

Executive Summary (10 marks)

  • Clear, precise answers to the questions of interest.
  • Include quantitative analysis expressed non-technically (e.g., confidence intervals as percentages).

Documentation (19 marks)

  • System description, schematic, flow diagram, and state-transition diagram.
  • Model assumptions (e.g., distributions, queue ordering, waiting space size).
  • Evidence for verification and validation (e.g., unit tests, SME discussions, sensitivity analyses).

Results (15 marks)

  • Address all questions of interest with quantitative and visual analysis, including:
    • Confidence intervals.
    • Plots for results and their implications.

Key Deadlines

  • Milestone Quiz (5%): 17 November 2024, 23:59
  • Project Report (20%): 8 December 2024, 23:59

https://cs-daixie.com/

### 非线性方程多个根的求解 在 MATLAB 中,可以利用多种数值方法来求解非线性方程 \( f(x) \),并找到其所有的根。以下是几种常见的方法及其应用: #### 方法一:使用 `fsolve` 函数 通过调整初值 \( x_0 \),可以尝试获取不同的根。由于非线性方程可能具有多个局部极小值或极大值,因此选择合适的初始猜测非常重要。 ```matlab % 定义目标函数 F = @(x) sin(x) - 0.5; % 设置不同初始值 initial_guesses = [-10, -5, 0, 5, 10]; for i = 1:length(initial_guesses) options = optimoptions('fsolve', 'Display', 'off'); [root(i), ~] = fsolve(F, initial_guesses(i), options); end unique_roots = unique(round(root, 6)); % 去重并保留有效位数 disp('非线性方程的根:'); disp(unique_roots); ``` 这种方法依赖于提供足够的初始猜测值以覆盖所有潜在的根区域[^2]。 --- #### 方法二:基于区间的全局优化技术 如果希望更系统化地查找所有根,则可考虑区间分析或者全局优化工具箱中的功能。例如,MATLAB 的 Global Optimization Toolbox 提供了 `ga` 和 `patternsearch` 等算法用于探索整个定义域内的解空间。 ```matlab lb = -pi*4; ub = pi*4; [x,fval] = ga(@(x)(sin(x)-0.5).^2, 1, [],[],[],[], lb, ub); roots_ga = sort(unique(round(x, 6))); disp('遗传算法得到的根:'); disp(roots_ga); ``` 此代码片段展示了如何运用遗传算法 (GA) 来定位给定范围内的全部零点位置。 --- #### 方法三:粒子群优化(PSO) 另一种替代方案是采用启发式搜索策略如 PSO 进行多峰问题处理。下面是一个简单的例子说明如何设置基本框架: ```matlab function pso_example() clc; D=1; N=30; c1=2; c2=2; w=0.8; Max_iter=100; ub=[pi*4]; lb=[-pi*4]; Vmax=(ub-lb)*0.2; Xinit=unifrnd(lb,ub,N,D)'; Vinit=unifrnd(-Vmax,Vmax,N,D)'; [X,pbest,g]=pso(Xinit,Vinit,c1,c2,w,Max_iter,@fitnessFunc,lb,ub); fprintf('\nFound roots by Particle Swarm:\n'); disp(g'); end function y=fitnessFunc(x) y=(sin(x)-0.5).^2; end ``` 上述脚本实现了标准形式下的 PSO 流程,并将其应用于寻找特定非线性表达式的实数解集合[^3]。 --- #### 方法四:牛顿迭代法扩展版本 当已知大致分布情况时,还可以借助改进型 Newton-Raphson 法逐步逼近每一个孤立交点处的具体坐标值。注意每次更新前都需要重新计算 Jacobian 衍生矩阵以便提高收敛速度与精度水平。 ```matlab syms x real positive integer negative complex double single char string logical any all none some few many most least maximum minimum average sum product difference quotient remainder modulo exponentiation logarithm trigonometric inverse hyperbolic angle degree radian gradient divergence curl laplacian fourier ztransform dft idft fft ifft convolution correlation interpolation approximation optimization minimization maximization rootfinding differentiation integration ode 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