小婧研学（79）：运筹学运输问题的模型

摘要：运筹学中的运输问题模型，是解决“如何把物资从多个供应地（产地）合理调配到多个需求地（销地）”的规划工具，核心目标是让总运输成本最低或总效益最高。

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Today, the editor brings you "Computer Solutions to Transportation Problems in Operations Research"

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运筹学中的运输问题模型，是解决“如何把物资从多个供应地（产地）合理调配到多个需求地（销地）”的规划工具，核心目标是让总运输成本最低或总效益最高。

The transportation problem model in operations research is a planning tool to solve the problem of "how to rationally allocate materials from multiple supply places (production areas) to multiple demand places (sales places)", and the core goal is to make the total transportation cost lowest or the total benefit highest.

一、关键要素

First, the key elements

供应端（产地）：有多个物资来源点，每个点有固定的物资供应量（比如工厂的产量）。

Supply side (origin): There are multiple sources of materials, each with a fixed supply of materials (such as the output of the factory).

需求端（销地）：有多个物资需求点，每个点有明确的需求量（比如超市的订货量）。

Demand side (sales place): There are multiple material demand points, and each point has a clear demand (such as the order volume of the supermarket).

运输成本：不同产地到不同销地的运输费用不同（比如从北京仓库运到上海门店，和从广州仓库运到上海门店的运费不一样）。

Shippingcosts:Thetransportationcostsfromdifferentoriginstodifferentsaleslocationsaredifferent(forexample, the shippingcostfromtheBeijingwarehousetotheShanghaistore is differentfrom the freightfromtheGuangzhouwarehousetotheShanghaistore).

二、核心逻辑

Second,thecorelogic

目标：在满足所有产地供应量和销地需求量的前提下，找到一个运输方案，让总运费最少（或利润最大）。

The goal: to find a transportation solution that minimizes (or maximizes profits) in total freight while meeting the supply and sales demand of all origins.

约束条件：

Constraints:

每个产地运出的物资总量不能超过自己的供应量（比如工厂最多只能运出100吨货）。

The total amount of material shipped from each origin cannot exceed its own supply (e.g. factories can only ship up to 100 tons of goods).

每个销地收到的物资总量必须满足自己的需求量（比如超市必须收到50吨货）。

The total amount of supplies received by each sales location must meet its own demand (e.g. the supermarket must receive 50 tons of goods).

运输量不能为负数（不能“反向运输”）。

The shipping volume cannot be negative (not "reverse shipping").

运输量不能为负数（不能“反向运输”）。

3. Common solutions

表上作业法：通过表格直观列出各产地和销地的供需关系，一步步调整运输方案，找到最优解（类似“试错优化”）。

Table-based operation method: Visually list the supply and demand relationship between each origin and sales area through the table, adjust the transportation plan step by step, and find the optimal solution (similar to "trial and error optimization").

匈牙利法：针对特殊场景（如一人对应一个任务的指派问题），快速匹配最优组合。

Hungarian method: for special scenarios (e.g., assignment problems for one person corresponding to one task), quickly match the optimal combination.

四、应用场景

Fourth, application scenarios

物流配送：规划仓库到门店的货物运输路线和数量，降低运费。

Logistics and distribution: plan the transportation route and quantity of goods from warehouse to store to reduce freight costs.

生产调度：分配不同工厂的产品到各地经销商，平衡产能和需求。

Production scheduling: Distribute products from different factories to distributors in various places to balance capacity and demand.

资源分配：调配不同地区的能源、原材料等资源，避免浪费或短缺。

Resource allocation: Allocate energy, raw materials and other resources in different regions to avoid waste or shortage.

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