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运筹学

Operations Research

课程介绍 Course Introduction

学分:3 | 先修课:微积分、线性代数 | 学期:秋季

运筹学是工业工程的核心基础课程,主要研究如何运用数学模型和优化方法解决复杂的决策问题。课程内容包括线性规划、整数规划、非线性规划、动态规划、网络优化、排队论和决策分析等。学生将学习使用单纯形法、分枝定界法等算法求解各类优化问题,并掌握Lingo、Excel Solver等优化工具的使用。

Operations Research is a core foundational course in industrial engineering that focuses on using mathematical models and optimization methods to solve complex decision problems. Topics include linear programming, integer programming, nonlinear programming, dynamic programming, network optimization, queuing theory, and decision analysis. Students learn algorithms such as the simplex method and branch-and-bound, and gain proficiency with optimization tools like Lingo and Excel Solver.

大作业 Final Project

作业标题:生产计划优化与运输调度模型求解 / Production Planning Optimization and Transportation Scheduling Model

针对指定生产-运输问题建立线性规划与整数规划模型,使用单纯形法或Lingo求解并分析最优方案与对偶价格。

Build linear programming and integer programming models for a specified production-transportation problem, solving with simplex method or Lingo and analyzing the optimal scheme and dual prices.

实施步骤 Implementation Steps

📋 示例:解决一个真实的调度问题,比如一个汽车零部件工厂的生产排程。你需要建立线性规划或混合整数规划模型,考虑设备产能、交货期和换线时间,然后用Lingo或Gurobi求解最优方案,对比优化前后总延期时间能减少多少。
步骤 1
问题描述与建模
本步骤建立工业系统的数学模型或仿真模型,为定量分析和优化决策提供工具。工业系统建模需要准确描述系统的逻辑关系、资源约束和随机特性,通过抽象和简化抓住系统本质。模型是工业工程分析和优化的基础,其准确性直接影响决策质量。

• 使用Arena、Flexsim或Plant Simulation建立离散事件仿真模型,定义实体、流程、资源和逻辑
• 建立数学规划模型(线性规划、整数规划、非线性规划),使用Lingo、MATLAB或Gurobi求解
• 进行输入数据分析,拟合概率分布,验证输入数据的准确性和代表性
产出:系统模型(含仿真模型/数学模型、输入数据、模型验证结果、参数设置说明) | 质量标准:模型准确、逻辑正确、验证充分、能真实反映系统
步骤 2
算法实现
本步骤是工业工程项目的重要环节,运用IE理论和方法系统优化生产与服务系统。工业工程以提高效率、降低成本、保证质量为目标,强调系统观念和持续改进。采用定量化分析方法和专业工具确保改进效果。

• 运用工业工程基础方法(方法研究、作业测定、流程分析)诊断和改进系统
• 使用专业工具(Arena/Flexsim/Minitab/Lingo等)进行建模、仿真和数据分析
• 从技术、经济、人因多角度评价方案,确保系统整体最优
产出:工业工程报告(含现状分析、改进方案、效果预测、实施建议) | 质量标准:方法科学、数据充分、方案可行、效果显著
步骤 3
优化求解
本步骤对工业系统进行优化改进,在满足约束条件下寻求系统性能的最优解。工业工程优化涉及多目标决策,需在效率、质量、成本、交付等多个目标间寻求平衡。采用精益生产、六西格玛、运筹学等方法持续改进系统性能。

• 确定优化目标和约束条件,建立优化模型,选择合适的优化算法(遗传算法、粒子群、模拟退火等)
• 运用精益生产工具(5S、SMED、看板、TPM等)消除浪费,提高生产效率和质量
• 进行多方案比较和敏感性分析,评估优化效果和风险,选择技术经济最优方案
产出:优化方案(含优化模型、改进措施、效果预测、成本效益分析、实施路线图) | 质量标准:目标明确、方法得当、效果显著、可实施性强
步骤 4
灵敏度分析
本步骤对工业工程问题进行系统分析,识别问题本质和改进机会。工业工程以系统优化为核心,通过数据分析和流程建模,从效率、质量、成本多个维度评估系统现状。采用价值流图、流程分析、数据统计等方法诊断问题根源。

• 进行现场调研和数据收集,使用秒表法、工作抽样法或视频分析法获取作业时间数据
• 绘制价值流图(VSM)或流程图,识别瓶颈工序、浪费环节和改进点
• 运用统计学方法进行数据分析,区分偶然波动和异常因素,确定关键影响变量
产出:现状分析报告(含数据收集表、流程图/价值流图、问题诊断、改进机会分析) | 质量标准:数据充分、分析深入、问题定位准确、改进机会清晰
步骤 5
方案评价与报告
本步骤对工业工程方案进行综合评价,从技术、经济、社会多维度评估方案价值。综合评价是决策的重要依据,通过建立评价指标体系,运用科学的评价方法,客观比较不同方案的优劣。需考虑定量和定性因素,形成全面的评价结论。

• 建立评价指标体系,包括技术指标(效率、质量、可靠性)、经济指标(投资、成本、收益)和社会指标(安全、环保、人机)
• 运用层次分析法(AHP)、模糊综合评价或TOPSIS等方法进行多指标综合评价
• 进行经济评价,计算投资回收期、净现值(NPV)、内部收益率(IRR)等指标
产出:综合评价报告(含指标体系、评价方法、计算过程、结果分析、推荐方案) | 质量标准:指标全面、方法科学、结果客观、决策支持有效

Steps

Step 1
Problem Description and Modeling
This step establishes mathematical models or simulation models of industrial systems, providing tools for quantitative analysis and optimal decision-making. Industrial system modeling requires accurate description of system logical relationships, resource constraints and stochastic characteristics, capturing system essence through abstraction and simplification. Models are the foundation of industrial engineering analysis and optimization, their accuracy directly affecting decision quality.

• Build discrete event simulation models using Arena, Flexsim or Plant Simulation, define entities, processes, resources and logic
• Establish mathematical programming models (linear programming, integer programming, nonlinear programming), solve using Lingo, MATLAB or Gurobi
• Perform input data analysis, fit probability distributions, verify accuracy and representativeness of input data
Deliverable: System model (including simulation model/mathematical model, input data, model validation results, parameter setting description) | Quality standard: Accurate model, correct logic, sufficient validation, realistically reflecting system
Step 2
Algorithm Implementation
This step is an important element in industrial engineering projects, using IE theory and methods to systematically optimize production and service systems. Industrial engineering aims to improve efficiency, reduce costs and ensure quality, emphasizing system concept and continuous improvement. Adopt quantitative analysis methods and professional tools to ensure improvement effects.

• Apply industrial engineering basic methods (method study, work measurement, process analysis) to diagnose and improve systems
• Use professional tools (Arena/Flexsim/Minitab/Lingo, etc.) for modeling, simulation and data analysis
• Evaluate schemes from technical, economic, ergonomic perspectives, ensuring overall system optimization
Deliverable: Industrial engineering report (including current state analysis, improvement scheme, effect prediction, implementation suggestions) | Quality standard: Scientific method, sufficient data, feasible scheme, significant effects
Step 3
Optimization Solution
This step performs optimization and improvement of industrial systems, seeking optimal solutions for system performance under constraint conditions. Industrial engineering optimization involves multi-objective decision-making, requiring balance among efficiency, quality, cost, delivery and other objectives. Continuously improve system performance using lean production, six sigma, operations research and other methods.

• Determine optimization objectives and constraints, establish optimization model, select appropriate optimization algorithms (genetic algorithm, particle swarm, simulated annealing, etc.)
• Apply lean production tools (5S, SMED, Kanban, TPM, etc.) to eliminate waste, improve production efficiency and quality
• Conduct multi-scheme comparison and sensitivity analysis, evaluate optimization effects and risks, select the optimal techno-economic scheme
Deliverable: Optimization scheme (including optimization model, improvement measures, effect prediction, cost-benefit analysis, implementation roadmap) | Quality standard: Clear objectives, appropriate methods, significant effects, strong implementability
Step 4
Sensitivity Analysis
This step performs systematic analysis of industrial engineering problems, identifying the nature of problems and improvement opportunities. Industrial engineering focuses on system optimization, evaluating system status from efficiency, quality, cost dimensions through data analysis and process modeling. Diagnose root causes using value stream mapping, process analysis, statistical data and other methods.

• Conduct site investigation and data collection, obtain operation time data using stopwatch method, work sampling or video analysis
• Draw value stream map (VSM) or process flow chart, identify bottleneck processes, waste links and improvement points
• Apply statistical methods for data analysis, distinguish random fluctuations from abnormal factors, determine key influencing variables
Deliverable: Current state analysis report (including data collection table, process flow/VSM, problem diagnosis, improvement opportunity analysis) | Quality standard: Sufficient data, in-depth analysis, accurate problem定位, clear improvement opportunities
Step 5
Scheme Evaluation and Report
This step performs comprehensive evaluation of industrial engineering schemes, assessing scheme value from technical, economic and social dimensions. Comprehensive evaluation is an important basis for decision-making, objectively comparing pros and cons of different schemes through establishing evaluation indicator system and applying scientific evaluation methods. Must consider quantitative and qualitative factors to form comprehensive evaluation conclusions.

• Establish evaluation indicator system, including technical indicators (efficiency, quality, reliability), economic indicators (investment, cost, revenue) and social indicators (safety, environmental protection, ergonomics)
• Apply methods such as AHP, fuzzy comprehensive evaluation or TOPSIS for multi-indicator comprehensive evaluation
• Conduct economic evaluation, calculate payback period, NPV, IRR and other indicators
Deliverable: Comprehensive evaluation report (including indicator system, evaluation method, calculation process, result analysis, recommended scheme) | Quality standard: Comprehensive indicators, scientific method, objective results, effective decision support
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