This tutorial is an andragogical guide for students and practitioners seeking to understand the fundamentals and practice of linear programming. The exercises demonstrate how to solve classical optimization problems with an emphasis on spatial analysis in supply chain management and transport logistics. All exercises display the Python programs and optimization libraries used to solve them. The first chapter introduces key concepts in linear programming and contributes a new cognitive framework to help students and practitioners set up each optimization problem. The cognitive framework organizes the decision variables, constraints, the objective function, and variable bounds in a format for direct application to optimization software. The second chapter introduces two types of mobility optimization problems (shortest path in a network and minimum cost tour) in the context of delivery and service planning logistics. The third chapter introduces four types of spatial optimization problems (neighborhood coverage, flow capturing, zone heterogeneity, service coverage) and contributes a workflow to visualize the optimized solutions in maps. The workflow creates decision variables from maps by using the free geographic information systems (GIS) programs QGIS and GeoDA. The fourth chapter introduces three types of spatial logistical problems (spatial distribution, flow maximization, warehouse location optimization) and demonstrates how to scale the cognitive framework in software to reach solutions. The final chapter summarizes lessons learned and provides insights about how students and practitioners can modify the Phyton programs and GIS workflows to solve their own optimization problem and visualize the results.

翻译：本教程面向学生及从业者，旨在引导其理解线性规划的基础理论与实践，采用成人教育学方法设计。练习环节聚焦供应链管理与运输物流中的空间分析，展示如何求解经典优化问题。所有练习均附有求解所用的Python程序及优化库代码。第一章介绍线性规划的核心概念，并提出一种新型认知框架，帮助学生和从业者构建每个优化问题的模型。该框架将决策变量、约束条件、目标函数及变量边界组织成可直接应用于优化软件的格式。第二章以配送与服务规划物流为背景，介绍两类移动优化问题（网络最短路径与最小成本巡回）。第三章引入四类空间优化问题（邻域覆盖、流捕获、区域异质性、服务覆盖），并提出一套工作流程，通过地图可视化优化解。该流程利用免费地理信息系统（GIS）软件QGIS和GeoDA，从地图生成决策变量。第四章介绍三类空间物流问题（空间分布、流最大化、仓库选址优化），并演示如何在软件中扩展认知框架以求解问题。最后一章总结核心要点，并提供见解，指导学生和从业者如何修改Python程序及GIS工作流，以解决自身优化问题并可视化结果。